A multi-redundancy robot cooperative motion planning control method

Abstract

The application discloses a kind of multi-redundancy mechanical arm cooperative motion planning control methods, the method includes the following steps: constructing multi-redundancy mechanical arm system model, the coupling joint between the position, velocity and physical limit of multi-redundancy mechanical arm is expressed as an equation and inequality constraint time-varying quadratic programming problem;Adaptive switching time-varying neural network is designed and realized to solve the motion trajectory of multi-redundancy mechanical arm system under three kinds of Markov switching topological structure;The calculation result is input to each mechanical arm, and the end trajectory cooperative control of multi-redundancy mechanical arm system is realized.The adaptive switching time-varying neural network containing error signal designed by the application has excellent convergence performance, can better and faster complete the cooperative control of multi-redundancy mechanical arm system;Meanwhile, the network designed can solve the system solving design problem caused by random switching topological structure.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of redundant robot cooperative control, and particularly relates to a multi-redundant manipulator cooperative motion planning control method. BACKGROUND

[0002] Manipulators play an important role in modern industry. Among them, redundant manipulators with more degrees of freedom are favored by engineers because they have better performance, such as obstacle avoidance and motion planning. Today, multi-manipulator systems have emerged, and in the fields of logistics, automobile assembly, welding, etc., multi-manipulator systems have been proven to be more advantageous than single-manipulator systems; in addition, multi-redundant manipulator systems can meet more complex requirements and be used in medical surgery, astronomical observation, etc. to improve the performance and function of the system, and complex tasks that a single manipulator cannot complete can be achieved by adjusting the structure of a group of redundant manipulators. The above results show that multi-redundant manipulator systems are more flexible and reliable.

[0003] Currently, neural networks are increasingly used to solve manipulator motion planning problems. Compared with traditional numerical analysis methods, neural networks have strong real-time computing power and large-scale information processing power, and perform excellently in manipulator motion planning. At present, most neural network solver designs are only suitable for single-redundant manipulators, and there are few neural network models involving multi-redundant manipulators.

[0004] The cooperative control of a multi-redundant robot arm is to keep the end trajectory of the robot arm or even each joint consistent. The existing neural network for solving the cooperative control problem of a multi-redundant robot arm mainly focuses on the construction of the algorithm, and ignores another important factor affecting the cooperation of the multi-redundant robot arm, that is, the topology. In a distributed system, subsystems achieve control objectives through information exchange with their adjacent subsystems, and the connection channels between the subsystems constitute the topology of the entire system. In the past design, the topology was assumed to be fixed. However, the communication between the multi-redundant robot arms is usually through wireless transmission. Considering the random factors such as electromagnetic interference, signal shielding, network fluctuation existing in the complex working ring, the communication topology may change temporarily, which poses new challenges to the existing multi-redundant robot arm control method. The existing research has not yet proposed an effective strategy to solve the cooperative control problem of the multi-redundant robot arm under the random switching topology. Fortunately, Markov process has been used to simulate random phenomena on distributed systems and has achieved good results. It is worth noting that in the traditional Markov process, all the information of the transition probability matrix is known; however, due to the difficulty of actual measurement, there are cases where part of the information in the transition probability matrix is unknown. In addition, the elements of the transition probability matrix in the semi-Markov process are time-varying, which means that the transition rate between two modes is variable, which is common in control systems. Therefore, it is of great significance to develop a new neural network model for the cooperative control of a multi-redundant robot arm under three kinds of Markov switching topologies. SUMMARY

[0005] In order to overcome the defects and deficiencies existing in the prior art, the present application provides a multi-redundant robot arm cooperative motion planning control method, which is based on the constructed adaptive switching time-varying neural network. The time-varying parameter design with error signal greatly improves the calculation efficiency and accuracy of the neural network. Combined with the Markov random theory, the motion planning problem of the multi-redundant robot arm system with switching topology that the previous neural network cannot calculate is solved. The designed adaptive time-varying neural network can efficiently and accurately solve the cooperative motion control problem of the multi-redundant robot arm under three kinds of random switching topologies.

