CN110549338B - A robot automatic assembly method for round-rectangular compound hole parts - Google Patents

Abstract

A robot automatic assembly method for round-rectangular compound hole parts relates to the technical field of robot assembly control. In order to solve the problems that the automatic assembly of circular-rectangular compound hole parts is faced with many contact states and the assembly strategy is difficult to determine, the invention discloses a method of contact state discrimination based on force feedback information, and a method for different contact states. Correspondingly adjusted round-rectangular compound hole parts automatic assembly method. The assembly process is divided into an approaching stage, a hole searching stage and an insertion stage. The approaching stage uses the 5-order spline trajectory planning method to make the assembly quickly approach the assembled part. There are four contact states in the hole searching stage. The states are divided into 7 categories and 41 types according to the number of contact points and their relative positions. The force analysis is carried out for each contact state, and the corresponding hole search or insert assembly strategy is proposed. The assembly simulation of the round-rectangular compound hole parts is carried out, and the results show that the proposed assembly method can complete the assembly under the premise of preventing excessive contact force.

Description

A robot automatic assembly method for round-rectangular compound hole parts

technical field

The invention relates to a robot automatic assembly strategy and method for parts with irregular shapes (circle-rectangular compound holes), and relates to the technical field of robot assembly control.

Background technique

Assembly is an important link in the product manufacturing process, and the assembly quality often directly affects the final product quality. At present, there are still a large number of assembly tasks in the industrial production process that still need to be completed by manual assembly operations. However, manual assembly has many problems, such as high work intensity, low work efficiency, high error rate, and high cost. Faced with these problems, the manufacturing industry has an increasingly urgent need to use robots to replace manual assembly operations. Robotic assembly can not only improve production efficiency, but also has a wider range of applications, such as high temperature, radiation and vacuum and other dangerous environments.

The full name of round-rectangular composite hole parts is cylindrical-rectangular composite shaft hole parts, which are a type of composite hole parts composed of cylindrical geometric features and rectangular geometric features. The assembly of the shaft is very common in the manufacturing industry, such as the assembly of flat keys, the assembly of splines, and the assembly of keyed round shaft parts.

At present, many patents and academic papers have been published for the automatic assembly of parts with only round holes or only square holes. The teaching and learning assembly method for the assembly of shaft parts. The robot uses the RCC flexible wrist to compensate for errors in the assembly process. The adjustment motion obtained by teaching is used to reduce the posture error between the shaft and the hole so that it can be kept within the range that can be compensated by the RCC wrist. The invention patent with the publication number of CN109531560A and the patent number of ZL201910018179.6 provides an automatic assembly method for small-gap circular shaft-hole fitting, and the position of the shaft piece relative to the hole piece is accurately determined by a micro-displacement measuring device. posture error, and then complete the assembly in one action. There is no patent disclosure for the assembly of square hole parts. In the academic paper published by Park et al. in 2012, the square shaft hole assembly process is divided into six stages, and the contact situation of each stage is analyzed. On this basis, an assembly strategy is formulated to gradually realize the assembly operation; Kim et al. designed a fixture with an angle measurement system for the assembly of square shaft hole parts in their academic paper published in 2018. Many experiments have shown that the fixture cooperates with six-dimensional force The sensor can accurately perceive the pose error between the square column and the hole.

Different from the case where the contact points in the round hole assembly are all in the cylindrical part and in the square hole assembly, the contact points are in the square column part, in the assembly of the round-rectangular compound hole type parts, the hole type parts and the matching shaft The contact points between the similar parts may be distributed on the cylinder and the square column and the intersection of the two at the same time, so the contact state will be more complicated than the case of the round hole assembly or the square hole assembly. The mechanical equilibrium equation corresponding to the contact state will also be very different. From this analysis, it can be seen that if the above-mentioned patents and academic papers on the round hole assembly and the square hole assembly method are simply applied, the assembly of the round-rectangular compound hole parts will not be completed.

To sum up, for the automatic robot assembly of circular-rectangular composite hole parts, there is no complete contact state analysis result in the existing published patents and academic research, and no contact state discrimination and corresponding Assembly strategies and specific implementation control methods.

SUMMARY OF THE INVENTION

The assembly method of the invention is oriented to solve the problem of automatic assembly of hole parts with arcs, rectangles, straight sides and right angles in geometric elements, and avoids excessive assembly contact force due to improper posture between shaft holes during assembly. damage to assemblies and robots. That is, in order to solve the problems that the automatic assembly of the round-rectangular compound hole parts is faced with many contact states and the assembly strategy is difficult to determine, the present invention refers to such hole parts as round-rectangular composite hole parts. , The matching shaft parts are called round-rectangular composite shaft parts. Several common forms of such parts include: flat key hub, spline hub, A-type flat key hole, C-type flat key hole, Special type round - rectangular hole and so on.

The technical scheme that the present invention takes for solving the above-mentioned technical problems is:

A robot automatic assembling method for circular-rectangular compound hole parts, the assembly objects of the assembling method are hole parts and shaft parts that have both circles and rectangles, straight sides and right angles in geometric elements, wherein there are compound parts. Parts with round holes and square holes are called round-rectangular composite hole parts, and parts with composite cylinders and square columns are called round-rectangular composite shaft parts (common parts in engineering practice belong to round-long Square compound hole/shaft parts include: splines, A-type flat keys, C-type flat keys, etc.),

The automatic assembly system for circular-rectangular compound hole parts using the assembly method is composed of: a host computer, a base, a six-degree-of-freedom robot, a six-dimensional force/torque sensor, and an assembly (shaft parts adapted to the hole parts) ), clamping and fixing base, and assembled parts (round-rectangular compound hole parts). Among them, a six-degree-of-freedom robot refers to any robot that can realize six-degree-of-freedom motion in space and whose position control accuracy meets assembly operations, and is not limited to an articulated serial six-degree-of-freedom manipulator; The drive/controller and the six-dimensional force/torque sensor communicate through the bus, and the bus used can be Ethernet (Ethernet), RS485 network, CAN bus, etc.

The assembly is clamped on the tool side interface of the 6D force/torque sensor, the robot side interface of the 6D force/torque sensor is fixedly connected with the end interface of the 6DOF robot, and the round-rectangular compound hole is mounted. The accessories are fixed in the interface of the clamping fixture, and the clamping fixture and the six-degree-of-freedom robot are both fixed on the base. The coordinate system ΣO-xyz is the base coordinate system whose origin is fixed at the center of the robot interface of the base. The origins of the coordinate systems ΣO _P -xyz and ΣO _S -xyz are respectively located at the center of the lower surface of the assembly and the measurement of the six-dimensional force/torque sensor. The center of force, these two coordinate systems always remain relatively stationary during assembly operations. In the ΣO _P system, the z-axis direction is parallel to the insertion direction of the assembly into the assembled part, the x-axis direction is parallel to the geometric profile symmetry plane of the assembly and perpendicular to the z-axis, and the y-axis direction is crossed by the unit vector of the z-axis. The direction of the vector obtained by multiplying the unit vector of the x-axis is determined.

The relative position of the circular-rectangular compound hole of the assembled part relative to the six-degree-of-freedom robot can be calculated according to the size of the design drawings of the base, the clamping fixture, and the assembled part, or according to the actual measurement results after the system is assembled. The relative position is defined as the estimated position of the assembled part, which is affected by uncertain factors such as manufacturing errors and measurement errors, and this estimated position is not equal to the actual position of the assembled part. The estimated position of the fitting controls the movement of the fitting, which is prone to interference between the fitting and the fitting. It is necessary to adjust the fitting according to the feedback of the six-dimensional force/torque sensor.

In the assembly method of the circular-rectangular compound hole parts, the six-degree-of-freedom robot needs to adjust the pose of the assembly according to the force feedback information measured by the six-dimensional force/torque sensor, so that it is finally installed in the workpiece. In the round-rectangular compound hole of the assembly. The above assembly process is divided into three stages: approach stage, hole search stage, and insertion stage.

At the beginning of the assembly operation, it first enters the approach stage. The assembly needs to quickly approach the assembled part from the initial position under the control of the six-degree-of-freedom robot to reach the assembly preparation position located above the estimated position of the assembled part. This preparation position can be added by the estimated position. The incremental vector [0,0,Δz] ^T is calculated. The trajectory planning of the above motion applies the sub-spline method, where the velocity and acceleration at the starting point (the initial position of the assembly) and the end point (the assembly preparation position) are both zero.

