CN104573347A

CN104573347A - Method for determining impact force of honeycomb buffer in landing buffering process

Info

Publication number: CN104573347A
Application number: CN201410829231.3A
Authority: CN
Inventors: 蒋万松; 王永滨; 王磊
Original assignee: Beijing Research Institute of Mechanical and Electrical Technology
Current assignee: Beijing Research Institute of Mechanical and Electrical Technology
Priority date: 2014-12-26
Filing date: 2014-12-26
Publication date: 2015-04-29

Abstract

The invention discloses a method for determining an impact force of a honeycomb buffer in a landing buffering process. The method comprises the following steps: firstly, establishing two coordinate systems on an inner barrel and an outer barrel of the buffer; secondly, in a landing process of the honeycomb buffer, acquiring the relative position and the impact speed of the two coordinate systems, and subtracting the original mounting length of the two coordinate systems from the obtained relative position to obtain an actuating stroke of the honeycomb buffer at the moment; finally, comparing the actuating stroke at the moment with a minimum value of a historical actuating stroke, calculating to obtain the impact force of the honeycomb buffer in the landing buffering process, and then updating the historical actuating stroke. According to the method, the problem of simulation of the landing buffering process based on a many-body dynamic model is solved, and higher simulation accuracy can be achieved; in addition, quick modeling and simulation analysis can be achieved, and the defects of large calculated amount and high hardware requirement of a finite element model are overcome.

Description

A Method of Determining Impact Force of Honeycomb Buffer During Landing Buffer

技术领域technical field

本发明涉及一种在月球及行星着陆探测任务的软着陆缓冲过程中基于塑性变形吸能实现缓冲时的冲击力计算方法，特别是一种确定蜂窝缓冲器在着陆缓冲过程中冲击力的方法。The invention relates to a method for calculating the impact force when buffering is realized based on plastic deformation energy absorption during the soft landing buffering process of the lunar and planetary landing exploration missions, in particular to a method for determining the impact force of the honeycomb buffer during the landing buffering process.

背景技术Background technique

天体表面着陆就位探测作为最有效的探测手段，其软着陆技术是实现行星表面着陆探测的一项关键技术。基于缓冲蜂窝材料的缓冲器具有结构简单可靠、缓冲性能平稳和缓冲效率高的特点，在各类月球和行星着陆器都有广泛应用。由于着陆器着陆条件复杂，经常使用典型工况试验和数值仿真手段评估着陆器的着陆缓冲性能和着陆稳定性，以降低试验成本，但是由于缓冲蜂窝利用塑性变形吸能实现着陆器缓冲，给着陆缓冲过程动力学分析和设计带来了很大困难。目前对着陆缓冲过程的仿真模拟主要分为有限元、多体系统和自编程序三类，第一种方法模拟过程复杂繁琐，计算数据量大，不但要求高性能计算，且耗费大量机时，不适合做为评估性能的手段；第二种方法对蜂窝缓冲器的模拟过于简化，不能反映蜂窝缓冲器动态冲击特性，且仿真模拟过程较难收敛；第三种方法只能针对特定构型编制，不但程序适应性差且容易出错，而且需要较高的理论水平和编程能力。As the most effective means of detection, the in-situ landing detection on the surface of celestial bodies, its soft landing technology is a key technology to realize the landing detection on the planetary surface. The buffer based on the buffer honeycomb material has the characteristics of simple and reliable structure, stable buffer performance and high buffer efficiency, and is widely used in various lunar and planetary landers. Due to the complex landing conditions of the lander, typical working condition tests and numerical simulation methods are often used to evaluate the landing buffer performance and landing stability of the lander to reduce the test cost. The kinetic analysis and design of the buffering process brings great difficulties. At present, the simulation of the landing buffer process is mainly divided into three categories: finite element system, multi-body system and self-programming. The first method is complex and cumbersome in the simulation process, with a large amount of calculation data, which not only requires high-performance computing, but also consumes a lot of computer time. It is not suitable as a means of evaluating performance; the second method is too simplified for the simulation of the cellular buffer, and cannot reflect the dynamic impact characteristics of the cellular buffer, and the simulation process is difficult to converge; the third method can only be compiled for a specific configuration , not only poor program adaptability and error-prone, but also requires a higher theoretical level and programming ability.