[0006] In order to achieve the above purpose, the technical scheme adopted by the present application is as follows:

[0007] The present application provides a multi-redundant robot arm cooperative motion planning control method, comprising the following steps:

[0008] A multi-redundant robot arm system model is constructed, and the coupling relationship between the position, velocity and physical limit of the joints of the multi-redundant robot arm is established;

[0009] A multi-redundancy robot system is modeled based on a plurality of random switching topologies, and is converted into a time-varying equation, wherein the random switching topologies satisfy corresponding random switching rules, including a semi-Markov process, a Markov process with a completely known transition probability matrix, and a Markov process with a partially unknown transition probability matrix;

[0010] An adaptive switching time-varying neural network is constructed to solve the time-varying equation, and real-time angle parameters of each joint in the multi-redundancy robot system are obtained;

[0011] The calculated real-time angle parameters are input into a robot motion control system, so that an end effector of the multi-redundancy robot system moves according to an expected trajectory, and the robots keep cooperation.

[0012] As a preferred technical solution, the model of the multi-redundancy robot system specifically comprises:

[0013] A motion trajectory of the i-th redundant robot is represented as:

[0014] g i (Φ i (t))=z e (t),i∈1,2,...,M

[0015]

[0016] wherein z e ∈R m represents an expected motion trajectory of the robot, m represents a degree of freedom of a workspace of an end effector of the robot, g i (·)∈R n →R m represents a unique mapping relationship from a joint angle of the robot to the end effector, and n represents a degree of freedom of the robot;

[0017] A kinematics equation at a joint speed level is constructed and is represented as:

[0018]

[0019] wherein, is a Jacobian matrix of the i-th redundant robot, and are joint speed and end effector speed, respectively;

[0020] The kinematics equation at the joint speed level is converted into a matrix form and is represented as:

[0021]

[0022]

[0023] wherein, denotes the joint angle to be solved, B = diag[b1, b2, …, b M ], b i = 0 and b i = 1 respectively indicate whether the i-th redundant manipulator can directly receive the desired trajectory, J2(Φ2(t)),...,J M (Φ M (t))];

[0024] The upper and lower limits of the joint angle and angular velocity are set as:

[0025]

[0026] wherein, and are the upper and lower limits of the joint angle and angular velocity respectively;

[0027] The velocity layer constraint is expressed as:

[0028]

[0029] wherein, is the parameter of the manipulator;

[0030] The boundary constraint is expressed as:

[0031]

[0032] The matrix form is:

[0033]

[0034] wherein,

[0035] As a preferred technical solution, the cooperative motion control problem of a multi-redundancy manipulator system based on multiple random switching topologies is modeled and converted into a time-varying equation, which specifically includes:

[0036] The coupling relationship of the multi-redundancy manipulator system in the position layer is constructed as:

[0037]

[0038] wherein, z ij denotes the fixed distance between the i-th manipulator and the j-th manipulator, a ij > 0 indicates that the manipulator j receives information from the manipulator i, a ij = 0 indicates that the manipulator j and the manipulator i cannot communicate, i, j = 1, 2, …, M;

[0039] The coupling relationship of the multi-redundant manipulator system at the speed layer is:

[0040]

[0041] Among them, the matrix form of the multi-redundant manipulator system at the position layer and speed layer is expressed as:

[0042]

[0043]

[0044] Where L = DA is the Laplace matrix, which represents the communication connection topology between the manipulators, and A = [a ij ]∈R M×M ,D=diag{A1,A2,...,A M}, L δ Represents the topological structure, It changes with time. is the total number of possible topological structures, and m is the degree of freedom of the manipulator workspace;

[0045] Taking the minimum velocity norm as the objective function and the collaborative control problem of the multi-redundant manipulator system as the constraint condition, the quadratic programming problem is constructed as follows:

[0046]

[0047]

[0048]

[0049]

[0050]

[0051]

[0052] To solve the quadratic programming problem, let the Lagrangian function be:

[0053]

[0054] Where χ(t) and φ(t) are Lagrange multiplier vectors;

[0055] Its Karush-Kuhn-Tucker condition is expressed as:

[0056]

[0057] In combination with the non-linear complementary problem, the Karush-Kuhn-Tucker condition is converted into a time-varying equation, which is expressed as:

[0058]

[0059] wherein, is the Fischer-Burmeister function, is a scalar close to 0, is the Hadamard product operator;

[0060] The cooperative motion control problem of the multi-redundancy manipulator system is converted into solving the solution of the time-varying equation.