After the assembly part 4 reaches the assembly preparation position, it enters the hole search stage. After this stage, the six-degree-of-freedom robot 2 will slowly move the assembly part 4 to the assembled part 6 for testing. When the contact force in the z-axis direction is greater than the threshold F _max , The control system of the assembly operation will judge the contact state between the assembly part 4 and the assembled part 6 according to the feedback of the six-dimensional force/torque sensor 3, and then lift the assembly part 4 a certain distance and adjust it according to the previous contact state. Pose, after the adjustment is completed, the trial process of the assembly 4 to the assembled part 6 will be repeated until the conditions are met:

F _z <F _max &h≥h _d (1)

Among them, F _z represents the z-axis force component measured by the six-dimensional force/torque sensor (transformed into the ΣOP system), h represents the distance that the assembly is inserted into the assembled part along the z-axis, and h _d is the insertion depth judgment threshold after hole search. , _Fmax is the contact force threshold.

When the conditions in formula (1) are satisfied, the end of the assembly has been inserted into the circular-rectangular compound hole of the assembled part, and the insertion depth reaches h _d , it is considered that the hole search has been completed, and the insertion stage can be switched. In the insertion stage, the assembly continues to advance in the negative direction of the z-axis. Whenever F _z (equivalent to the insertion resistance) reaches the threshold F _max , it is considered that the insertion process may be blocked. At this time, it is necessary to judge the contact state of the insertion, and then according to The contact state adjusts the pose of the assembly in the hole and continues to insert until the conditions are met:

F _z <F _max &h≥h _max (2)

where _hmax is the insertion depth discrimination threshold for assembly completion. When the condition in formula (2) is satisfied, the depth of the assembly part inserted into the assembled part reaches h _max , it is considered that the assembly part has been successfully inserted into the assembled part, and the assembly operation ends.

In the automatic assembly system applying the circular-rectangular compound hole type parts assembly method, it is necessary to use a force/position hybrid control system for control, and define X=[x,y,z,θ _P1 ,θ _P2 ,θ _P3 ] ^T is the pose vector of the assembly, where x, y, and z are the position coordinates of the ΣO _P system in the base coordinate system ΣO, respectively, and θ _P1 , θ _P2 , and θ _P3 are the three ohms of the ΣO _P system relative to the ΣO system, respectively. pull angle; θ=[θ ₁ ,θ ₂ ,θ ₃ ,θ ₄ ,θ ₅ ,θ ₆ ] ^T and τ=[τ ₁ ,τ ₂ ,τ ₃ ,τ ₄ ,τ ₅ ,τ ₆ ] ^T are respectively Defined as the joint angle and joint driving torque vector of the six-degree-of-freedom robot, where θ _i and τ _i (i=1, 2,..., 6) represent the joint angle and driving torque of the ith joint, respectively; ^S F _e is the six The original data of the force screw (including three force components and three torque components) measured by the force/torque sensor 3 in the ΣO _S system, ^P F _e is the force screw converted from ^S F _e to the ΣO _P system ; X _d , F _d , θ _d are the target values of X, F, θ in the control process, respectively, δX, δF are the adjustment of X in the control process and the deviation of the theoretical value of F from the actual value.

For the above force-position hybrid control system, the control process in each control cycle is divided into the following steps:

Step 1: Feedback sampling. Read the servo motor encoder and the six-dimensional force/torque sensor of the six-degree-of-freedom robot, and obtain the joint angle vector θ of the robot and the force screw ^S F _e in the ΣO _S system, respectively. According to the positive kinematics of the six-degree-of-freedom robot In the simulation, the pose vector X of the assembly can be obtained from θ, and the force screw ^P Fe in the _{ΣO P} system can be calculated according to formula (3).

In formula (3), R is the rotation transformation matrix from the ΣO _S system to the ΣO _P system, _{P S} is the position vector of the OS point in the ΣO _P system, and 0 _{3 × 3} is a third-order all-zero square matrix.

The second step is trajectory planning. The pose planning of the assembly is carried out according to the assembly process. If the assembly process is in the approaching stage, the target pose X _d of the assembly at the current moment is calculated by the 5th-order spline function; if the assembly process is in the hole searching stage or the insertion stage, it is necessary to Determine whether the z-axis component F _z of the contact force reaches the threshold F _max , if F _z < F _max , press the assembly to continue approaching or insert the assembled part to generate X _d , otherwise, the pose adjustment amount of the assembly is obtained according to the contact state , and then generate X _d based on this adjustment.

Step 3: Impedance control. According to the deviation δF of the target force screw F _d and the force feedback ^P F _e , the adjustment amount δX of the pose X of the assembly is calculated, and the impedance control model used is shown in formula (4).

Among them, M, B, and K are the inertia matrix, damping matrix and stiffness matrix of the virtual impedance model between the assembly and the assembled part, respectively. For the model in formula (4), the transfer function from δF to δX is shown in formula (5). During actual control, δX can also be calculated according to δF and this transfer function.

where s represents the Laplace variable in the transfer function.

Step four, position control. The target pose X _d obtained by trajectory planning and the adjustment amount δX obtained by impedance control are superimposed, and the joint angle target vector θ _d is calculated according to the inverse kinematics equation of the six-degree-of-freedom robot, and then the feedforward + The PD feedback control law calculates the joint driving torque τ, and sends it to the servo drive/controller of each joint of the robot to complete the command output of the current control cycle.

where _MR is the estimated value of the generalized inertial matrix of the six-degree-of-freedom robot, _CR and _GR are the estimated value of the centrifugal force/Coriolis force term and the estimated value of the gravity term, respectively, and K _v and K _p are the PD feedback control. Differential term coefficient matrix and proportional term coefficient matrix.

In the hole search stage of the circular-rectangular composite hole type part assembly method, the hole search movement of the assembly is planned according to the contact state every time it contacts with the assembled part, and the contact state is determined according to the number of contact points and the The position on the bottom surface of the assembly (the plane in contact with the assembly in the hole search stage) is divided into four types. Definition l and θ _C respectively represent the phase angle and radial length of the contact point in the xO _P y plane of the ΣO _P system, a, b, c, r are the geometric dimensions of the bottom surface of the assembly, r is the arc radius, a is the width of the rectangular part, b is the distance from the intersection of the arc part and the rectangular part to the OP point, and _c is the length of the rectangular part.

In the first contact state in the hole search stage, a single contact point is located inside the incomplete arc of the bottom contour of the assembly, which means that a point in the bottom contour of the assembly interferes with the edge of the circular-rectangular compound hole of the assembly. The accessory should move away from the point of contact.

In the second contact state in the hole search stage, a single contact point is located on the incomplete arc boundary of the bottom surface of the assembly, indicating that the assembly and the assembled part are in a state of sharp-corner contact at the edge. This state is before the hole search is completed. Critical state, the assembly should move a small distance away from the contact point.

In the third contact state of the hole searching stage, the two contact points are located on the incomplete arc boundary of the bottom surface of the assembly, indicating that the fox hunting segment determined by the two contact points is suspended from the circular-rectangular compound hole of the assembly. Therefore, the assembly should move away from the line connecting the contact points. This contact state can be equivalent to the first contact state. The two contact points are regarded as a contact point at the midpoint of the line. The strategy is exactly the same.

In the fourth contact state of the hole search stage, a single contact point is located in the rectangular part of the bottom surface contour of the assembly, indicating that the assembly and the assembled part interfere with the rectangular part due to the non-parallel symmetry plane, and the assembly should be placed around the z-axis. The fitting is rotated so that the contact point is screwed out of the square section.

Under the above four contact states, the force balance equation in the ΣO _P system can be written uniformly:

Among them, F _x , F _y , and F _z are respectively the three force components that transform the force feedback measured by the six-dimensional force/torque sensor 3 into the ΣO _P system, and M _x , My _y , and M _z respectively convert the six-dimensional force/torque The force feedback measured by the torque sensor 3 is transformed into three force components in the ΣO _P system, and f is the normal force at the contact point (for the third contact state, the equivalent contact point) in the hole search stage. . Solving equation (7), we can get:

According to the definitions of various contact states and the solution results in equation (8), the contact state discriminants in the hole search stage and the corresponding assembly adjustment strategies for each contact state can be summarized in Table 1.

