WO2019100891A1

WO2019100891A1 - Dual neural network solution method for extended solution set for robot motion planning

Info

Publication number: WO2019100891A1
Application number: PCT/CN2018/111622
Authority: WO
Inventors: 张智军; 陈思远
Original assignee: 华南理工大学
Priority date: 2017-11-22
Filing date: 2018-10-24
Publication date: 2019-05-31
Also published as: CN108015765A; CN108015765B

Abstract

Provided is a dual neural network solution method for an extended solution set for robot motion planning, the method comprising the steps of: acquiring a current state of a robot via a sensor, and carrying out inverse kinematics analysis on a robot trajectory at a speed layer by using a quadratic optimization scheme; converting a quadratic optimization scheme of a minimum speed two-norm index into a standard quadratic planning problem; converting the quadratic planning problem into a solution of a Karush-Kuhn-Tucker optimality condition; utilizing a dual neural network solver of an extended solution set for solving; and transferring a result obtained by means of solving to a robot controller, and driving a robot body to carry out trajectory tracking. By means of designing a non-linear equality constraint in the method, a convex set constraint and a non-convex set constraint can be compatible, an initial error problem occurring in robot control can be eliminated, and an error accumulation problem in a robot control process can be overcome.

Description

An extended solution set for robot motion planning, dual neural network solution

Technical field

The invention relates to the technical field of robot motion planning and control, in particular to a method for expanding a dual solution neural network for robot motion planning.

Background technique

In recent years, robotic arms have been used in various fields, such as medical rehabilitation, aviation manufacturing, and home services. More and more researchers are also investing in the control of robotic arms and various complex trajectory tracking.

A redundant robot is a robot that has a degree of freedom greater than the minimum degree of freedom required to complete a task. This makes redundant robots more flexible and fault tolerant. Additional degrees of freedom can be designed to optimize some of the secondary subtasks when the end effector's original task is completed.

How to obtain the inverse motion solution in real time and accurately is a challenging problem in redundant robot motion planning. This is because the nonlinear characteristics of the forward kinematic mapping equation of redundant robots make it difficult to obtain analytical solutions in most cases. A common linearization technique is to solve the inverse kinematics problem at the motion level. Due to the redundancy of the robot, the inverse kinematics problem is an underdetermined problem at the speed level. This means that the inverse of the Jacobian matrix may not exist. The traditional pseudo-inverse method provides a minimum two-norm solution, but it does not solve the inequality problem, and there is no way to flexibly set the optimization index. In addition, the traditional pseudo-inverse method does not consider constraints under the influence of system or environmental factors. In recent years, a method based on quadratic programming has been proposed for its superior flexibility. However, the existing equality constraints in the quadratic programming-based method are directly substituted into the forward kinematics equation of the robot. Such equality constraints cannot overcome the initial error and error accumulation problems. In addition, most of these methods only consider the robot working in the convex set space. It is necessary to extend the application of the traditional quadratic programming-based method to the non-convex set space and overcome the above two problems.

In the framework of the quadratic programming method, developing a real-time quadratic programming solver is an important step. There are mainly two kinds of solvers: neural network and numerical method. Because of the intrinsic properties of neural network parallel computing, neural networks have the advantage of being faster and more accurate than numerical methods. In recent years, many recurrent neural networks have been applied to the problem of robot redundancy, but these neural network methods are mainly for robot motion planning problems with convex set constraints.

In order to expand the inverse kinematics solution of the robot, a method is proposed to solve the inverse kinematics problem of the robot on the convex and non-convex solution sets.

Summary of the invention

The main object of the present invention is to overcome the shortcomings and shortcomings of the prior art, and to provide an extended solution set of dual-neural neural network solutions for robot motion planning, which can be compatible with convex and non-convex constraint sets and can overcome initial error and error accumulation problems.