[0061] As a preferred technical solution, the random switching topology satisfies the corresponding random switching rules, including semi-Markov process, Markov process with completely known and partially unknown transition probability matrix, which is specifically expressed as:

[0062] The Markov switching rule has a transition matrix with completely known probability and conforms to the following process:

[0063]

[0064] wherein, π δr ≥ 0, δ ≠ r respectively represent the probability of transferring from mode δ to mode r, o represents an infinitesimal operator;

[0065] The Markov switching rule has a transition matrix with partially unknown probability

[0066] The semi-Markov switching rule is subject to the following constraint rules:

[0067]

[0068] wherein π δr (Δt) is a time-varying transition probability.

[0069] As a preferred technical solution, an adaptive switching time-varying neural network is constructed to solve the time-varying equation, and the real-time angle parameters of each joint in the multi-redundancy manipulator system are obtained, specifically including:

[0070] Define the error function:

[0071]

[0072]

[0073]

[0074]

[0075] The derivative of the error function is:

[0076]

[0077]

[0078]

[0079]

[0080]

[0081]

[0082] wherein, represents the Hadamard division;

[0083] According to the neural dynamic design method, the adaptive switching neural dynamic design formula with error information is constructed by combining the time-varying characteristics of the system:

[0084]

[0085] wherein, λ is a parameter for adjusting the convergence speed, and F(·) is an activation function;

[0086] The implicit dynamic equation used by the adaptive switching time-varying neural network is represented as:

[0087]

[0088]

[0089]

[0090]

[0091] As a preferred technical solution, the activation function adopts a monotone increasing odd function.

[0092] Compared with the prior art, the present application has the following advantages and beneficial effects:

[0093] (1) The technical scheme of the adaptive time-varying neural network is adopted in the present application, which solves the problem of slow convergence speed of the traditional time-varying neural network, and achieves the technical effect of efficiently and accurately solving the redundancy manipulator motion planning control.

[0094] (2) The technical scheme of the Markov random switching theory is adopted, the technical problem that the traditional fixed topology structure cannot adapt to the topology structure switching caused by the disturbance in the actual environment is solved, and the technical effect of more accurately simulating the real environment is achieved.

[0095] (3) The adaptive switching time-varying neural network is adopted, the technical problem that the previous neural network cannot calculate the motion planning of the multi-redundancy manipulator system under the switching topology is solved, and the technical effect of real-time solving the cooperative motion control of the multi-redundancy manipulator system is achieved. BRIEF DESCRIPTION OF DRAWINGS

[0096] Figure 1 It is a flowchart of the multi-redundancy manipulator cooperative motion planning control method of the present application.

[0097] Figure 2 It is a schematic diagram of the switching topology structure.

[0098] Figure 3 It is a cooperative motion effect diagram of the multi-redundancy manipulator based on the adaptive switching time-varying neural network.

[0099] Figure 4 It is a cooperative position error diagram of the manipulator in the three-dimensional space. DETAILED DESCRIPTION

[0100] In order to make the purpose, technical scheme and advantages of the present application more clear, the present application is further described in detail below in combination with the drawings and examples. It should be understood that the specific examples described herein are only used to explain the present application, and are not used to limit the present application.

