CN101804627A

CN101804627A - Redundant manipulator motion planning method

Info

Publication number: CN101804627A
Application number: CN 201010144515
Authority: CN
Inventors: 张雨浓; 张智军; 李克讷
Original assignee: Sun Yat Sen University
Current assignee: Sun Yat Sen University
Priority date: 2010-04-02
Filing date: 2010-04-02
Publication date: 2010-08-18
Anticipated expiration: 2030-04-02
Also published as: CN101804627B

Abstract

The invention provides a method for motion planning of a redundant manipulator, comprising the following steps: 1) through the host computer, adopting quadratic optimization to analyze the inverse kinematics of the manipulator on the velocity layer, the minimum performance index of the design can be the speed Norm, repetitive motion or kinetic energy, constrained by velocity Jacobian equation, inequality and joint angular velocity limit, which varies with joint angle; 2) Transform the quadratic optimization of step 1) into a quadratic programming problem ; 3) solving the quadratic programming problem in step 2) with a linear variational inequality primal dual neural network solver or a numerical method; 4) passing the solution result of step 3) to the lower computer controller to drive the mechanical arm to move. The original dual neural network based on the linear variational inequality of the present invention has global exponential convergence, and does not involve complex operations such as matrix inversion, greatly improves calculation efficiency, and has strong real-time performance and can adapt to limit changes of joint angular velocities.

Description

A Motion Planning Method for Redundant Manipulator

技术领域technical field

本发明属于冗余度机械臂运动规划方法，特别是涉及一种关节角速度变极限的冗余度机械臂运动规划方法。The invention belongs to a motion planning method of a redundant manipulator, in particular to a motion planning method of a redundant manipulator in which joint angular velocity changes to a limit.

背景技术Background technique

冗余度机械臂是一种自由度大于任务空间所需最少自由度的末端能动机械装置，其运动任务包括焊接、油漆、组装、挖掘和绘图等，广泛应用于装备制造、产品加工、机器作业等国民经济生产活动中。冗余度机械臂的逆运动学问题是指已知机械臂末端位姿，确定机械臂的关节角问题。传统的冗余度解析方法以及工业机械臂控制方法主要是基于伪逆的方法：即，把问题的解转化成求一个最小范数解加上一个同类解。次目标可以被指定到同类解上，去控制机械臂的自运动以躲避障碍物、关节极限、奇异点和优化其它目标函数。其缺点是在处理不等式约束上有困难，计算量大，实时性差，而且它会遇到奇异情况而生成不可行解，在实际机械臂的应用中受到很大的制约。The redundant manipulator is a terminal active mechanical device with a degree of freedom greater than the minimum degree of freedom required by the task space. Its motion tasks include welding, painting, assembly, excavation, and drawing, etc. It is widely used in equipment manufacturing, product processing, and machine operations. and other national economic production activities. The inverse kinematics problem of the redundant manipulator refers to the problem of determining the joint angle of the manipulator given the end pose of the manipulator. Traditional redundancy analysis methods and industrial manipulator control methods are mainly based on the pseudo-inverse method: that is, the solution of the problem is transformed into a minimum norm solution plus a similar solution. Secondary objectives can be assigned to homogeneous solutions to control the ego-motion of the manipulator to avoid obstacles, joint limits, singularities, and optimize other objective functions. Its disadvantages are that it is difficult to deal with inequality constraints, the amount of calculation is large, the real-time performance is poor, and it will encounter singular situations and generate infeasible solutions, which are greatly restricted in the application of actual manipulators.

发明内容Contents of the invention

本发明的目的在于克服现有技术的不足，提供一种计算量小、实时性强且能适应关节角速度极限变化的冗余度机械臂运动规划方法。The purpose of the present invention is to overcome the deficiencies of the prior art, and provide a redundant mechanical arm motion planning method with small calculation amount, strong real-time performance and adaptability to limit changes of joint angular velocities.