The object of the invention is achieved by the following technical solutions:

An extended solution to the dual-neural neural network solution for robot motion planning includes the following steps:

S1. Based on the given problem, the current state of the robot is acquired by the sensor, and the inverse kinematics analysis of the robot trajectory is performed on the velocity layer by using the quadratic optimization scheme. The designed performance index is the minimum velocity two norm, which is constrained to each robot. Joint angle limit and joint angular velocity limit of the joint and a nonlinear equation related to the motion of the robot;

S2. Converting the quadratic optimization scheme of the minimum speed two norm index of the robot designed in step S1 into a standard quadratic programming problem;

S3, converting the quadratic programming problem of the robot in step S2 into a solution of the Karush-Kuhn-Tucker optimization condition;

S4. Using a dual neural network solver that expands the solution set to solve the Karush-Kuhn-Tucker optimization condition of step S3;

S5. Pass the result obtained in step S4 to the robot controller, and drive the robot body to perform trajectory tracking.

Preferably, the step S1 is specifically: acquiring the current state of the robot by the sensor based on the given problem, and performing inverse kinematics analysis on the robot trajectory on the velocity layer by using the quadratic optimization scheme, and the designed performance index is the minimum velocity two. Norm

The joint angular velocity feasible range Ω constrained by the joint angle limit and joint angular velocity limit of each joint of the robot and a nonlinear equation related to the kinematics of the robot

among them

For the robot minimum speed two norm indicator,

Indicates the joint angular velocity column vector composed of the derivatives of the joint angles of the redundant robots, and the superscript T indicates the matrix transposition; the equality constraint

It is a nonlinear equation based on the kinematics equation of the robot and considering the convex and non-convex set constraints; where J is the Jacobian matrix of the redundant robot; ε is the adjustment parameter of the error convergence rate;

r _d and r are respectively the velocity vector of the desired path in three-dimensional space, the position vector of the desired path in three-dimensional space and the position vector of the actual trajectory of the robot in three-dimensional space; P _Ω (·) is from n-dimensional on the Ω set A mapping function from real space to Ω space, defined as P _Ω (x)=y= _{argmin y∈Ω} ||yx||, where the constraint set Ω is effectively compatible with convex and non-convex set constraints;

And _{Ω in} P _Ω (·) both represent a feasible space set of redundant robot joint angular velocity, the space set is a convex space set or a non-convex space set;

The designed quadratic optimization scheme of the minimum two norm index can be expressed as:

Further, the linear equality constraints is designed to cause the error e = r _d -r from any initial error e ₀ converges to zero with time, the robot tracking means that tracks the disturbance can be eliminated and the error control process suffered.

Preferably, step S2 is specifically: in order to solve the quadratic optimization scheme in step S1, it is first standardized as a standard quadratic programming problem:

Min.x ^T Wx/2+c ^T x,

s.t.Ax=q,

x ^- ≤ x ≤ x ⁺ ;

The standardized secondary planning problem has a one-to-one correspondence with the originally designed minimum norm index secondary optimization scheme:

c=0∈R ⁿ , A=J∈R ^m×n ,

W = I _{n × n} ∈ R ^{n × n} , Ω = [x ^- , x ⁺ ] ∈ R ⁿ , where x ^- and x ⁺ are the generalized lower bound and the generalized upper bound of the set Ω, respectively.

Preferably, step S3 is specifically: after converting into a standard quadratic programming problem, converting it into a solution of a Karush-Kuhn-Tucker optimization problem:

In this case, the Lagrange function is

L(x,λ)=x ^T x/2+λ ^T (Ax-q),

Where λ ∈ ^{R n} is the Lagrange multiplier vector, and the partial derivative of the function is:

According to the Karush-Kuhn-Tucker optimization, the partial derivative of the Lagrange function is zero and the domain of the independent variable x is considered. It can be seen that the standard quadratic programming problem of the robot is equivalent to the solution of the following equations:

Ax=q;

In the case where Ω is a convex set, according to the definition P _Ω (x)=y= _{argmin y∈Ω} ||yx||, the i-th calculated element of P _Ω (x) is defined as:

In the case where Ω is a non-convex set, the concrete function expression needs to be deformed according to the definition.