Table 1 The contact state discriminant in the hole search stage and the corresponding assembly adjustment strategy for each contact state

In the hole-searching stage of the automatic assembly operation, the hole-searching trajectories after the tentative contact between the assembly part 4 and the assembled part 6 can be planned according to the following steps:

Step 1. According to the force screw ^P F _e obtained by the force feedback transformation, solve the force balance equation in the second column of Table 1 according to formula (8) to obtain f, l, θ _C ;

Step 2: Determine the contact state type in the hole search stage according to the discriminant in the third column of Table 1;

Step 3: From the adjustment strategy in the fourth column of Table 1, obtain the pose adjustment amount of the assembly in the next trial, and superimpose it on the normal adjustment motion trajectory to obtain the hole search trajectory of the assembly 4 in the next trial. .

In the insertion stage of the circular-rectangular composite hole component assembly method, whenever the z-axis force feedback F _z measured by the six-dimensional force/torque sensor 3 reaches the threshold value F _max , the assembly part 4 needs to be adjusted according to the current contact state. , so that the assembly process can continue without getting stuck. In the insertion stage, the side and bottom edges of the assembly 4 may be in contact with the assembled part 6. In order to identify the contact state, four basic contact points are defined according to the position of the contact point on the assembly 4, respectively. :

The first type of contact point is located on the side of the cylindrical part of the fitting 4 , and its mechanical balance equation is shown in equation (9), where μ is the friction coefficient between the fitting 4 and the fitted part 6 .

The second type of contact point is located at the edge of the bottom surface of the cylindrical part, and its mechanical equilibrium equation is shown in equation (10).

The third type of contact point is located on the side of the square column, and its mechanical equilibrium equation is shown in equation (11).

The third type of contact point is located on the edge of the bottom surface of the square column part, and its mechanical equilibrium equation is shown in formula (12).

According to the number of contact points in the actual contact state, the basic contact point type, and the relative position, the contact states in the insertion stage are divided into 7 categories and 41 types. The seven categories are: containing a first or second Single-point contact of the first type with a basic contact point of the first type (Fig. 8), single-point contact of the second type with a third or fourth basic contact point (Fig. 9), with a basic contact point of the first type and a Two-point first-type contact with a second-type basic contact point (Figure 10), two-point second-type contact with one first or second type of basic contact point and a third or fourth type of basic contact point (Figure 11) , a two-point contact of the third type with one basic contact point of the third type and one basic contact point of the fourth type (Fig. 12), containing one basic contact point of the first or second type and two basic contact points of the third or fourth type A three-point first-type contact (Fig. 13) of the contact points, a three-point second-type contact (Fig. 14) with two first or second basic contact points and one third or fourth basic contact point. The above 7 categories contain 2, 8, 1, 16, 4, 2, and 8 contact states, respectively. For the convenience of later presentation, P-i-j is used as the code of the contact category in the insertion stage, where i represents the number of contact points, j represents the serial number of the contact category after the number of contact points is determined; P-i-j-k is used as the contact state code belonging to the P-i-j category in the insertion stage, and k represents the contact state number in the P-i-j category. For example, the second type of contact with two points is P2-2 means that the 10th contact state will be written as P2-2-10.

For the contact states in Figures 8 to 14, the mechanical equilibrium equations are obtained by combining the mechanical equations of the basic contact points in equations (9) to (12). The characteristic classification is given, and the derivation results of the above-mentioned mechanical equilibrium equation and discriminant conditions are given in Table 2, where c _i and s _i (i=1, 2, 3) are the abbreviations for cosθ _Ci and sinθ _Ci , respectively, θ _Ci and f _i are the polar angle and normal contact force of the i-th contact point in the ΣO _P system, respectively, and k _mn (m=1, 2,..., 7; n=1, 2, 3, 4) is the m-th contact force The nth discriminant parameter of the contact state category is used to discriminate the specific contact state within the category, and the values of k _mn are all within the closed interval [-1, 1].

Table 2 Mechanical equilibrium equations and discriminant conditions for the categories of contact states in the insertion stage

For the contact state categories in Table 2, Table 3 gives the discriminant conditions and corresponding adjustment motions of each contact state in each category, among which there are 5 kinds of adjustment motions of the assembly, namely the inner edge of the ΣOP system. The two translations of the x-axis and the y-axis and the three rotations around the x-axis, the y-axis and the z-axis are represented by x, y, θ _x , θ _y , and θ _z to represent the above-mentioned five adjustment movements; each adjustment movement There are both positive and negative directions, which are represented by "+" and "-"respectively; then the adjustment motion is abbreviated as the compound form of the variable sign and the positive and negative sign, for example, the assembly 4 rotates in the negative direction around the x-axis at It is abbreviated as "θ _x -" in Table 3. Since some contact states correspond to the same adjustment motion of the assembly, it is not necessary to distinguish them in the control of the insertion stage. Therefore, after taking the union of the discrimination conditions of the contact states corresponding to the same adjustment motion, these contact states are merged in Table 3. Write a line.

Table 3 Discrimination conditions of contact state types in the insertion stage and the pose adjustment strategy of the assembly

In the insertion phase of the automatic assembly job, each time the assembly force F _z of the downward assembly of the assembly reaches the threshold value F _max , the adjustment movement of the assembly can be planned as follows:

Step 1. According to the force and moment components in the force screw ^P _Fe obtained by the force feedback transformation, judge the contact category to which the current contact state belongs according to the category discrimination conditions in the fourth column of Table 2;

Step 2, solve the mechanical equilibrium equation of the third row in table 2, obtain the θ _C1 and the basic species discrimination parameter k _mn of the reaction contact point position;

Step 3: Determine the specific contact state according to the discrimination conditions in the third column of Table 3, and find the adjustment motion corresponding to the current contact state in the fourth column of Table 3.

The beneficial effects of the present invention are:

The assembly theory and method of the round-rectangular composite hole parts of the present invention divides the assembly movement process into three stages: approach, search and insertion. In the approach stage, PD feedback control based on dynamic feedforward is adopted, so that the robotic arm can Fast approach to hole parts improves the dynamic control performance of the manipulator; in the search stage, a plane hole search method based on a six-dimensional force sensor is adopted, and a hole search strategy is formulated according to the contact state, which is suitable for the hole search task of compound hole parts; In the insertion stage, the force information and joint angle information fed back by the sensor are used to identify the contact state during the extreme insertion process. The trajectory planner of the control system generates the corresponding pose adjustment scheme based on the contact state identification, and combines the compliance control strategy to realize the circle. -The robot assembly task of rectangular compound hole parts fills the gap in the assembly theory and method of robot assembly for compound hole parts at home and abroad.

Round-rectangular composite hole parts are common parts, but because they have the characteristics of round holes and square holes at the same time, the automatic assembly of such parts faces the problems of many contact states and difficult to determine the assembly strategy. The present invention completely solves the above-mentioned problems. question.

According to the invention, the contact state is judged according to the force feedback information, and the automatic assembly method of the circle-rectangular compound hole parts is adjusted correspondingly according to different contact states. The assembly process is divided into an approaching stage, a hole searching stage and an insertion stage. The approaching stage uses the 5-order spline trajectory planning method to make the assembly quickly approach the assembled part. There are four contact states in the hole searching stage. The states are divided into 7 categories and 41 types according to the number of contact points and their relative positions. The force analysis is carried out for each contact state, and the corresponding hole search or insert assembly strategy is proposed. The assembly simulation of the round-rectangular compound hole parts is carried out, and the results show that the proposed assembly method can complete the assembly under the premise of preventing the contact force from being too large.