为了实现上述发明目的，采用的技术方案如下：In order to realize the above-mentioned purpose of the invention, the technical scheme adopted is as follows:

一种冗余度机械臂运动规划方法，包括如下步骤：A method for motion planning of a redundant mechanical arm, comprising the steps of:

1)通过上位机采用二次型优化在速度层上对机械臂的逆运动学解析，设计的最小性能指标可为速度范数、重复运动或动能，受约束于速度雅可比等式、不等式和关节角速度极限，该角速度极限是随关节角度变化的；1) The upper computer adopts quadratic optimization to analyze the inverse kinematics of the manipulator on the velocity layer. The minimum performance index designed can be the velocity norm, repetitive motion or kinetic energy, which is constrained by the velocity Jacobian equation, inequality and Joint angular velocity limit, the angular velocity limit changes with the joint angle;

2)将步骤1)的二次型优化转化为二次规划问题；2) converting the quadratic optimization of step 1) into a quadratic programming problem;

3)将步骤2)的二次规划问题用线性变分不等式原对偶神经网络求解器或数值方法求解；3) the quadratic programming problem of step 2) is solved with linear variational inequality original dual neural network solver or numerical method;

4)将步骤3)的求解结果传递给下位机控制器驱动机械臂运动。4) Pass the solution result of step 3) to the lower computer controller to drive the movement of the mechanical arm.

本发明基于线性变分不等式的原对偶神经网络具有全局指数收敛性，且没有涉及到矩阵求逆等复杂运算，大大地提高了计算效率，同时实时性强且能适应关节角速度极限变化。The original dual neural network based on the linear variational inequality of the present invention has global exponential convergence, and does not involve complex operations such as matrix inversion, greatly improves calculation efficiency, and has strong real-time performance and can adapt to limit changes of joint angular velocities.

附图说明Description of drawings

图1为本发明的流程图；Fig. 1 is a flowchart of the present invention;

图2为实现本发明的机械臂结构主视图；Fig. 2 is the front view of the mechanical arm structure realizing the present invention;

图3为实现本发明的机械臂结构俯视图；Fig. 3 is the top view of the mechanical arm structure realizing the present invention;

图4为机械臂局部示意图。Fig. 4 is a partial schematic diagram of the mechanical arm.

具体实施方式Detailed ways

下面结合附图对本发明做进一步的说明。The present invention will be further described below in conjunction with the accompanying drawings.

图1所示的冗余度机械臂运动规划方法主要由目标问题1、二次规划问题2、基于线性变分不等式原对偶神经网络求解器或二次规划数值算法3、下位机控制器4和机械臂5组成。先将逆运动学求解在速度层上设计为最小化

且受约束于

θ^-≤θ≤θ⁺，

欲优化的性能指标

可以是最小速度范数函数

重复运动指标

或最小动能函数

将上述的各种冗余度解析方案转化为通用的二次型优化标准形式2，再使用基于线性变分不等式的原对偶神经网络或二次规划数值方法3求解，并将求解结果传递给下位机控制器4驱动机械臂5运动。The redundant manipulator motion planning method shown in Figure 1 mainly consists of the target problem 1, the quadratic programming problem 2, the linear variational inequality-based primal dual neural network solver or the quadratic programming numerical algorithm 3, the lower computer controller 4 and The mechanical arm is composed of 5. First, the inverse kinematics solution is designed to minimize the velocity layer

and is subject to

θ ⁻ ≤ θ ≤ θ ⁺ ,

Performance indicators to be optimized

Can be the minimum velocity norm function

repetitive motion metrics

or minimum kinetic energy function

Transform the above-mentioned various redundancy analysis schemes into a general quadratic optimization standard form 2, and then use the original dual neural network or quadratic programming numerical method 3 based on linear variational inequality to solve the problem, and pass the solution result to the next Machine controller 4 drives mechanical arm 5 to move.

图2和图3所示的机械臂由机械臂连杆1、推杆2、关节3、关节与推杆施力点连结部4和基座5组成。其中推杆2的存在使其不同于传统无推杆串联机械臂的角速度恒定极限方式，而是一种变极限机械臂。在实时计算机械臂的逆解时，这个角速度极限是角度的函数。因此，通过改变二次规划的约束条件

从而实现变极限的控制。The mechanical arm shown in FIG. 2 and FIG. 3 is composed of a connecting rod 1 of the mechanical arm, a push rod 2 , a joint 3 , a connection part 4 between the joint and the force application point of the push rod, and a base 5 . The existence of the push rod 2 makes it different from the constant angular velocity limit mode of the traditional series manipulator without push rod, but a variable limit manipulator. This angular velocity limit is a function of angle when calculating the inverse solution of the manipulator in real time. Therefore, by changing the constraints of the quadratic programming

Thereby realizing variable limit control.