Preferably, step S4 is specifically: designing a dual neural network solver to obtain the parameter symbols in the original optimization scheme, and the dual-pair neural network solver designed to expand the solution set is as follows:

0<ζ<<1 is an adjustment parameter that expands the convergence rate of the dual neural network of the solution set.

Compared with the prior art, the present invention has the following advantages and beneficial effects:

By designing a nonlinear equality constraint, the invention can be compatible with convex set constraints and non-convex set constraints, eliminates the initial error problem occurring in robot control, and overcomes the error accumulation problem in the robot control process.

DRAWINGS

1 is a schematic flow chart of an embodiment method;

2 is a schematic diagram of a redundancy robot model of an embodiment.

The figure shows: 1-redundant robot; 2-first rotating joint; 3-second rotating joint; 4 third rotating joint; 5-fourth rotating joint; 6-fifth rotation Joint; 7-sixth rotating joint.

Detailed ways

The present invention will be further described in detail below with reference to the embodiments and drawings, but the embodiments of the present invention are not limited thereto.

Example 1

A dual neural network solution for expanding the motion planning of a solution robot includes the following steps:

specific:

Based on the given problem, the current state of the robot is acquired by the sensor, and the inverse kinematics analysis of the robot trajectory is performed on the velocity layer by the quadratic optimization scheme. The performance index of the design is the minimum velocity two norm.

among them

For the robot minimum speed two norm indicator,

r _d and r are respectively the velocity vector of the desired path in three-dimensional space, the position vector of the desired path in three-dimensional space and the position vector of the actual trajectory of the robot in three-dimensional space; P _Ω (·) is from n-dimensional on the Ω set A mapping function from real space to Ω space, defined as P _Ω (x)=y= _{argmin y∈Ω} ||yx||, where the constraint set Ω is effectively compatible with convex and non-convex set constraints. In addition, the linear equality constraints is designed to cause the error e = r _d -r from any initial error e ₀ converges to zero with time, which means that the trajectory tracking of the robot can be eliminated and the error control process disturbance suffered;

Both _Ω and _{Ω in} P _Ω (·) represent a feasible spatial set of redundant robot joint angular velocities, which are convex space sets or non-convex space sets.

In order to solve the above quadratic optimization scheme, it is first standardized as a standard quadratic programming problem:

Min.x ^T Wx/2+c ^T x,

s.t.Ax=q,

x ^- ≤ x ≤ x ⁺ ;

c=0∈R ⁿ , A=J∈R ^m×n ,

W=I _n×n ∈R ^n×n , Ω=[x ⁻ ,x ⁺ ]∈R ⁿ , where x ⁻ and x ⁺ are the generalized lower bound and the generalized upper bound of the set Ω, respectively, and also the angular velocity of the joint of the robot The generalized lower bound and the generalized upper bound of the constraint.

After converting to a standard quadratic programming problem, turn it into a solution to the Karush-Kuhn-Tucker optimization problem:

In this case, the Lagrange function is

L(x,λ)=x ^T x/2+λ ^T (Ax-q),

Ax=q.

In the case where Ω is a non-convex set, the concrete function expression needs to be deformed according to the definition, and it cannot be exhaustive here. Where n is the dimension of the joint space of the redundant robot.

After transforming the optimization scheme into a Karush-Kuhn-Tucker optimization problem, a dual neural network solver is designed to be obtained and substituted into the parameter symbols in the original optimization scheme. The dual-pair neural network designed to expand the solution set is designed. The network solver is as follows:

Finally, the joint angle obtained by the above-mentioned unicorn neural network solver for expanding the solution set is transmitted to the robot controller, and then the redundant robot body is controlled to realize the trajectory tracking function of the end effector, and the method of the embodiment is realized. .

The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and combinations thereof may be made without departing from the spirit and scope of the invention. Simplifications should all be equivalent replacements and are included in the scope of the present invention.