发明内容Contents of the invention

本发明解决的技术问题是：克服现有技术的不足，对通过发生塑性变形吸能实现缓冲的缓冲器进行力学分析，提供了一种确定蜂窝缓冲器在着陆缓冲过程中冲击力的方法。The technical problem solved by the present invention is: to overcome the deficiencies of the prior art, perform mechanical analysis on the buffer which achieves buffering through plastic deformation and energy absorption, and provide a method for determining the impact force of the honeycomb buffer during landing buffering.

本发明的技术解决方案是：一种确定蜂窝缓冲器在着陆缓冲过程中冲击力的方法，包括如下步骤：The technical solution of the present invention is: a kind of method for determining the impact force of the honeycomb buffer in the landing buffer process, comprising the following steps:

(1)在蜂窝缓冲器内筒上建立坐标系1，在蜂窝缓冲器外筒上建立坐标系2，其中坐标系1、坐标系2的x轴均指向内筒向外筒靠近的方向，y轴均指向内筒外筒径向方向，将坐标系1、坐标系2的相对距离相对于两个坐标系初始距离的位移变化作为蜂窝缓冲器作动行程，蜂窝缓冲器历史作动行程的最大值和最小值初始值为0，负值代表蜂窝缓冲器压缩，正值代表蜂窝缓冲器拉伸；(1) Establish coordinate system 1 on the inner cylinder of the honeycomb buffer, and establish coordinate system 2 on the outer cylinder of the honeycomb buffer, wherein the x-axis of coordinate system 1 and coordinate system 2 both point to the direction that the inner cylinder approaches the outer cylinder, and y The axes point to the radial direction of the inner cylinder and the outer cylinder, and the displacement change of the relative distance between coordinate system 1 and coordinate system 2 relative to the initial distance of the two coordinate systems is taken as the actuating stroke of the honeycomb buffer. The maximum historical actuating stroke of the honeycomb buffer is The initial value of value and minimum value is 0, the negative value represents the cellular buffer compression, and the positive value represents the cellular buffer stretch;

(2)在蜂窝缓冲器着陆过程中的t时刻，获取坐标系1与坐标系2的相对位置和冲击速度，并将得到相对位置将掉坐标系1与坐标系2的原始安装长度，得到t时刻的蜂窝缓冲器作动行程x；所述冲击速度为坐标系1与坐标系2的相对速度；(2) At time t during the landing process of the cellular buffer, obtain the relative position and impact velocity of coordinate system 1 and coordinate system 2, and obtain the relative position by subtracting the original installation lengths of coordinate system 1 and coordinate system 2 to obtain t The actuating stroke x of the honeycomb buffer at the moment; the impact velocity is the relative velocity between the coordinate system 1 and the coordinate system 2;

(3)如果t时刻的蜂窝缓冲器的作动行程x大于历史作动行程的最大值或者小于最小值，则转入步骤(4)，否则转入步骤(6)；(3) If the actuation stroke x of the cellular buffer at time t is greater than the maximum value of the historical actuation stroke or less than the minimum value, then proceed to step (4), otherwise proceed to step (6);

(4)蜂窝缓冲器在着陆过程中t时刻的冲击力为(4) The impact force of the honeycomb buffer at time t during the landing process is

$\begin{matrix} η η \cdot &Center Dot; {p p}_{c c} \cdot &Center Dot; [[\frac{11 - - tanh tanh ((x x + + {x x}_{00}))}{22} δ δ ((min min - - x x)) + + \frac{11 - - tanh tanh ((x x + + {x x}_{00} - - min min))}{22} δ δ ((x x - - min min))]] + + \\ η η \cdot &Center Dot; {p p}_{t t} \cdot &Center Dot; [[\frac{11 + + tanh tanh ((x x - - {x x}_{00}))}{22} δ δ ((x x - - max max)) + + \frac{11 + + tanh tanh ((x x - - {x x}_{00} - - max max))}{22} δ δ ((max max - - x x))]] \end{matrix}$