图4所示机械臂局部示意图，在通常的设计中，认为机械的动力产生于内部电机力矩，即假设动力不是来自于推杆，或者认为4非常小，几乎可以忽略，这样1和2就会重合在一起。本发明涉及的机械臂设计中，推杆是存在的，即4不可能忽略。这样，由于推杆的存在使得原来的角速度极限在每时每刻都会变化，是角度的函数。假设1的长度为a，4的长度为b，2的长度为c。具体推导过程如下：The partial schematic diagram of the mechanical arm shown in Figure 4, in the usual design, it is considered that the mechanical power is generated by the internal motor torque, that is, it is assumed that the power does not come from the push rod, or that 4 is very small and can be ignored, so 1 and 2 will be overlap together. In the design of the mechanical arm involved in the present invention, the push rod exists, that is, 4 cannot be ignored. In this way, due to the existence of the push rod, the original angular velocity limit will change every moment, which is a function of the angle. Suppose 1 has length a, 4 has length b, and 2 has length c. The specific derivation process is as follows:

${c c}^{22} = = {a a}^{22} + + {b b}^{22} - - 22 a a * * b b * * cos cos ((\frac{π π}{22} + + θ θ));; - - - - - - ((11))$

将上述公式对时间t求导，得Deriving the above formula with respect to time t, we get

$22 c c * * \frac{dc dc}{dt dt} = = 22 a a * * b b * * sin sin ((\frac{π π}{22} + + θ θ)) * * \overset{\cdot \cdot}{θ θ};; - - - - - - ((22))$

其中，c＝c₀+v*Δt*Δc，c₀为初始的c边长，v为步进电机的转速，Δc为电机转一圈对应的电推杆伸长量。进一步可得Among them, c=c ₀ +v*Δt*Δc, c ₀ is the initial side length of c, v is the speed of the stepping motor, and Δc is the elongation of the electric push rod corresponding to one revolution of the motor. further available

$22 c c * * ((v v * * Δc Δ c)) = = 22 a a * * b b * * sin sin ((\frac{π π}{22} + + θ θ)) * * \overset{\cdot &Center Dot;}{θ θ} = = 22 a a * * b b * * cos cos θ θ * * \overset{\cdot &Center Dot;}{θ θ};; - - - - - - ((33))$

即 $c * Δc * v = a * b * \cos θ * \overset{\cdot}{θ};$ (4)Right now $c * Δ c * v = a * b * \cos θ * \overset{&Center Dot;}{θ};$ (4)

所以 $\overset{\cdot}{θ} = \frac{c * Δc * v}{a * b * \cos θ} = \frac{Δc * v * \sqrt{a^{2} + b^{2} - 2 a * b * \cos (\frac{π}{2} + θ)}}{a * b * \cos θ}, - - - (5)$ so $\overset{\cdot}{θ} = \frac{c * Δ c * v}{a * b * \cos θ} = \frac{Δ c * v * \sqrt{a^{2} + b^{2} - 2 a * b * \cos (\frac{π}{2} + θ)}}{a * b * \cos θ}, - - - (5)$

因此可得关节速度的变极限为Therefore, the variable limit of the joint velocity can be obtained as

$\frac{Δc * v^{-} * \sqrt{a^{2} + b^{2} - 2 a * b * \cos (\frac{π}{2} + θ)}}{a * b * \cos θ} : = {\overset{\cdot}{θ}}^{-} (θ) \leq \overset{\cdot}{θ}$ (6) $\frac{Δ c * v^{-} * \sqrt{a^{2} + b^{2} - 2 a * b * \cos (\frac{π}{2} + θ)}}{a * b * \cos θ} : = {\overset{&Center Dot;}{θ}}^{-} (θ) \leq \overset{&Center Dot;}{θ}$ (6)