Description of drawings

Fig. 1 is the geometrical modeling schematic diagram of the assembly object (circle-rectangular compound hole type part) of the assembling method, in the figure: a) special-shaped circular rectangular compound hole, b) open special-shaped circular rectangular compound hole , c) keyed hub, d) c-type flat keyway, e) a-type flat keyway, f) splined hub;

Fig. 2 is the composition diagram of the automatic assembly system applying the assembly method proposed by the present invention; Fig. 3 is the virtual prototype three-dimensional entity of the automatic assembly system; Fig. 4 is the assembly flow chart of the circle-rectangular compound hole class parts proposed by the present invention; Fig. 5 is the control system block diagram of described automatic assembly system; Fig. 6 is the schematic diagram of four kinds of contact states in the search hole stage;

Figure 7 is a schematic diagram of four basic contact points in the insertion stage; Figure 8 is a schematic diagram of the first type of contact state of a single point in the insertion stage; Figure 9 is a schematic diagram of the second type of contact state of a single point in the insertion stage; Schematic diagram of the contact state of the first type of point (two points of the first type of contact state P-2-1-1); Figure 11 is a schematic diagram of the two-point contact state of the second type in the insertion stage; Figure 12 is the two-point contact state of the third type in the insertion stage Schematic diagram of the contact state; Figure 13 is a schematic diagram of the three-point first-type contact state in the insertion stage; Figure 14 is a schematic diagram of the three-point second-type contact state in the insertion stage;

Figure 15 is the assembly object size parameter diagram in the assembly simulation of the round-rectangular compound hole type parts (in the figure: the upper left is the main view of the assembly part, the lower left is the top view; the upper right is the main view of the assembled part, and the bottom right is the top view);

Fig. 16 is the contact force of the hole search simulation and the generated moment and the pose error curve; Fig. 17 is the contact force curve of the contact state identification simulation in the insertion stage; Fig. 18 is the assembly simulation of the circle-rectangular compound hole type parts Screenshot of the video; Figure 19 is the contact force and pose error curve diagram of the circle-rectangular compound hole assembly simulation.

Detailed ways

Embodiment 1: The assembly method is oriented to solve the problem of automatic assembly of hole-like parts with arcs, rectangles, straight sides and right angles in geometric elements, and avoid assembly contact due to improper posture between shaft holes during assembly. Excessive force can cause damage to the assembly and the robot. Such hole-type parts are called round-rectangular composite hole-type parts, and the matching shaft parts are called circular-rectangular composite shaft-type parts. Figure 1 shows several common types of such parts. Forms, including flat key hub, spline hub, A-type flat key hole, C-type flat key hole, special round-oblong hole and so on.

The common parts in engineering practice belong to the round-rectangular compound hole/shaft parts: splines, A-type flat keys, C-type flat keys and so on.

As shown in Figure 2, the automatic assembly system for circular-rectangular compound hole parts using the assembly method consists of: a host computer, a base 1, a six-degree-of-freedom robot 2, a six-dimensional force/torque sensor 3, and an assembly 4 ( It is composed of shaft parts adapted to hole parts), clamping and fixing base 5, and assembled parts 6 (round-rectangular compound hole parts). Among them, the six-degree-of-freedom robot 2 refers to any robot that can realize the six-degree-of-freedom motion in space and the position control accuracy meets the assembly operation, and is not limited to the articulated serial six-degree-of-freedom manipulator arm; The 6 servo drives/controllers and the six-dimensional force/torque sensor 3 communicate through the bus, and the bus used can be Ethernet (Ethernet), RS485 network, CAN bus, etc.

Figure 3 shows a picture of the virtual prototype of the above automatic assembly system, in which the assembly 4 is clamped on the tool-side interface of the six-dimensional force/torque sensor 3, and the robot-side interface of the six-dimensional force/torque sensor 3 is connected with the six degrees of freedom. The end interface of the robot 2 is fixed, and the assembled part 6 with the round-rectangular compound hole is fixed in the interface of the clamping and fixing base 5. The clamping and fixing base 5 and the six-degree-of-freedom robot 2 are both fixed on the base 1. .

In Fig. 3, the coordinate system ΣO-xyz is the base coordinate system whose origin is fixed at the center of the robot interface of the base 1, and the origins of the coordinate systems ΣO _P -xyz and ΣO _S -xyz are respectively located at the center of the lower surface of the assembly 4 and the six-dimensional force /The force measuring center of the torque sensor 3, these two coordinate systems always remain relatively static during the assembly operation. In the ΣO _P system, the z-axis direction is parallel to the insertion direction of the assembly 4 into the assembled part 6, the x-axis direction is parallel to the geometric profile symmetry plane of the assembly 4 and perpendicular to the z-axis, and the y-axis direction is determined by the z-axis. The direction of the vector obtained by multiplying the unit vector by the unit vector of the x-axis is determined.

According to the size of the design drawings of the base 1, the clamping base 5, and the assembled part 6, or according to the actual measurement results after the system is assembled, it can be calculated that the circular-rectangular compound hole of the assembled part 6 is relative to the six-degree-of-freedom robot. The relative position of 2 is defined as the estimated position of the assembled part 6, which is affected by uncertain factors such as manufacturing errors and measurement errors. This estimated position is not equal to the actual position of the assembled part 6. Therefore, in the assembly process If the movement of the fitting 4 is controlled directly according to the estimated position of the fitting 6 , interference between the fitting 6 and the fitting 4 is likely to occur, and the fitting 4 needs to be adjusted according to the feedback of the six-dimensional force/torque sensor 3 .

Specific embodiment 2: In the assembling method of the circular-rectangular compound hole type parts, the six-degree-of-freedom robot 2 needs to perform the position and orientation of the assembly part 4 according to the force feedback information measured by the six-dimensional force/torque sensor 3. Adjust so that it finally fits into the round-rectangular compound hole of the assembled part 6 . The above assembly process is divided into three stages: approach stage, hole search stage, and insertion stage. The flow chart of the assembly is shown in Figure 4, where F _z represents the z-axis force component (transformation) measured by the six-dimensional force/torque sensor 3. to the ΣOP system), h represents the distance that the assembly 4 is inserted into the assembled part 6 along the z-axis, h _d and h _max are the insertion depth judgment thresholds for hole search and assembly completion, respectively, and F _max is the contact force threshold.

At the beginning of the assembly operation, it first enters the approach stage. The assembly part 4 needs to quickly approach the assembled part 6 from the initial position under the control of the six-degree-of-freedom robot 2 to reach the assembly preparation position located above the estimated position of the assembled part 6. This preparation position can be set by Calculated by adding the incremental vector [0,0,Δz] ^T to the estimated position. The trajectory planning of the above motion applies the 5th-order spline method, in which the velocity and acceleration at the start point (initial position of assembly 4) and the end point (assembly preparation position) are both zero.

After the assembly part 4 reaches the assembly preparation position, it enters the hole search stage. After this stage, the six-degree-of-freedom robot 2 will slowly move the assembly part 4 to the assembled part 6 for testing. When the contact force in the z-axis direction is greater than the threshold F _max , The control system of the assembly operation will judge the contact state between the assembly part 4 and the assembled part 6 according to the feedback of the six-dimensional force/torque sensor 3, and then lift the assembly part 4 a certain distance and adjust it according to the previous contact state. Pose, after the adjustment is completed, the trial process of the assembly 4 to the assembled part 6 will be repeated until the conditions are met:

F _z <F _max &h≥h _d (1)

When the conditions in formula (1) are satisfied, the end of the assembly 4 has been inserted into the circular-rectangular composite hole of the assembled part 6, and the insertion depth reaches h _d , the hole search is considered to be completed, and the insertion stage can be switched. In the insertion stage, the assembly 4 continues to advance in the negative direction of the _z -axis. Whenever Fz (equivalent to the resistance of insertion) reaches the threshold value _Fmax , it is considered that the insertion process may be blocked. At this time, it is necessary to judge the contact state of the insertion, and then Adjust the pose of assembly 4 in the hole according to the contact state, and continue to insert until the conditions are met:

F _z <F _max &h≥h _max (2)

When the condition in formula (2) is satisfied, the depth of the fitting 4 inserted into the fitting 6 reaches h _max , it is considered that the fitting 4 has been inserted into the fitting 6 successfully, and the assembling operation ends. Other steps are the same as in the first embodiment.

Specific embodiment 3: In the automatic assembly system applying the circular-rectangular composite hole type parts assembly method, it is necessary to build a force/position hybrid control system as shown in Figure 5, and define X=[x, y, z, θ _P1 , θ _P2 , θ _P3 ] ^T is the pose vector of assembly 4, where x, y, z are the position coordinates of the ΣO _P system in the base coordinate system ΣO, respectively, θ _P1 , θ _P2 , θ _P3 are ΣO _{The 3 Euler angles of} the _{P system with respect} to the _ΣO ^system _; ,τ ₅ ,τ ₆ ] ^T are defined as the joint angle and joint driving torque vector of the six-degree-of-freedom robot 2, respectively, where θ _i and τ _i (i=1,2,...,6) represent the ith joint's Joint angle and driving torque; ^S F _e is the original data of the force screw (including three force components and three torque components) measured by the six-dimensional force/torque sensor 3 in the ΣO _S system, ^P F _e is the ^S F _e transformed into force screw in ΣO _P system; X _d , F _d , θ _d are the target values of X, F, θ in the control process, respectively, δX, δF are the adjustment of X and the theoretical value of F in the control process, respectively Deviation from the actual value.