其中，η为蜂窝的硬化效应因子，η＝1+a×v+b×v²，v为冲击速度，a、b对于不同类型的蜂窝均为定值；p_c为静压缩载荷；p_t为静拉伸载荷，对于同类型的蜂窝，p_c和p_t均为定值；tanh(x)为双曲正切函数；x₀为平移量，用于限定双曲正切函数tanh(x)变量的取值；min为历史作动行程的最小值；max为历史作动行程的最大值；δ为bool逻辑函数Among them, η is the hardening effect factor of the honeycomb, η=1+a×v+b×v ² , v is the impact velocity, a and b are constant values for different types of honeycomb; p _c is the static compression load; p _t is the static tensile load, for the same type of honeycomb, p _c and p _t are constant values; tanh(x) is the hyperbolic tangent function; x ₀ is the translation amount, which is used to limit the variable of the hyperbolic tangent function tanh(x) The value of ; min is the minimum value of the historical actuation stroke; max is the maximum value of the historical actuation stroke; δ is a bool logic function

$δ δ ((x x)) = = \{\begin{matrix} 11 & x x &GreaterEqual; &Greater Equal; 00 \\ 00 & x x < < 00 \end{matrix};;$

(5)如果t时刻的蜂窝缓冲器的作动行程x大于历史作动行程的最大值，则用t时刻的蜂窝缓冲器的作动行程x替换历史作动行程的最大值，如果t时刻的蜂窝缓冲器的作动行程x小于历史作动行程的最小值，则用t时刻的蜂窝缓冲器的作动行程x替换历史作动行程的最小值；(5) If the actuating stroke x of the cellular buffer at time t is greater than the maximum value of the historical actuating stroke, then replace the maximum value of the historical actuating stroke with the actuating stroke x of the cellular buffer at time t, if If the actuation stroke x of the cellular buffer is less than the minimum value of the historical actuation stroke, then replace the minimum value of the historical actuation stroke with the actuation stroke x of the cellular buffer at time t;

(6)蜂窝缓冲器在着陆过程中t时刻的冲击力为(6) The impact force of the honeycomb buffer at time t during the landing process is

$\frac{11 - - tanh tanh ((x x - - {x x}_{00} - - min min))}{22} {f f}_{c c} ((min min)) + + \frac{11 + + tanh tanh ((x x + + {x x}_{00} - - max max))}{22} {f f}_{t t} ((max max))$

其中， $f_{c} (x) = η \cdot p_{c} \cdot [\frac{1 - \tanh (x + x_{0})}{2} δ (\min - x) + \frac{1 - \tanh (x + x_{0} - \min)}{2} δ (x - \min)],$ in, $f_{c} (x) = η &Center Dot; p_{c} &Center Dot; [\frac{1 - \tanh (x + x_{0})}{2} δ (\min - x) + \frac{1 - \tanh (x + x_{0} - \min)}{2} δ (x - \min)],$

${f f}_{t t} ((x x)) = = η η \cdot &Center Dot; {p p}_{t t} \cdot &Center Dot; [[\frac{11 + + tanh tanh ((x x - - {x x}_{00}))}{22} δ δ ((x x - - max max)) + + \frac{11 + + tanh tanh ((x x - - {x x}_{00} + + max max))}{22} δ δ ((max max - - x x))]] . .$

本发明与现有技术相比的优点在于：The advantage of the present invention compared with prior art is:

(1)本发明解决了基于多体动力学模型的着陆缓冲过程模拟仿真难题，并能达到较高的仿真精度；(1) The present invention solves the difficult problem of simulating the landing buffer process based on the multi-body dynamics model, and can achieve higher simulation accuracy;