$\leq \leq {\overset{\cdot &Center Dot;}{θ θ}}^{+ +} ((θ θ)) : : = = \frac{Δc Δ c * * {v v}^{+ +} * * \sqrt{{a a}^{22} + + {b b}^{22} - - 22 a a * * b b * * cos cos ((\frac{π π}{22} + + θ θ))}}{a a * * b b * * cos cos θ θ},,$

其中，v⁺和v^-分别为相关关节步进电机的转速正极限和负极限。通过考虑角速度的极限为随角度变化的函数，在设计控制方法时，修改相应的约束条件，组成带有变极限参数的角速度极限条件，从而实现对变极限问题的解决。Among them, v ⁺ and v ^- are the positive limit and negative limit of the speed of the stepper motor of the relevant joint, respectively. Considering that the limit of angular velocity is a function that varies with the angle, when designing the control method, modify the corresponding constraint conditions to form the limit condition of angular velocity with variable limit parameters, so as to realize the solution to the variable limit problem.

基于前面的分析，机械臂的逆运动学求解在速度层上可设计为：Based on the previous analysis, the inverse kinematics solution of the manipulator can be designed at the velocity layer as:

$min min φ φ ((θ θ,, \overset{\cdot \cdot}{θ θ})) - - - - - - ((77))$

$s the s . . t t . . J J \overset{\cdot &Center Dot;}{θ θ} = = \overset{\cdot &Center Dot;}{r r},, - - - - - - ((88))$

$A A \overset{\cdot &Center Dot;}{θ θ} \leq \leq b b,, - - - - - - ((99))$

θ^-≤θ≤θ⁺， (10)θ ⁻ ≤ θ ≤ θ ⁺ , (10)

${\overset{\cdot &Center Dot;}{θ θ}}^{- -} ((θ θ)) \leq \leq \overset{\cdot \cdot}{θ θ} \leq \leq {\overset{\cdot \cdot}{θ θ}}^{+ +} ((θ θ));; - - - - - - ((1111))$

其中，

代表欲优化的性能指标；等式约束

表述机械臂末端运动轨迹；不等式约束

可以用于环境障碍物的躲避或其它性能约束；θ^-≤θ≤θ⁺、

分别是关节角度极限、关节角速度极限。in,

Represents the performance index to be optimized; equality constraints

Express the motion trajectory of the end of the manipulator; inequality constraints

Can be used for avoidance of environmental obstacles or other performance constraints; θ ^- ≤ θ ≤ θ ⁺ ,

They are joint angle limit and joint angular velocity limit respectively.

欲优化的性能指标

可以设计为各种冗余度解析方案的优化判据。其可以是最小速度范数函数，即

也可是重复运动指标，即

其中z＝λ(θ-θ(0))，λ＞0是用来控制关节位移幅值的正设计参数；还可以是最小动能函数

等。Performance indicators to be optimized

It can be designed as an optimization criterion for various redundancy resolution schemes. It can be the minimum velocity norm function, namely

It can also be a repetitive exercise index, that is,

Where z=λ(θ-θ(0)), λ>0 is a positive design parameter used to control the amplitude of joint displacement; it can also be the minimum kinetic energy function

wait.

如图1所示的步骤1，将上述问题转化为一个标准的二次规划问题去求解才能应用到机械臂的控制上去。该二次规划问题可写为如下通用形式：Step 1 shown in Figure 1, the above problem is transformed into a standard quadratic programming problem to be solved before it can be applied to the control of the manipulator. The quadratic programming problem can be written in the following general form:

minx^TWx/2+q^Tx， (12)minx ^T Wx/2+q ^T x, (12)

s.t.Jx＝d， (13)s.t.Jx=d, (13)

Ax≤b， (14)Ax≤b, (14)

x^-≤x≤x⁺。 (15)x ⁻ ≤ x ≤ x ⁺ . (15)