For the above force-position hybrid control system, the control process in each control cycle is divided into the following steps:

Step 1: Feedback sampling. Read the servo motor encoder and the six-dimensional force/torque sensor 3 of the six-degree-of-freedom robot 2 to obtain the joint angle vector θ of the robot and the force screw ^S F _e in the ΣO _S system, respectively. In the forward kinematics simulation, the pose vector X of the assembly can be obtained from θ, and the force screw ^P F _e in the ΣO _P system can be calculated according to formula (3).

In formula (3), R is the rotation transformation matrix from the ΣO _S system to the ΣO _P system, _{P S} is the position vector of the OS point in the ΣO _P system, and 0 _{3 × 3} is a third-order all-zero square matrix.

The second step is trajectory planning. Carry out the pose planning of the assembly part 4 according to the introduced assembly process (Fig. 4). If the assembly process is in the approaching stage, calculate the target pose X _d of the assembly part 4 at the current moment according to the 5th order spline function; In the hole stage or the insertion stage, it is necessary to first judge whether the z-axis component F _z of the contact force reaches the threshold value F _max , if F _z < F _max , press the assembly part 4 to continue approaching or insert the assembled part 6 to generate X _d , otherwise, according to The contact state obtains the pose adjustment amount of the assembly 4, and then generates X _d according to this adjustment amount.

Step 3: Impedance control. According to the deviation δF of the target force screw F _d and the force feedback ^P F _e , the adjustment amount δX of the pose X of the assembly is calculated, and the impedance control model used is shown in formula (4).

Among them, M, B, and K are the inertial matrix, damping matrix and stiffness matrix of the virtual impedance model between assembly part 4 and assembled part 6, respectively. For the model in formula (4), the transfer function from δF to δX is shown in formula (5). During actual control, δX can also be calculated according to δF and this transfer function.

where s represents the Laplace variable in the transfer function.

Step four, position control. The target pose X _d obtained by trajectory planning and the adjustment amount δX obtained by impedance control are superimposed, and the joint angle target vector θ _d is calculated according to the inverse kinematics equation of the six-degree-of-freedom robot 2, and then the feedforward of formula (6) is used. The +PD feedback control law calculates the joint driving torque τ, and sends it to the servo drive/controller of each joint of the robot to complete the command output of the current control cycle.

where _MR is the estimated value of the generalized inertial matrix of the six-degree-of-freedom robot 2, _CR and _GR are the estimated value of the centrifugal force/Coriolis force term and the estimated value of the gravity term, respectively, and K _v and K _p are the PD feedback control. The differential term coefficient matrix and the proportional term coefficient matrix of . Other steps are the same as in the second embodiment.

Embodiment 4: In the hole search stage of the circular-rectangular composite hole type part assembly method, the hole search movement of the assembly part 4 is planned according to the contact state every time it contacts with the assembled part 6, and the contact state According to the number of contact points and their positions on the bottom surface of the assembly (the plane in contact with the assembly in the hole search stage), they are divided into 4 types as shown in Figure 6, where the contact points are represented by red circles, l and θ _C represents the phase angle and the radial length of the contact point in the xO _P y plane of the ΣO _P system, respectively, a, b, c, and r are the geometric dimensions of the bottom surface of the assembly, r is the arc radius, and a is the length. The width of the square part, b is the distance from the intersection of the arc part and the rectangular part to the OP point, and _c is the length of the rectangular part.

Figure 6a) shows the first contact state in the hole search stage. A single contact point is located inside the incomplete arc of the bottom contour of the assembly, indicating that a point within the contour of the bottom of the assembly is connected to the edge of the circular-rectangular compound hole of the assembly. Interference occurs and the assembly should move away from the point of contact.

Fig. 6b) is the second contact state in the hole searching stage. A single contact point is located on the incomplete arc boundary of the bottom surface of the assembly part, indicating that the assembly part 4 and the assembled part 6 are in a state of sharp corner contact on the edge. This state is the critical state before the hole search is completed, and the assembly should move a small distance away from the contact point.

Figure 6c) shows the third contact state in the hole search stage. The two contact points are located on the incomplete circular arc boundary of the bottom contour of the assembly, indicating that the fox hunting segment determined by the two contact points hangs out of the circle of the assembly 6. - The boundary of the rectangular compound hole, so the assembly should move away from the connection line of the contact points. This contact state can be equivalent to the first contact state in Figure 6a), and the two contact points are regarded as a connection line A touch point at the midpoint so that the adjustment strategy is exactly the same.

Fig. 6d) is the fourth contact state in the hole searching stage. A single contact point is located in the rectangular part of the bottom surface contour of the assembly part, indicating that the assembly part 4 and the assembled part 6 interfere with the rectangular part due to the non-parallel symmetry plane. The assembly should be rotated about the z-axis (direction of the axis perpendicular to the outward face of the paper in Figure 5) so that the contact points are unscrewed out of the square.

Under the above four contact states, the force balance equation in the ΣO _P system can be written uniformly:

Among them, F _x , F _y , and F _z are respectively the three force components that transform the force feedback measured by the six-dimensional force/torque sensor 3 into the ΣO _P system (the F _z here is the same as the definition of F _z in Fig. 3 ). ), M _x , _{My , and M z respectively} transform the force feedback measured by the six-dimensional force/torque sensor 3 into three force components in the ΣO _P system, f is the contact point in the hole search stage (for the third contact state refers to the magnitude of the normal force at the equivalent contact point). Solving equation (7), we can get:

According to the definitions of various contact states and the solution results in equation (8), the contact state discriminants in the hole search stage and the corresponding assembly adjustment strategies for each contact state can be summarized in Table 1.

Table 1 The contact state discriminant in the hole search stage and the corresponding assembly adjustment strategy for each contact state

In the hole-searching stage of the automatic assembly operation, the hole-searching trajectories after the tentative contact between the assembly part 4 and the assembled part 6 can be planned according to the following steps:

Step 1. According to the force screw ^P F _e obtained by the force feedback transformation, solve the force balance equation in the second column of Table 1 according to formula (8) to obtain f, l, θ _C ;

Step 2: Determine the contact state type in the hole search stage according to the discriminant in the third column of Table 1;

Step 3: From the adjustment strategy in the fourth column of Table 1, obtain the pose adjustment amount of the assembly in the next trial, and superimpose it on the normal adjustment motion trajectory to obtain the hole search trajectory of the assembly 4 in the next trial. . Other steps are the same as in the third embodiment.

Embodiment 5: In the insertion stage of the circular-rectangular composite hole component assembly method, whenever the z-axis force feedback F _z measured by the six-dimensional force/torque sensor 3 reaches the threshold value F _max , the current contact The state adjusts the pose of the assembly 4 so that the assembly process can continue without being stuck. In the insertion stage, the side and bottom edges of the assembly 4 may be in contact with the assembled part 6. In order to identify the contact state, according to the difference in the position of the contact point on the assembly 4, four types as shown in Figure 7 are defined. Basic touchpoints.

In the order of Figure 7a) ~ d), the four basic contact points defined are:

The first type of contact point is located on the side of the cylindrical part of the fitting 4 , and its mechanical balance equation is shown in equation (9), where μ is the friction coefficient between the fitting 4 and the fitted part 6 .

The second type of contact point is located at the edge of the bottom surface of the cylindrical part, and its mechanical equilibrium equation is shown in equation (10).

The third type of contact point is located on the side of the square column, and its mechanical equilibrium equation is shown in equation (11).

The third type of contact point is located on the edge of the bottom surface of the square column part, and its mechanical equilibrium equation is shown in formula (12).