(2)本发明中冲击力计算方法能够实现快速建模与模拟仿真分析，克服了有限元模型计算量大、硬件要求高的缺点；(2) The calculation method of impact force in the present invention can realize fast modeling and simulation analysis, overcomes the shortcomings of large amount of calculation and high hardware requirements of the finite element model;

(3)本发明方法与蜂窝缓冲器的构型无关，克服了计算方法与构型相关而适应性差的缺陷。(3) The method of the present invention has nothing to do with the configuration of the cellular buffer, and overcomes the defect that the calculation method is related to the configuration and has poor adaptability.

附图说明Description of drawings

图1为本发明缓冲蜂窝缓冲器的力学模型示意图；Fig. 1 is the schematic diagram of the mechanical model of buffer honeycomb buffer of the present invention;

具体实施方式Detailed ways

基于蜂窝等通过塑性变形吸能实现缓冲的缓冲器，其工作原理一般是通过缓冲器的内外筒相对运动实现，而相对运动过程受制于内部缓冲材料力学特性，缓冲材料在缓冲器相对运动过程中做负功而吸能从而实现缓冲。Based on honeycomb and other buffers that achieve buffering through plastic deformation and energy absorption, the working principle is generally realized through the relative movement of the inner and outer cylinders of the buffer, and the relative motion process is subject to the mechanical properties of the internal buffer material. Doing negative work and absorbing energy to achieve buffering.

(1)对于以单向受力为特性的蜂窝缓冲器，将缓冲蜂窝抽象为无质量轴向力单元，通过缓冲器当前外筒和内筒之间的相对位置、相对速度和运动历程信息，以及蜂窝静态压缩载荷及其动态特性，确定出当前时刻缓冲器冲击力值；(1) For the honeycomb buffer characterized by unidirectional force, the buffer honeycomb is abstracted as a massless axial force unit, and through the current relative position, relative velocity and motion history information between the outer cylinder and the inner cylinder of the buffer, As well as the honeycomb static compression load and its dynamic characteristics, the impact force value of the buffer at the current moment is determined;

(2)对于缓冲蜂窝压缩载荷的阶跃特性，对应缓冲器冲击力确定方法的数学表达式，采用了基于双曲正切函数的复合函数；(2) For the step characteristics of the buffer honeycomb compression load, the mathematical expression corresponding to the determination method of the impact force of the buffer adopts a compound function based on the hyperbolic tangent function;

(3)缓冲蜂窝的塑性变形特性以及蜂窝缓冲器冲击力与运动历程相关特性，对应缓冲器冲击力确定方法的数学表达式，采用了逻辑判断函数处理。(3) The plastic deformation characteristics of the buffer honeycomb and the correlation characteristics between the impact force of the honeycomb buffer and the movement history, corresponding to the mathematical expression of the determination method of the impact force of the buffer, are processed by a logical judgment function.

蜂窝缓冲器的力学模型如图1所示，内筒和外筒可沿轴线滑动，忽略缓冲器蜂窝的质量，将蜂窝缓冲器的缓冲抽象为一个轴向力单元，在内筒和外筒分别固定两个坐标系(某一轴与缓冲器轴线平行)。两个坐标系之间的相对位置相对于初始状态沿共轴方向的位移变化定义为作动行程，用x表示，负值表示压缩，正值表示拉伸，记录作动行程的最大值(max)和最小值(min)。The mechanical model of the honeycomb buffer is shown in Figure 1. The inner cylinder and the outer cylinder can slide along the axis. The mass of the buffer honeycomb is ignored, and the buffering of the honeycomb buffer is abstracted as an axial force unit. The inner cylinder and the outer cylinder are respectively Fix two coordinate systems (one axis is parallel to the buffer axis). The displacement change of the relative position between the two coordinate systems relative to the initial state along the coaxial direction is defined as the actuation stroke, which is represented by x. Negative values represent compression, and positive values represent stretching. Record the maximum value of the actuation stroke (max ) and the minimum value (min).