其中，决策变量x可以被定义为

W，q，J，d，A，b，x^-，x⁺为已知的相对应的系数矩阵和向量，比如，在最小速度范数方案中，W为单位矩阵，q＝0，J为雅可比矩阵，

而A，b可以是障碍物躲避参数或者由优化指标转化得到的不等式约束，x^-，x⁺由公式(10)、(11)通过变换获得。where the decision variable x can be defined as

W, q, J, d, A, b, x ^- , x ⁺ are known corresponding coefficient matrices and vectors, for example, in the minimum speed norm scheme, W is the identity matrix, q=0, and J is Jacobian matrix,

And A, b can be obstacle avoidance parameters or inequality constraints obtained by transforming the optimization index, x ⁻ , x ⁺ are obtained by transforming formulas (10) and (11).

下面说明关节物理极限的处理和变换过程，即如何由公式(10)、(11)转换得到公式(15)。在速度层上解析的时候，需要将(10)式转换为速度层

上的表达形式：The following describes the processing and transformation process of joint physical limit, that is, how to convert formula (10) and (11) to get formula (15). When parsing on the speed layer, it is necessary to convert formula (10) into the speed layer

The expression on the form:

$μ μ (({θ θ}^{- -} - - θ θ)) \leq \leq \overset{\cdot &Center Dot;}{θ θ} \leq \leq μ μ (({θ θ}^{+ +} - - θ θ)),, - - - - - - ((1616))$

其中系数μ＞0是用来调节关节角速度的可行域，系数μ的选取应该使(16)式转换后的可行域比原来的关节角速度可行域在一般情况下略大。由此，双端约束公式(10)和(11)可以合并为一个统一的双端约束：x^-≤x≤x⁺，其中x^-和x⁺的第i个元素分别定义如下：Among them, the coefficient μ > 0 is used to adjust the feasible region of the joint angular velocity. The selection of the coefficient μ should make the feasible region transformed by (16) slightly larger than the original feasible region of the joint angular velocity under normal circumstances. Thus, the double-ended constraint formulas (10) and (11) can be combined into a unified double-ended constraint: x ^- ≤ x ≤ x ⁺ , where the i-th elements of x ^- and x ⁺ are defined as follows:

${x x}_{i i}^{- -} = = max max {{{\overset{\cdot \cdot}{θ θ}}_{i i}^{- -} ((θ θ)),, μ μ (({θ θ}_{i i}^{- -} - - {θ θ}_{i i}))}},, - - - - - - ((1717))$

${x x}_{i i}^{+ +} = = min min {{{\overset{\cdot \cdot}{θ θ}}_{i i}^{+ +} ((θ θ)),, μ μ (({θ θ}_{i i}^{+ +} - - {θ θ}_{i i}))}} . . - - - - - - ((1818))$

本发明用双端不等式来表述关节物理极限的躲避，以上相关参数μ的选择可以基于理论分析或基于经验。The present invention uses a double-terminal inequality to express the avoidance of the physical limit of the joint, and the selection of the above relevant parameter μ can be based on theoretical analysis or experience.

得到上述的二次规划问题(12)-(15)式后，本发明的求解方法是采用基于线性变分不等式的原对偶神经网络或二次规划数值算法来实时求解此二次规划问题。After obtaining the above-mentioned quadratic programming problem (12)-(15), the solution method of the present invention is to use the original dual neural network or quadratic programming numerical algorithm based on the linear variational inequality to solve the quadratic programming problem in real time.

以下就是基于线性变分不等式的原对偶神经网络来求解带约束的二次规划问题(12)-(15)的神经网络求解器的构造过程。The following is the construction process of the neural network solver for solving the constrained quadratic programming problems (12)-(15) based on the primal dual neural network of the linear variational inequality.