According to the number of contact points in the actual contact state, the basic contact point type, and the relative position, the contact states in the insertion stage are divided into 7 categories and 41 types. The seven categories are: containing a first or second Single-point contact of the first type with a basic contact point of the first type (Fig. 8), single-point contact of the second type with a third or fourth basic contact point (Fig. 9), with a basic contact point of the first type and a Two-point first-type contact with a second-type basic contact point (Figure 10), two-point second-type contact with one first or second type of basic contact point and a third or fourth type of basic contact point (Figure 11) , a two-point contact of the third type with one basic contact point of the third type and one basic contact point of the fourth type (Fig. 12), containing one basic contact point of the first or second type and two basic contact points of the third or fourth type A three-point first-type contact (Fig. 13) of the contact points, a three-point second-type contact (Fig. 14) with two first or second basic contact points and one third or fourth basic contact point. The above 7 categories contain 2, 8, 1, 16, 4, 2, and 8 contact states, respectively. For the convenience of later presentation, P-i-j is used as the code of the contact category in the insertion stage, where i represents the number of contact points, j represents the serial number of the contact category after the number of contact points is determined; P-i-j-k is used as the contact state code belonging to the P-i-j category in the insertion stage, and k represents the contact state number in the P-i-j category. For example, the second type of contact with two points is P2-2 means that the 10th contact state will be written as P2-2-10.

For the contact states in Figures 8 to 14, the mechanical equilibrium equations are obtained by combining the mechanical equations of the basic contact points in equations (9) to (12). The characteristic classification is given, and the derivation results of the above-mentioned mechanical equilibrium equation and discriminant conditions are given in Table 2, where c _i and s _i (i=1, 2, 3) are the abbreviations for cosθ _Ci and sinθ _Ci , respectively, θ _Ci and f _i are the polar angle and normal contact force of the i-th contact point in the ΣO _P system, respectively, and k _mn (m=1, 2,..., 7; n=1, 2, 3, 4) is the m-th contact force The nth discriminant parameter of the contact state category is used to discriminate the specific contact state within the category, and the values of k _mn are all within the closed interval [-1, 1].

Table 2 Mechanical equilibrium equations and discriminant conditions for the categories of contact states in the insertion stage

For the contact state categories in Table 2, Table 3 gives the discriminant conditions and corresponding adjustment motions of each contact state in each category, among which there are 5 kinds of adjustment motions of the assembly, namely the inner edge of the ΣOP system. The two translations of the x-axis and the y-axis and the three rotations around the x-axis, the y-axis and the z-axis are represented by x, y, θ _x , θ _y , and θ _z to represent the above-mentioned five adjustment movements; each adjustment movement There are both positive and negative directions, which are represented by "+" and "-"respectively; then the adjustment motion is abbreviated as the compound form of the variable sign and the positive and negative sign, for example, the assembly 4 rotates in the negative direction around the x-axis at It is abbreviated as "θ _x -" in Table 3. Since some contact states correspond to the same adjustment motion of the assembly, it is not necessary to distinguish them in the control of the insertion stage. Therefore, after taking the union of the discrimination conditions of the contact states corresponding to the same adjustment motion, these contact states are merged in Table 3. Write a line.

Table 3 Discrimination conditions of contact state types in the insertion stage and the pose adjustment strategy of the assembly

In the insertion phase of the automatic assembly operation, every time the assembly force F _z of the downward assembly of the assembly 4 reaches the threshold value F _max , the adjustment movement of the assembly can be planned as follows:

Step 1. According to the force and moment components in the force screw ^P _Fe obtained by the force feedback transformation, judge the contact category to which the current contact state belongs according to the category discrimination conditions in the fourth column of Table 2;

Step 2, solve the mechanical equilibrium equation of the third row in table 2, obtain the θ _C1 and the basic species discrimination parameter k _mn of the reaction contact point position;

Step 3: Determine the specific contact state according to the discrimination conditions in the third column of Table 3, and find the adjustment motion corresponding to the current contact state in the fourth column of Table 3. Other steps are the same as in the fourth embodiment.

Embodiment 6: As the feasibility verification of the hole search stage, the insertion stage, and the overall automatic assembly control method proposed in the present invention, the automatic assembly simulation of the circular-rectangular compound hole parts is carried out. In this simulation, the automatic assembly system uses the virtual prototype system in Figure 3, and the assembly and the assembled part select a clearance-fit circular-rectangular compound hole type part used in the nuclear industry, and its specific size parameters are shown in Figure 15 As shown, the radius of the cylindrical part is 1.5mm, the length and width of the square column part are 28mm and 1.8mm respectively, the thickness of the cylinder and the square column in the assembly is 30mm, and the gap between the shaft hole of the assembly and the assembled part is 0.03mm .

The automatic assembly simulation carried out is divided into three parts: hole search simulation, the simulation of the contact state discrimination in the insertion stage and the overall automatic assembly simulation. The purpose of the hole search simulation is to verify the proposed hole search method. In the initial state, only the estimated pose of the assembled part 6 exists in the automatic assembly control system, and this pose and the true value of the assembled part 6 pose. The deviation is called the hole search error, and the search hole error along the x-axis and y-axis is called the position error of the search hole. The initial search hole position error is a random number within the range of ±1mm; the rotation around the z-axis The hole search error is called the angle error of the hole search, and the initial angle error of the hole search is a random number within the range of ±4° (the hole search error is not set in the translational direction along the z-axis, and the rotation around the x-axis and the y-axis). For different initial hole search errors within the above range, multiple groups of hole search simulations were carried out. Figure 16 shows the contact force curve and hole search error curve of one of the group of hole search simulations.

In the simulation process shown in Figure 16, in order to simplify the adjustment movement of the pose of the assembly, the hole search errors in the three directions (translation along the x-axis and y-axis, and rotation around the z-axis) are separately compensated. During the hole searching process, the position error and angle error of hole search show a certain fluctuation. At the end of the hole search, the positions are all less than 0.1mm, and the angle error is less than 0.3°. At the same time, the contact force is less than 10N and the moment generated by the contact force is less than 0.1Nm during the entire hole search process. It can be seen that the proposed hole search method can Under the premise of not damaging the assembly and the assembled parts (the contact force and moment are small), the hole search error is reduced to the level where the insertion can be started, which proves the effectiveness of the proposed method.

In order to verify the proposed method for discriminating the contact state in the insertion stage, the second part of the simulation is the simulation of the contact state discrimination in the insertion stage. During the simulation process, a contact state is randomly selected from each type of contact, and each contact state lasts for 300 sampling cycles, and then switch to the next category of contact states, so that a 2100-point sampling sequence corresponding to 7 contact states can be obtained. The judgment result of the contact state can be obtained.

)，可以看出识别结果的正确率为100％。According to the above method, multiple sets of contact state discrimination simulations are carried out, and the preset 7 contact states in one set of simulations are P-1-1-1, P-1-2-2, and P-2-1 respectively. -1, P-2-2-9, P-2-3-3, P-3-1-2, P-3-2-7, Figure 17 shows the discrimination results obtained in the simulation process (the upper part of the figure contact state schematic diagram and code) and contact force curve (among which

), it can be seen that the accuracy of the recognition results is 100%.

In order to verify the complete feasibility of the proposed automatic assembly method, a coherent assembly simulation including the approach stage, the hole search stage, and the insertion stage is carried out. Screenshot of the long-range video at the stage; after 6s, it is mainly the fine-tuning of the assembly 4 near the assembled part 6, so switch to the close-up video, you can see that the hole search process ends around 20s, and the assembly 4 is basically aligned with the assembled part. 6; The insertion stage begins after 20s. By 45s, the assembly 4 has been completely loaded into the assembled part 6, and the assembly operation is completed.

Figure 19 shows the error curve of the assembly force and the distance between the assembly part 4 and the assembly completion position during the assembly process. It can be seen that the assembly force in the entire assembly process is less than 16N and the torque is less than 0.04Nm. It can be seen that the proposed circle-length The assembly method of the square compound hole type parts can complete the automatic assembly operation of the round-rectangular compound hole type parts under the premise of ensuring the assembly flexibility.