Claims

An extended solution set for robot motion planning is a dual neural network solution, which is characterized in that it comprises the following steps:

S1. Based on the given problem, the current state of the robot is acquired by the sensor, and the inverse kinematics analysis of the robot trajectory is performed on the velocity layer by using the quadratic optimization scheme. The designed performance index is the minimum velocity two norm, which is constrained to each robot. Joint angle limit and joint angular velocity limit of the joint and a nonlinear equation related to the motion of the robot;

S2. Converting the quadratic optimization scheme of the minimum speed two norm index of the robot designed in step S1 into a standard quadratic programming problem;

S3, converting the quadratic programming problem of the robot in step S2 into a solution of the Karush-Kuhn-Tucker optimization condition;

S4. Using a dual neural network solver that expands the solution set to solve the Karush-Kuhn-Tucker optimization condition of step S3;

S5. Pass the result obtained in step S4 to the robot controller, and drive the robot body to perform trajectory tracking.
The method according to claim 1, wherein the step S1 is specifically: acquiring a current state of the robot by a sensor based on a given problem, and performing inverse kinematics on the robot trajectory on the velocity layer by using a quadratic optimization scheme. Parsing, design performance index is minimum speed two norm
The joint angular velocity feasible range Ω constrained by the joint angle limit and joint angular velocity limit of each joint of the robot and a nonlinear equation related to the kinematics of the robot

among them
For the robot minimum speed two norm indicator,
Indicates the joint angular velocity column vector composed of the derivatives of the joint angles of the redundant robots, and the superscript T indicates the matrix transposition; the equality constraint
It is a nonlinear equation based on the kinematics equation of the robot and considering the convex and non-convex set constraints; where J is the Jacobian matrix of the redundant robot; ε is the adjustment parameter of the error convergence rate;
r d and r are respectively the velocity vector of the desired path in three-dimensional space, the position vector of the desired path in three-dimensional space and the position vector of the actual trajectory of the robot in three-dimensional space; P Ω (·) is from n-dimensional on the Ω set A mapping function from real space to Ω space, defined as P Ω (x)=y= argmin y∈Ω ||yx||, where the constraint set Ω is effectively compatible with convex and non-convex set constraints;
And Ω in P Ω (·) both represent a feasible space set of redundant robot joint angular velocity, the space set is a convex space set or a non-convex space set;

The designed quadratic optimization scheme of the minimum two norm index can be expressed as:
The method of claim 2 wherein the design of the nonlinear equality constraint is capable of causing the error e = r d - r to converge to zero from any initial error e 0 over time.
The method according to claim 2, wherein the step S2 is specifically: to solve the quadratic optimization scheme in the step S1, first standardize it into a standard quadratic programming problem:

Min.x T Wx/2+c T x,

s.t.Ax=q,

x - ≤ x ≤ x + ;

The standardized secondary planning problem has a one-to-one correspondence with the originally designed minimum norm index secondary optimization scheme:

c=0∈R n , A=J∈R m×n ,
W = I n × n ∈ R n × n , Ω = [x - , x + ] ∈ R n , where x - and x + are the generalized lower bound and the generalized upper bound of the set Ω, respectively.
The method according to claim 3, wherein the step S3 is specifically: after converting into a standard quadratic programming problem, converting it into a solution of a Karush-Kuhn-Tucker optimization problem:

In this case, the Lagrange function is

L(x,λ)=x T x/2+λ T (Ax-q),

Where λ ∈ R n is the Lagrange multiplier vector, and the partial derivative of the function is:

According to the Karush-Kuhn-Tucker optimization, the partial derivative of the Lagrange function is zero and the domain of the independent variable x is considered. It can be seen that the standard quadratic programming problem of the robot is equivalent to the solution of the following equations:

Ax=q;

In the case where Ω is a convex set, according to the definition P Ω (x)=y= argmin y∈Ω ||yx||, the i-th calculated element of P Ω (x) is defined as:

In the case where Ω is a non-convex set, the concrete function expression needs to be deformed according to the definition.
The method according to claim 2, wherein the step S4 is specifically: designing a dual neural network solver to obtain the parameter symbols in the original optimization scheme, and designing the dual pair of the extended solution set. The neural network solver is as follows:

0<ζ<<1 is an adjustment parameter that expands the convergence rate of the dual neural network of the solution set.