[0101] Example 1

[0102] As shown in the figure, the present embodiment provides a multi-redundancy manipulator cooperative motion planning control method, which comprises the following steps: Figure 1

[0103] S1: Build a multi-redundancy manipulator model, and uniformly represent the coupling relationship between the position, velocity and physical limit of the joints of the multi-redundancy manipulator as equality and inequality constraints;

[0104] In the present embodiment, the specific steps of constructing the multi-redundancy manipulator system model include:

[0105] Suppose the desired motion trajectory of the manipulator is z e ∈R m , where m is the degree of freedom of the manipulator end effector workspace, then the motion trajectory of the i-th redundant manipulator can be described as:

[0106] ​

[0107] where n denotes the degree of freedom of the manipulator, Φ i denotes the angle of each joint of i manipulators, for one manipulator, g i (·)∈R n →R m denotes the unique mapping relationship from the joint angle of the manipulator to the end effector;

[0108] Derivation of the above manipulator model can obtain the kinematics equation of joint speed level:

[0109]

[0110] where is the Jacobian matrix of the i-th redundant manipulator, and are the joint speed and the end effector speed respectively, and M denotes the total number of manipulators;

[0111] In order to facilitate subsequent description, the above formula can be written in a compact matrix form:

[0112]

[0113] where, is the joint angle to be solved, B=diag[b1,b2,...,b M ],b i =0 and b i =1 respectively indicate whether the i-th redundant manipulator can directly receive the expected trajectory signal. Such setting means that only part of the manipulators (leaders) can directly track the target trajectory, and the other manipulators (followers) track the trajectory of the leaders through algorithm, so as to ensure the overall coordination and complete the given task cooperatively. In addition,

[0114] In order to avoid the calculated joint angle and angular velocity exceeding the specified limit range of the manipulator, it is necessary to limit them. Therefore, the upper limit of the joint angle and angular velocity is defined as:

[0115]

[0116] where, and are the upper and lower bounds of the joint angle and angular velocity respectively, and the above constraint can be written in the speed level as:

[0117]

[0118] where is a parameter specific to the robot arm, which specifically represents the joint angle parameter, such as the angle limit of this joint is 5 rad, and each robot arm corresponds to a specific parameter;

[0119] Therefore, the boundary constraint can be written as:

[0120]

[0121] The matrix form is:

[0122]

[0123] wherein

[0124] S2: Based on three kinds of random switching topological structures, the cooperative motion control problem of the multi-redundancy robot arm system in step S1 is modeled and converted into a time-varying equation, wherein the random switching rules satisfy the semi-Markov process, the Markov process with completely known transition probability matrix and partially unknown transition probability matrix, respectively;

[0125] The specific steps include:

[0126] In order to realize the end trajectory cooperative motion planning control of the multi-redundancy robot arm system, combined with formula (1) and the related knowledge of graph theory, the coupling relationship of the multi-redundancy robot arm system at the position layer is constructed as:

[0127]

[0128] wherein z ij represents the fixed distance between the i th robot arm and the j th robot arm, a ij > 0 represents that the robot arm j can receive the information sent by the robot arm i, otherwise, a ij = 0 represents that the robot arm j and the robot arm i cannot communicate, i, j = 1, 2, …, M.

[0129] Similarly, the coupling relationship at the velocity layer is:

[0130]

[0131] The matrix form of the multi-redundancy robot arm system at the position layer and the velocity layer (formula (4)-(5)) can be written as:

[0132]

[0133]

[0134] wherein L = D-A is the Laplace matrix, which represents the communication connection topological relationship between the robot arms, A = [a ij ] ∈ R M×M, D = diag{A1, A2,..., A M}, Since wireless communication often changes due to random disturbances in nature, the topology will also change, resulting in multiple topologies, i.e. L δ where, is time-varying, is the total number of topologies that may exist, Φ i , represent the upper limits of angle and angular velocity, respectively;

[0135] The above switching topologies satisfy three different random switching rules, as follows:

[0136] The Markov switching rule has a transition matrix with completely known probability and meets the following process:

[0137]

[0138] where π δr ≥ 0, δ ≠ r, is a known constant representing the probability of transitioning from mode δ to mode r, In addition, o represents an infinitesimal operator.

[0139] The semi-Markov switching rule has a transition matrix with partially unknown probability Its switching rule satisfies the above process:

[0140] The semi-Markov switching rule is subject to the following constraint rule:

[0141]

[0142] where π δr (Δt) is a time-varying transition probability.