Claims (3)

1. A robot automatic assembly method for round-rectangular composite hole parts is characterized in that the assembly objects of the assembly method are hole parts and shaft parts which have round and rectangular straight sides and right angles in geometric elements, wherein the parts with the composite round holes and square holes are called round-rectangular composite hole parts, the parts with the composite round columns and square columns are called round-rectangular composite shaft parts,

the automatic assembly system for the round-rectangular composite hole type parts, which is applied to the assembly method, is characterized by comprising the following steps: the robot comprises an upper computer, a base (1), a six-degree-of-freedom robot (2), a six-dimensional force/torque sensor (3), an assembly part (4), a clamping fixing seat (5) and an assembled part (6); wherein the six-degree-of-freedom robot 2 is any robot which can realize spatial six-degree-of-freedom motion and has position control precision meeting assembly operation, the upper computer is communicated with 6 servo driving/controllers and a six-dimensional force/torque sensor (3) of the six-degree-of-freedom robot (2) through a bus, the assembly part (4) is a round-rectangular composite shaft part, the assembled part (6) is a round-rectangular composite hole part,

the assembly part (4) is clamped on a tool side interface of the six-dimensional force/torque sensor (3), a robot side interface of the six-dimensional force/torque sensor (3) is fixedly connected with a tail end interface of the six-degree-of-freedom robot (2), the assembly part (6) with a round-rectangular composite hole is fixed in an interface of the clamping fixed seat (5), and the clamping fixed seat (5) and the six-degree-of-freedom robot (2) are both fixed on the base (1);

according to the design drawing sizes of the base (1), the clamping fixed seat (5) and the assembled part (6) or the actual measurement result after the system is assembled, the relative position of the round-rectangular composite hole of the assembled part (6) relative to the six-degree-of-freedom robot (2) can be calculated, the relative position is defined as the estimated position of the assembled part (6), and the estimated position is not equal to the actual position of the assembled part (6), so if the motion of the assembled part (4) is directly pressed against the estimated position of the assembled part (6) in the assembling process, the interference between the assembled part (6) and the assembled part (4) is easy to generate, and the assembled part (4) needs to be adjusted according to the feedback of the six-dimensional force/torque sensor (3);

the assembling process is divided into three stages, namely an approaching stage, a hole searching stage and an inserting stage;

the assembling operation is started by entering an approaching stage, the assembling part (4) needs to rapidly approach the assembled part (6) from an initial position under the control of the six-freedom-degree robot (2) to an assembling preparation position above the estimated position of the assembled part (6), and the preparation position can be added with an increment vector [0,0, delta z ] from the estimated position]^TCalculating to obtain delta z as position increment in the vertical direction; trajectory planning for the above described motion applies a 5-th order spline, where the velocity and acceleration at the start and end points are both0, the starting point refers to the initial position of the assembly (4), and the end point refers to the assembly preparation position;

after the assembly part (4) reaches the assembly preparation position, the hole searching stage is started, after the stage is started, the six-degree-of-freedom robot (2) enables the assembly part (4) to slowly move towards the assembled part (6) for trial, and when the contact force in the vertical direction is larger than a threshold value F_maxThe control system of the assembly operation judges the contact state between the assembly part (4) and the assembled part (6) according to the feedback of the later six-dimensional force/torque sensor (3), then lifts the assembly part (4) for a distance and adjusts the pose of the assembly part according to the previous contact state, and the trial process of the assembly part (4) to the assembled part (6) is repeated after the adjustment is completed until the conditions are met:

F_z＜F_max&h≥h_d (1)

wherein F_zRepresents the vertical force component, F, measured by a six-dimensional force/moment sensor (3)_maxIs a threshold value of the contact force, h represents the depth of the assembly part (4) inserted into the assembled part (6), h_dJudging a threshold value of the insertion depth after hole searching is completed;

the contact states of the assembly parts (4) and the assembled parts (6) in the hole searching stage are 4, and the hole searching movement of the assembly parts (4) can be determined according to the contact state after each trial;

in the first contact state of the hole searching stage, a single contact point is positioned inside an incomplete arc of the bottom surface contour of the assembly part, which indicates that one point in the bottom surface contour of the assembly part interferes with the edge of the round-rectangular composite hole of the assembled part, and the assembly part moves in a direction away from the contact point;

in the second contact state of the hole searching stage, a single contact point is positioned on the incomplete arc boundary of the bottom surface outline of the assembly part, which indicates that the assembly part (4) and the assembled part (6) are in a sharp-angle contact state of the edge, the state is a critical state before the hole searching is finished, and the assembly part moves a small distance in a direction away from the contact point;

in the third contact state of the hole searching stage, two contact points are positioned on the incomplete arc boundary of the bottom surface outline of the assembly part, which indicates that the fox hunting section determined by the two contact points is suspended out of the circle-rectangle composite hole boundary of the assembled part (6), so that the assembly part should move towards the direction far away from the connecting line of the contact points, the contact state can be equivalent to the first contact state of the hole searching stage, and the two contact points are regarded as one contact point at the middle point of the connecting line, so that the adjustment strategies are completely the same;

in the fourth contact state of the hole searching stage, a single contact point is positioned in a rectangular part of the bottom surface outline of the assembly part, the interference of the rectangular part is generated by the fact that the symmetry plane of the assembly part (4) and the assembled part (6) is not parallel, and the assembly part is rotated around the z axis to enable the contact point to be screwed out of the rectangular part;

in the above four contact states, Sigma O_PThe force balance equations within the system can all be written uniformly as:

wherein F_x、F_y、F_zRespectively, the force feedback measured by the six-dimensional force/torque sensor (3) is converted into sigma-delta O_PThree force components within the system;

M_x、M_y、M_zrespectively converting the force feedback measured by the six-dimensional force/torque sensor (3) into sigma-delta O_PThree force components in the system, wherein f is the size of the normal force at the contact point in the hole searching stage; solving equation (7) can obtain:

according to the definitions of various contact states and the solving result in the formula (8), the contact state discriminant and the assembly adjustment strategy corresponding to each contact state in the hole searching stage are summarized in table 1:

TABLE 1 discriminant of contact status in hole-searching stage and adjustment strategy for each assembly corresponding to contact status

In the hole searching stage of the automatic assembly operation, the hole searching track after the assembly part (4) and the assembled part (6) are in trial contact each time can be planned according to the following steps:

step one, according to the force feedback transformation, the force rotation quantity is obtained^PF_eThe force balance equation in column 2 of Table 1 was solved according to equation (8) to obtain f, l, and θ_C；

Step two, determining the contact state type of the hole searching stage according to the discriminant in the 3 rd column of the table 1;

step three, obtaining the pose adjustment amount of the assembly part in the next trial by the adjustment strategy in the 4 th column of the table 1, and superposing the pose adjustment amount to the normal adjustment motion track to obtain the hole searching motion track of the assembly part (4) in the next trial;

when the condition in the formula (1) is met, the tail end of the assembly part (4) is inserted into the round-rectangular composite hole of the assembled part (6), and the insertion depth reaches h_dWhen the hole searching is finished, switching to an insertion stage; during the insertion phase the insert (4) is continuously advanced in the negative z-axis direction, i.e. in the direction in which the insert is inserted vertically downwards into the component to be assembled, whenever F_zReaches the threshold value F_maxAnd when the plugging process is considered to be possibly blocked, judging the inserted contact state, adjusting the position of the assembly part (4) in the hole according to the contact state, and continuing to insert until the conditions are met:

F_z＜F_max&h≥h_max(2) wherein h is_maxIs an insertion depth discrimination threshold for completion of assembly;

when the condition in the formula (2) is met, the depth of the assembly part (4) inserted into the assembled part (6) reaches h_maxThe assembly member (4) is considered to be successfully assembled into the assembled member (6), and the assembly operation is finished.

2. The method for the robotic automatic assembly of circular-rectangular composite hole parts as claimed in claim 1, wherein the six-degree-of-freedom robot (2) during the assembly operation is controlled by a force/position hybrid control system,

firstly, a coordinate system is defined, the origin of a base coordinate system sigma-xyz is fixed at the center of a robot interface of a base (1), and an assembly coordinate system sigma-O_P-xyz sum of measurements Σ O_S-the origin of xyz is located at the centre of the circle of the lower surface of the fitting (4) and the force measuring center of the six-dimensional force/torque sensor (3), respectively; in sigma O_PIn the system, the z-axis direction is parallel to the insertion direction of the assembly part (4) into the assembled part (6), the x-axis direction is parallel to the symmetry plane of the geometric outline of the assembly part (4) and is vertical to the z-axis, and the y-axis direction is determined by the vector direction obtained by multiplying the unit vector of the z-axis by the unit vector of the x-axis;