缓冲蜂窝通过压缩时塑性变形吸能实现缓冲，表现为弹塑性和不可恢复，静态压缩时的压缩载荷较平稳，基本在一个定值附近波动，此值称为静压缩载荷，在有相对冲击速度时的蜂窝压缩载定义为动压缩载荷，动压缩载荷相对静压缩载荷会有所提高，称为硬化效应(用因子η表征)。The buffer honeycomb achieves buffering through plastic deformation and energy absorption during compression, which is elastic-plastic and non-recoverable. The compression load during static compression is relatively stable and basically fluctuates around a certain value. This value is called static compression load. When there is a relative impact velocity The honeycomb compressive load at the time is defined as the dynamic compressive load, and the dynamic compressive load will increase relative to the static compressive load, which is called the hardening effect (characterized by factor η).

单级蜂窝压缩时的动压缩载荷(冲击力)可表达为The dynamic compression load (impact force) during single-stage honeycomb compression can be expressed as

${f f}_{c c} ((x x)) = = η η \cdot &Center Dot; {p p}_{c c} \cdot &Center Dot; [[\frac{11 - - tanh tanh ((x x + + {x x}_{00}))}{22} δ δ ((min min - - x x)) + + \frac{11 - - tanh tanh ((x x + + {x x}_{00} - - min min))}{22} δ δ ((x x - - min min))]] - - - - - - ((11))$

单级蜂窝拉伸时的动态冲击力可表达为The dynamic impact force of single-stage honeycomb stretching can be expressed as

${f f}_{t t} ((x x)) = = η η \cdot \cdot {p p}_{t t} \cdot &Center Dot; [[\frac{11 + + tanh tanh ((x x - - {x x}_{00}))}{22} δ δ ((x x - - max max)) + + \frac{11 + + tanh tanh ((x x - - {x x}_{00} + + max max))}{22} δ δ ((max max - - x x))]] - - - - - - ((22))$

其中，min表示历史作动行程的最小值(负值)；max表示历史作动行程的最大值(正值)；x₀＝平移量用于限定双曲正切函数tanh(x)变量的取值(该值可取3)；p_c＝静压缩载荷；p_t＝静拉伸载荷，对于同类型的蜂窝，p_c和p_t均为定值，由试验得到；tanh(x)为双曲正切函数；δ为bool逻辑函数Among them, min represents the minimum value (negative value) of the historical actuation stroke; max represents the maximum value (positive value) of the historical actuation stroke; x ₀ = translation amount is used to limit the value of the hyperbolic tangent function tanh (x) variable (this value can be taken as 3); p _c = static compressive load; p _t = static tensile load, for the same type of honeycomb, p _c and p _t are fixed values, obtained by experiment; tanh(x) is the hyperbolic tangent Function; δ is a bool logic function

$δ δ ((x x)) = = \{\begin{matrix} 11 & x x &GreaterEqual; &Greater Equal; 00 \\ 00 & x x < < 00 \end{matrix} - - - - - - ((33))$

η为蜂窝的硬化效应因子，例如冲击速度在10m/s，η＝1.2-1.3，可用二次多形式近似η is the hardening effect factor of the honeycomb, for example, the impact velocity is 10m/s, η=1.2-1.3, which can be approximated by quadratic multiple forms

η＝1+a×v+b×v² (4)η=1+a×v+b×v ² (4)

其中，v为冲击速度(m/s)，a、b对于不同类型的蜂窝均为定值。Among them, v is the impact velocity (m/s), and a and b are constant values for different types of honeycombs.