首先，将二次规划问题(12)-(15)式转化为一个线性变分不等式，即求一个原对偶变量

使得

First, transform the quadratic programming problem (12)-(15) into a linear variational inequality, that is, find a primal dual variable

make

(y-y^*)^T(My^*+p)≥0， (19)(yy ^* ) ^T (My ^* +p) ≥ 0, (19)

其中，原对偶变量y及其上下限定义如下：Among them, the original dual variable y and its upper and lower limits are defined as follows:

$y = [\begin{matrix} x \\ u \\ v \end{matrix}],$

the y = [\begin{matrix} x \\ u \\ v \end{matrix}],

对偶变量u和v分别与等式约束(13)和不等式约束(14)相对应；1_v：＝[1，...，1]^T是元素都为1的相应维数向量；是足够大的常数，用于数值上替代无穷大+∞，而扩展矩阵M、p分别定义如下：The dual variables u and v correspond to the equality constraint (13) and the inequality constraint (14) respectively; 1 _v :=[1,...,1] ^T is the corresponding dimension vector whose elements are all 1; is a constant large enough to numerically replace infinity + ∞, and the expansion matrices M and p are defined as follows:

$M m = = [\begin{matrix} W W & {- - J J}^{T T} & {A A}^{T T} \\ J J & 00 & 00 \\ - - A A & 00 & 00 \end{matrix}],,$ $p p = = [\begin{matrix} q q \\ - - d d \\ b b \end{matrix}];;$

由此可总结归纳为：至少存在一个最优解x^*时，二次规划问题(12)-(15)可转化为线性变分不等式问题(19)。Therefore, it can be summarized as follows: when there is at least one optimal solution x ^* , quadratic programming problems (12)-(15) can be transformed into linear variational inequality problems (19).

其次，线性变分不等式问题(19)又等价于线性投影方程，即P_Ω(y-(My+p))-y＝0，其中P_Ω(·)为空间R^{dim(x)+dim(d)+dim(b)}到集合Ω的分段线性投影算子，P_Ω(y)的第i个计算单元定义为Secondly, the linear variational inequality problem (19) is equivalent to the linear projection equation, that is, P _Ω (y-(My+p))-y=0, where P _Ω ( ) is the space R ^dim(x)+dim The piecewise linear projection operator of ^(d)+dim(b) to the set Ω, the i-th computational unit of P _Ω (y) is defined as

$\{\begin{matrix} {y the y}_{i i}^{- -} & if if & {y the y}_{i i} < < {y the y}_{i i}^{- -} \\ {y the y}_{i i} & if if & {y the y}_{i i}^{- -} \leq \leq {y the y}_{i i} \leq \leq {y the y}_{i i}^{+ +} \\ {y the y}_{i i}^{+ +} & if if & {y the y}_{i i} > > {y the y}_{i i}^{+ +} \end{matrix},, &ForAll; &ForAll; i i &Element; &Element; {{1,2 1,2,, . . . . . .,, dim dim ((x x)) + + dim dim ((d d)) + + dim dim ((b b))}} . .$

接着，用下面的动力学系统(作为基于线性变分不等式的原对偶神经网络的动力学描述形式，如图1的步骤3)来求解上述线性变分不等式问题及二次规划问题：Then, use the following dynamical system (as the dynamical description form of the original dual neural network based on linear variational inequality, as shown in step 3 of Figure 1) to solve the above-mentioned linear variational inequality problem and quadratic programming problem:

$\overset{\cdot &Center Dot;}{y the y} = = γ γ ((I I + + {M m}^{T T})) {{{P P}_{Ω Ω} ((y the y - - ((My My + + p p)))) - - y the y}},, - - - - - - ((2020))$

其中，设计参数γ＞0用来调节网络的收敛性，γ越大该网络收敛得越快。此外，当(12)-(15)至少存在一个最优解x^*时，从任何初始状态出发，线性变分不等式原对偶神经网络(20)的状态向量y(t)都将收敛至某平衡点y^*，其前dim(x)个元素组成了二次规划问题(12)-(15)的最优解x^*。如果存在一个常数ρ＞0，使得||y-P_Ω(y-(My+p))||²≥ρ||y-y^*||²成立，则神经网络(20)全局指数收敛于平衡点y^*和问题最优解x^*(其收敛率正比于γρ)。将计算得到的角速度再传送给下位机控制器从而控制机械臂的运动，实现本发明的方法。Among them, the design parameter γ>0 is used to adjust the convergence of the network, and the larger the γ is, the faster the network converges. In addition, when (12)-(15) has at least one optimal solution x ^* , starting from any initial state, the state vector y(t) of the linear variational inequality original dual neural network (20) will converge to a certain equilibrium Point y ^* , whose first dim(x) elements constitute the optimal solution x ^* of the quadratic programming problem (12)-(15). If there is a constant ρ>0 such that ||yP _Ω (y-(My+p))|| ² ≥ ρ||yy ^* || ² holds, then the global exponential of the neural network (20) converges to the equilibrium point y ^* and the optimal solution to the problem x ^* (its convergence rate is proportional to γρ). The calculated angular velocity is then transmitted to the lower computer controller to control the movement of the mechanical arm to realize the method of the present invention.