the variables of the control system are defined as follows: x ═ X, y, z, θ_P1,θ_P2,θ_P3]^TIs the pose vector of the assembly member (4), wherein x, y and z are respectively sigma O_PAt a position coordinate, theta, within a base coordinate system sigma O_P1、θ_P2、θ_P3Are respectively sigma O_P3 Euler angles relative to the Σ O system; theta is ═ theta₁,θ₂,θ₃,θ₄,θ₅,θ₆]^TAnd τ ═ τ [ τ ]₁,τ₂,τ₃,τ₄,τ₅,τ₆]^TAre respectively defined as a joint angle and a joint driving moment vector of the six-degree-of-freedom robot (2), wherein theta_iAnd τ_i(i-1, 2, …,6) represents the joint angle and drive torque of the ith joint, respectively; SF_eIs a six-dimensional force/torque sensor (3) in sigma-delta O_SRaw data of the torque measured in the system, PF_eIs to be^SF_eConversion to Σ O_PThe amount of internal rotation of the system; x_d、F_d、θ_dX, F and theta target values in the control process respectively, and δ X and δ F are the adjustment quantity of X and the deviation of F theoretical value and actual value in the control process respectively;

for a force/position hybrid control system for automatically assembling circular-rectangular composite hole parts, the control flow in each control period comprises the following steps:

step one, feedback sampling: servo motor encoder and six-dimensional force/torque transmission for six-degree-of-freedom robot (2)The sensors 3 read the data to respectively obtain the joint angle vectors theta and Sigma O of the robot_SAmount of rotation of force in the system^SF_eThe pose vector X, Sigma O of the assembly part can be obtained from theta according to the positive kinematic simulation of the six-degree-of-freedom robot 2_PIntrinsic torque PF_eCan be calculated according to the formula (3);

in formula (3), R is Σ O_SIs tied to sigma O_PRotational transformation matrix of the system, P_SIs O_SPoint-in-Sigma O_PPosition vector within the system, 0_3×3Is a 3-order all-zero square matrix;

step two, planning a track: planning the pose track of the assembly part (4) according to the assembly flow, and if the assembly process is in an approaching stage, calculating the target pose X of the assembly part (4) at the current moment according to a 5-time spline function_d(ii) a If the assembly process is in the hole searching stage or the inserting stage, the z-axis component F of the contact force needs to be judged firstly_zWhether or not the threshold value F is reached_maxIf F is_z<F_maxX is generated by the assembly part (4) continuously approaching or inserting the assembly part (6)_dOtherwise, the pose adjustment amount of the assembly part 4 is obtained according to the contact state, and then X is generated according to the adjustment amount_d；

Step three, impedance control: according to the target force screw quantity F_dAnd force feedback PF_eThe deviation delta F of the assembly part calculates the adjustment quantity delta X of the pose X of the assembly part, the used impedance control model is shown as a formula (4),

m, B, K are respectively an inertia array, a damping array and a rigidity array of the virtual impedance model between the assembly part (4) and the assembled part (6); for the model in the formula (4), the transfer function from δ F to δ X is shown in the formula (5), δ X is calculated according to δ F and the transfer function during actual control,

wherein s represents the laplace variable in the transfer function;

step four, position control: planning the track to obtain the target pose X_dSuperposed with the adjustment delta X obtained by impedance control, and calculated according to the inverse kinematics equation of the six-freedom-degree robot (2) to obtain a joint angle target vector theta_dThen calculating the joint driving torque tau according to the feedforward + PD feedback control law of the formula (6), sending the joint driving torque tau to a servo driving/controlling device of each joint of the robot, finishing the instruction output of the current control period,

wherein M is_RIs a generalized inertial array estimation value, C, of a six-degree-of-freedom robot 2_RAnd G_RRespectively an estimate of the centrifugal/Coriolis force term and an estimate of the gravity term, K_vAnd K_pThe coefficient matrix of differential terms and the coefficient matrix of proportional terms in the PD feedback control are respectively.

3. The method for robotic assembly of circular-rectangular composite hole-like parts according to claim 2, wherein there are four main types of 41 contact states in the insertion stage, and each contact state corresponds to an independent assembly adjustment strategy,

z-axis force feedback F measured by the six-dimensional force/torque sensor (3) every time during the insertion phase_zReaches the threshold value F_maxIn the process, the pose of the assembly part (4) needs to be adjusted according to the current contact state, so that the assembly process can be continued without being stuck; the lateral and bottom edges of the interior fitting (4) may come into contact with the fitting part (6) during the insertion phase, and for the purpose of identifying the contact state, four basic contact points are defined, differing from the positions of the contact points on the fitting part (4), in each case:

the first type of contact point is positioned on the side surface of the cylindrical part of the assembly part (4), the mechanical balance equation is shown as a formula (9), mu is the friction coefficient between the assembly part (4) and the assembled part (6),

the second type of contact point is positioned at the edge of the bottom surface of the cylindrical part, the mechanical balance equation of the second type of contact point is shown as a formula (10),

the third type of contact point is positioned on the side surface of the square column part, the mechanical balance equation of the third type of contact point is shown as the formula (11),

the third type of contact point is positioned on the edge of the bottom surface of the square column part, the mechanical balance equation is shown as the formula (12),

according to the number of contact points in the actual contact state, the types of the basic contact points and the relative positions, the contact states in the insertion stage are divided into 7 types of 41 types, and the seven types are respectively: a single point first type contact comprising a first or second type of base contact point, a single point second type contact comprising a third or fourth type of base contact point, a two point first type contact comprising a first type of base contact point and a second type of base contact point, a two point second type contact comprising a first or second type of base contact point and a third or fourth type of base contact point, a two point third type contact comprising a third type of base contact point and a fourth type of base contact point, a three point first type contact comprising a first or second type of base contact point and two third or fourth type of base contact point, a three point second type contact comprising two first or second type of base contact point and a third or fourth type of base contact point; the 7 major categories respectively contain 2, 8, 1, 16, 4, 2 and 8 contact states, and for the convenience of later representation, P-i-j is taken as the code of the contact major category in the insertion stage, wherein i represents the number of the contact points, and j represents the serial number of the contact major category after the number of the contact points is determined; p-i-j-k is taken as the contact state number belonging to the P-i-j large class in the insertion stage, k represents the contact state serial number in the P-i-j large class, for example, the second-class contact with two points is taken as P2-2, wherein the 10 th contact state is written as P2-2-10;

for the above 7 types of contact states, the mechanical balance equations are obtained according to the combination of the mechanical equations of the basic contact points in the equations (9) to (12), the mechanical balance equations and the corresponding judgment conditions for the types of contact states are given in table 2,

TABLE 2 mechanical equilibrium equation and discrimination condition for large class of contact state at insertion stage

C in Table 2_iAnd s_i(i ═ 1,2,3) are cos θ, respectively_CiAnd sin θ_CiAbbreviation of (a), theta_CiAnd f_iRespectively, the ith contact point is at Sigma O_PPolar angle and normal contact force in the system, k_mn(m is 1,2, …, 7; n is 1,2,3,4) is the nth discrimination parameter for the mth major category of contact states for discriminating the specific contact state within the major category, k is_mnAll values of (A) are in a closed range of [ -1,1 [ ]]Internal;

for the broad categories of contact conditions in Table 2, the criteria and correspondence for each contact condition in each broad category are given in Table 3Wherein the adjusting movement of the assembly member has a total of 5, namely two translation movements along the x-axis and the y-axis and three rotation movements around the x-axis, the y-axis and the z-axis in the Σ OP system, and the two translation movements are equal to each other in x, y and θ_x、θ_y、θ_zRespectively showing the above 5 adjustment movements; each adjustment movement has a positive direction and a negative direction, which are respectively indicated by a plus sign and a minus sign; the adjustment movement is abbreviated to a combination of the sign of the variables and the sign, so that a negative rotation of the assembly 4 about the x-axis is abbreviated in table 3 to "θ_x- "; after the judgment conditions of the contact states corresponding to the same adjustment motion are merged together, these contact states are merged and written as one row in table 3,

TABLE 3 Distinguishing Condition for contact State type in insertion phase and Assembly pose adjustment strategy

Assembly force F for each downward assembly of the assembly part (4) during the insertion phase of an automatic assembly operation_zReaches the threshold value F_maxThe adjustment movement of the fitting can then be planned as follows:

step one, according to the force feedback transformation, the force rotation quantity is obtained^PF_eJudging the contact large class to which the current contact state belongs according to the large class judgment conditions in the fourth column in the table 2 by the force and moment components in the table;

step two, solving the mechanical equilibrium equation of the third column in the table 2 to obtain the position theta of the reaction contact point_C1And a base class discrimination parameter k_mn；

And step three, determining a specific contact state according to the judgment conditions in the third column of the table 3, and checking the adjustment motion corresponding to the current contact state in the fourth column of the table 3.

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