多级蜂窝的动态冲击力可由上述方法通过叠加得到，下面以含有一级拉伸和一级压缩组合的缓冲器为例，说明在进行整个着陆缓冲时一种计算蜂窝缓冲器冲击力的方法，具体实现步骤如下所示The dynamic impact force of multi-stage honeycomb can be obtained by superposition of the above methods. The following is an example of a buffer with a combination of one-stage tension and one-stage compression to illustrate a method for calculating the impact force of a honeycomb buffer during the entire landing buffer. The specific implementation steps are as follows

1)在缓冲器内筒上建立坐标系1，在缓冲器外筒上建立坐标系2(其中，坐标系1、坐标系2的x轴均指向回转轴向)，蜂窝缓冲器作动行程最大值和最小值初始值为0；1) Coordinate system 1 is established on the inner cylinder of the buffer, and coordinate system 2 is established on the outer cylinder of the buffer (wherein, the x-axis of coordinate system 1 and coordinate system 2 both point to the rotation axis), and the actuating stroke of the honeycomb buffer is the largest value and min are initially 0;

2)在蜂窝缓冲器着陆过程中t时刻，获取坐标系1与坐标系2的相对位置和相对速度(如图1中，坐标系2相对于坐标系1在x轴方向的位置和速度)；2) At time t during the landing process of the cellular buffer, obtain the relative position and relative velocity of the coordinate system 1 and the coordinate system 2 (as shown in Figure 1, the position and velocity of the coordinate system 2 relative to the coordinate system 1 in the x-axis direction);

3)用第2步中得到的相对位置，减掉第1步获取到的固定在缓冲器内外筒上的两个坐标系相对位置初始值(即原始安装长度)，得到t时刻缓冲器的作动行程，此作动行程为正表示缓冲器拉伸作动，为负表示缓冲器压缩作动，第2步中的相对速度即为缓冲器冲击速度。3) Using the relative position obtained in step 2, subtract the initial value of the relative position of the two coordinate systems fixed on the inner and outer cylinders of the buffer (that is, the original installation length) obtained in step 1 to obtain the function of the buffer at time t. If the stroke is positive, it means that the buffer is stretched, and if it is negative, it means that the buffer is compressed. The relative speed in the second step is the impact speed of the buffer.

4)若当前时刻作动行程大于历史记录的最大值或者小于最小值，则转入步骤(5)，否则转入步骤(6)；4) If the actuating stroke at the current moment is greater than the maximum value or smaller than the minimum value of the historical record, then go to step (5), otherwise go to step (6);

5)将式(1)和式(2)相加得到蜂窝缓冲器在着陆缓冲过程中的冲击力，并等待下一个计算冲击力时刻的到来；5) Add the formula (1) and formula (2) to get the impact force of the honeycomb buffer during the landing buffering process, and wait for the arrival of the next moment to calculate the impact force;

6)将t时刻作动行程、历史最大和最小作动行程和冲击速度综合确定出的冲击力值作为此缓冲器在该时刻的冲击力返回值，即6) The impact force value determined comprehensively by the actuating stroke at time t, the historical maximum and minimum actuating stroke, and the impact velocity is taken as the return value of the impact force of the buffer at this moment, that is,

$\frac{11 - - tanh tanh ((x x - - {x x}_{00} - - min min))}{22} {f f}_{c c} ((min min)) + + \frac{11 + + tanh tanh ((x x + + {x x}_{00} - - max max))}{22} {f f}_{t t} ((max max)) - - - - - - ((55))$

得到蜂窝缓冲器在着陆缓冲过程中的冲击力，并等待下一个计算冲击力时刻的到来。Obtain the impact force of the honeycomb buffer during the landing buffer process, and wait for the next moment to calculate the impact force.

本发明说明书中未作详细描述的内容属本领域技术人员的公知技术。The content that is not described in detail in the description of the present invention belongs to the well-known technology of those skilled in the art.