[0143] The minimum velocity norm is taken as the objective function, and a quadratic programming problem is constructed as a constraint condition for the cooperative control problem of a multi-redundancy robot arm system:

[0144]

[0145] where, denotes the derivative of the workspace;

[0146] The above formula can be written as:

[0147]

[0148] where is the joint angle and angular velocity constraint.

[0149] represents the derivative of Z;

[0150] To solve the quadratic programming problem (9), let the Lagrangian function be:

[0151]

[0152] where χ(t) and φ(t) are Lagrange multiplier vectors.

[0153] The Karush-Kuhn-Tucker condition in the above equation can be written as:

[0154]

[0155] Combined with the nonlinear complementarity problem, equation (11) can be written as:

[0156]

[0157] in, is the Fischer-Burmeister function, is a scalar close to 0, is the Hadamard product operator symbol, and p represents the parameter of the inequality constraint in the above formula;

[0158] At this point, based on the three random switching topologies, the cooperative motion control problem of the multi-redundant manipulator system is transformed into the solution of the time-varying equation (12), as follows: Figure 2 As shown, the communication structure of the multi-manipulator switches among three topologies, in which only the robot R1 knows the desired trajectory, and the other robots follow the robot R1 to achieve collaborative operation;

[0159] S3: Design an adaptive switching time-varying neural network to solve the time-varying problem in step S2 and obtain the real-time angle parameters of each joint in the multi-redundant robotic arm system. The specific calculation steps are as follows:

[0160] Define the error function:

[0161]

[0162] Taking the derivative of the error function, we get

[0163]

[0164] in Represents Hadamard division.

[0165] According to the neurodynamic design method and combined with the time-varying characteristics of the system, the adaptive switching neurodynamic design formula with error information is constructed as follows:

[0166]

[0167] wherein λ is a parameter to adjust the convergence speed, and F(·) is an activation function, which can be any common monotonically increasing odd function, such as linear-type, sigmoid-type, power-type or power-sigmoid-type, etc.

[0168] According to equations (13)-(15), the implicit dynamic equation used by the adaptive switching neural network model can be expressed as:

[0169]

[0170] wherein

[0171]

[0172]

[0173]

[0174] As shown in Figure 3 , the collaborative motion effect of the multi-redundant manipulator based on the adaptive switching time-varying neural network is obtained, which shows the collaborative motion of 5 manipulators in different initial states to achieve a 6-point star trajectory;

[0175] S4: input the angle calculated in step S3 into the manipulator motion control system, so that the end effector of the multi-redundant manipulator system moves according to the expected trajectory, and the manipulators keep collaborative.

[0176] As shown in Figure 4 , the collaborative position error between the manipulators in the three-dimensional space is obtained, and it can be seen that the collaborative error between the manipulators is kept in a very small range.

[0177] The above embodiments are the preferred embodiments of the present application, but the embodiments of the present application are not limited by the above embodiments, and any changes, modifications, substitutions, combinations, simplifications made without departing from the spirit and principles of the present application should be equivalent replacement methods, which are all included in the protection scope of the present application.