Claims

1. A redundant manipulator motion planning method is characterized by comprising the following steps:

1) the upper computer analyzes the inverse kinematics of the mechanical arm on a speed layer by quadratic optimization, the designed minimum performance index can be speed norm, repetitive motion or kinetic energy and is constrained by a speed Jacobian equation, an inequality and a joint angular speed limit, and the angular speed limit is changed along with a joint angle;

2) converting the quadratic form optimization of the step 1) into a quadratic programming problem;

3) solving the quadratic programming problem in the step 2) by a primal-dual neural network solver or a quadratic programming numerical method based on a linear variational inequality;

4) and transmitting the solving result of the step 3) to a lower computer controller to drive the mechanical arm to move.

2. The method for redundant manipulator motion planning according to claim 1, wherein the quadratic optimization redundancy resolution scheme of step 1) designs the inverse kinematics solution of the manipulator on the velocity level as: minimization

Is constrained to

θ^-≤θ≤θ⁺，

Wherein

Representing performance indicators to be optimized, equality constraints

Expressing the motion trail of the tail end of the mechanical arm and inequality constraint

Representing avoidance Performance constraints for environmental obstacles, θ^-≤θ≤θ⁺、Respectively representing joint angle limit and joint angular velocity limit;

said property to be optimizedEnergy index

For optimization criteria of various redundancy resolution schemes, at the speed level

Using a minimum velocity norm function, i.e.

Or repetitive motion indicators, i.e.

Where z is λ (θ - θ (0)), λ > 0 is a positive design parameter, or minimum kinetic energy function, used to control the amplitude of joint displacement

Wherein H is the arm inertia matrix.

3. The method of claim 2, wherein the quadratic programming problem of step 2) is transformed into a linear variational inequality, i.e. a primal-dual variational solutionSo that

(y-y^*)^T(My^*+ p) is greater than or equal to 0, wherein the primal-dual variable y and the upper and lower limits thereof are defined as follows:

y = [\begin{matrix} x \\ u \\ v \end{matrix}],

the dual variables u and v correspond to an equality constraint (7) and an inequality constraint (8), respectively; 1_v：＝[1，...，1]^TAre corresponding dimension vectors with elements all being 1;are constants large enough to numerically replace infinity + ∞, and the spreading matrix M, p is defined as follows:

M = [\begin{matrix} W & - J^{T} & A^{T} \\ J & 0 & 0 \\ - A & 0 & 0 \end{matrix}],

p = [\begin{matrix} q \\ - d \\ b \end{matrix}] .

4. the linear variational inequality according to claim 3 characterized in that it is equivalent to the linear projection equation P_Ω(y- (My + P)) -y ═ 0, where P is_Ω(. is a space R)^{dim(x)+dim(d)+dim(b)}Piecewise linear projection operator, P, to the set Ω_ΩThe i-th calculation unit of (y) is defined as

<math><mrow><mo>&ForAll;</mo><mi>i</mi><mo>&Element;</mo><mo>{</mo><mn>1,2,3</mn><mo>,</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>,</mo><mi>dim</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>+</mo><mi>dim</mi><mrow><mo>(</mo><mi>d</mi><mo>)</mo></mrow><mo>+</mo><mi>dim</mi><mrow><mo>(</mo><mi>b</mi><mo>)</mo></mrow><mo>}</mo><mo>.</mo></mrow></math>

Then, using a kinetic system

Solving the linear variational inequality problem and the quadratic programming problem, wherein the design parameter gamma is more than 0 to adjust the convergence of the network, and the larger the gamma is, the faster the network converges.