Claims

1. A method for determining the impact force of the honeycomb buffer in the landing buffering process, is characterized in that comprising the steps:

(1) Establish coordinate system 1 on the inner cylinder of the honeycomb buffer, and establish coordinate system 2 on the outer cylinder of the honeycomb buffer, wherein the x-axis of coordinate system 1 and coordinate system 2 both point to the direction that the inner cylinder approaches the outer cylinder, and y The axes point to the radial direction of the inner cylinder and the outer cylinder, and the displacement change of the relative distance between coordinate system 1 and coordinate system 2 relative to the initial distance of the two coordinate systems is taken as the actuating stroke of the honeycomb buffer. The maximum historical actuating stroke of the honeycomb buffer is The initial value of value and minimum value is 0, the negative value represents the cellular buffer compression, and the positive value represents the cellular buffer stretch;

(2) At time t during the landing process of the cellular buffer, obtain the relative position and impact velocity of coordinate system 1 and coordinate system 2, and obtain the relative position by subtracting the original installation lengths of coordinate system 1 and coordinate system 2 to obtain t The actuating stroke x of the honeycomb buffer at the moment; the impact velocity is the relative velocity between the coordinate system 1 and the coordinate system 2;

(3) If the actuation stroke x of the cellular buffer at time t is greater than the maximum value of the historical actuation stroke or less than the minimum value, then proceed to step (4), otherwise proceed to step (6);

(4) The impact force of the honeycomb buffer at time t during the landing process is

\begin{matrix} η η \cdot &Center Dot; {p p}_{c c} \cdot \cdot [[\frac{11 - - tanh tanh ((x x + + {x x}_{00}))}{22} δ δ ((min min - - x x)) + + \frac{11 - - tanh tanh ((x x + + {x x}_{00} - - min min))}{22} δ δ ((x x - - min min))]] + + \\ η η \cdot \cdot {p p}_{t t} \cdot &Center Dot; [[\frac{11 + + tanh tanh ((x x - - {x x}_{00}))}{22} δ δ ((x x - - max max)) + + \frac{11 + + tanh tanh ((x x - - {x x}_{00} - - max max))}{22} δ δ ((max max - - x x))]] \end{matrix}

Among them, η is the hardening effect factor of the honeycomb, η=1+a×v+b×v ² , v is the impact velocity, a and b are constant values for different types of honeycomb; p _c is the static compression load; p _t is the static tensile load, for the same type of honeycomb, p _c and p _t are constant values; tanh(x) is the hyperbolic tangent function; x ₀ is the translation amount, which is used to limit the variable of the hyperbolic tangent function tanh(x) The value of ; min is the minimum value of the historical actuation stroke; max is the maximum value of the historical actuation stroke; δ is a bool logic function

δ δ ((x x)) = = \{\begin{matrix} 11 & x x &GreaterEqual; &Greater Equal; 00 \\ 00 & x x < < 00 \end{matrix};;

(5) If the actuating stroke x of the cellular buffer at time t is greater than the maximum value of the historical actuating stroke, then replace the maximum value of the historical actuating stroke with the actuating stroke x of the cellular buffer at time t, if If the actuation stroke x of the cellular buffer is less than the minimum value of the historical actuation stroke, then replace the minimum value of the historical actuation stroke with the actuation stroke x of the cellular buffer at time t;

(6) The impact force of the honeycomb buffer at time t during the landing process is

\frac{11 - - tanh tanh ((x x - - {x x}_{00} - - min min))}{22} {f f}_{c c} ((min min)) + + \frac{11 + + tanh tanh ((x x + + {x x}_{00} - - max max))}{22} {f f}_{t t} ((max max))

in,

f_{c} (x) = η \cdot p_{c} \cdot [\frac{1 - \tanh (x + x_{0})}{2} δ (\min - x) + \frac{1 - \tanh (x + x_{0} - \min)}{2} δ (x - \min)],

{f f}_{t t} ((x x)) = = η η \cdot &Center Dot; {p p}_{t t} \cdot &Center Dot; [[\frac{11 + + tanh tanh ((x x - - {x x}_{00}))}{22} δ δ ((x x - - max max)) + + \frac{11 + + tanh tanh ((x x + + {x x}_{00} - - max max))}{22} δ δ ((max max - - x x))]] . .