Claims

1. A method for cooperative motion planning control of multi-redundant manipulators, characterized in that, The method comprises the following steps: A multi-redundancy robot arm system model is constructed, and a coupling relationship between joint positions, velocities and physical limits of the multi-redundancy robot arm is established; The multi-redundancy robot arm system model is constructed in particular as follows: The motion trajectory of the ithredundancy robot arm is expressed as: g i (Φ i (t))=z e (t),i∈1,2,...,M wherein z e ∈R m denotes the desired motion trajectory of the robot arm, m denotes the degrees of freedom of the robot arm end effector workspace, g i (·)∈R n →R m denotes the unique mapping relationship from the joint angle of the robot arm to the end effector, n denotes the degrees of freedom of the robot arm, and M denotes the total number of robot arms; A kinematics equation at a joint velocity level is constructed and expressed as: wherein, is the ithredundant manipulator Jacobian matrix, and are joint and end-effector velocities, respectively. The kinematics equation at the joint velocity level is converted into a matrix form and expressed as: wherein, denotes the joint angles to be solved, B = diag[b1, b2,..., b M ], b i = 0 and b i = 1 respectively indicate whether the i-th redundant manipulator can directly receive the desired trajectory, Upper limits of joint angles and angular velocities are set as: wherein, and are upper and lower bounds for the joint angle and angular velocity, respectively; A velocity layer constraint is expressed as: wherein is a parameter of the joint angle; A boundary constraint is expressed as: The matrix form is: wherein A multi-redundancy robot arm system is modeled based on multiple random switching topological structures for a cooperative motion control problem, and is converted into a time-varying equation, wherein the random switching topological structures satisfy corresponding random switching rules, including a semi-Markov process, a Markov process with a completely known transition probability matrix and a partially unknown transition probability matrix; An adaptive switching time-varying neural network is constructed to solve the time-varying equation, and real-time angle parameters of each joint in the multi-redundancy robot arm system are obtained. The calculated real-time angle parameters are input into a robot arm motion control system, so that an end effector of the multi-redundancy robot arm system moves according to an expected trajectory, and each robot arm maintains cooperation.

2. The method of claim 1, wherein, A multi-redundancy robot arm system is modeled based on multiple random switching topological structures for a cooperative motion control problem, and is converted into a time-varying equation, in particular as follows: A coupling relationship of the multi-redundancy robot arm system at a position level is constructed as: wherein z ij represents the fixed distance between the ith robot arm and the jth robot arm, a ij > 0 indicates that the robot arm j receives information from the robot arm i, a ij = 0 indicates that the robot arm j and the robot arm i cannot communicate, i, j = 1, 2, …, M; A coupling relationship of the multi-redundancy robot arm system at a velocity level is constructed as: The matrix form of the multi-redundancy robot arm system at the position level and the velocity level is expressed as: where L = D - A is the Laplacian matrix, representing the communication connection topological relationship between the manipulators, A = [a ij ]∈R M×M , D = diag{A1, A2,..., A M}, L δ represents the topological structure, is time-varying, is the total number of topological structures that may exist, and m is the degree of freedom of the manipulator workspace; A quadratic programming problem is constructed with a minimum velocity norm as an objective function and the cooperative control problem of the multi-redundancy robot arm system as a constraint condition as: A Lagrange function is set for solving the quadratic programming problem as: where χ(t) and φ(t) are Lagrange multipliers vectors, are joint angle and angular velocity constraints; A Karush-Kuhn-Tucker condition thereof is expressed as: In combination with a non-linear complementary problem, the Karush-Kuhn-Tucker condition is converted into a time-varying equation and expressed as: wherein is the Fischer-Burmeister function, is a scalar close to 0, is the Hadamard product operator. The cooperative motion control problem of the multi-redundancy robot arm system is converted into a solution of the time-varying equation.

3. The method of claim 2, wherein, The random switching topological structures satisfy corresponding random switching rules, including a semi-Markov process, a Markov process with a completely known transition probability matrix and a partially unknown transition probability matrix, and are specifically expressed as: The Markov switching rule has a transition matrix whose probabilities are completely known and conforms to the following procedure: wherein, π δr δ≠r respectively represent the probability of transition from mode δ to mode r, Δt > 0, o denotes an infinitesimal operator; Markov switching rules with a transition matrix whose probability part is unknown The semi-Markov switching rule is subject to the following constraint rules: where π δr (Δt) is the time-varying transition probability.

4. The method of claim 3, wherein, An adaptive switching time-varying neural network is constructed to solve the time-varying equation, and real-time angle parameters of each joint in the multi-redundancy robot arm system are obtained, in particular as follows: An error function is defined as: Derivation of the error function is as follows: wherein denotes the Hadamard division; An adaptive switching neural dynamic design formula with error information is constructed according to a neural dynamic design method in combination with time-varying characteristics of the system as: Wherein, λ is a parameter for adjusting a convergence speed, and F(·) is an activation function. An implicit dynamic equation used by the adaptive switching time-varying neural network is expressed as:

5. The method of claim 4, wherein, The activation function adopts a monotonically increasing odd function.

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