A multi-arm distributed collaborative control method based on recurrent neural network

Abstract

The application discloses a kind of based on recursive neural network multi-mobile arm cooperative control method, its method includes the following steps: a. the hardware parameter of mobile manipulator's moving platform and mechanical arm is measured;B. according to the demand design multiple mobile manipulator cooperative movement desired trajectory function;C. based on D-H parameter method and mobile manipulator overall model, the kinematics equation of mechanical arm end effector about world coordinate system is obtained;D. for multiple mobile manipulator cooperative control problem, a distributed communication scheme is used, and a quadratic programming problem with repetitive motion as objective function and distributed cooperative control as equality constraint is constructed;E. recursive neural network is proposed to solve the quadratic programming problem of multiple mobile manipulator cooperative control with noise disturbance.The application uses the distributed scheme for repetitive motion, can be under the condition that each mobile manipulator is limited between each other Communication, cooperative movement is completed given main task, and reaches optimum under repetitive motion optimization index.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of mobile robots, in particular to a multi-mobile manipulator distributed cooperative control algorithm based on distributed communication and recurrent neural network. BACKGROUND

[0002] Currently, there are mainly three kinds of coordination schemes for the mobile platform and manipulator of the mobile manipulator: the first kind is to consider two subsystems separately for individual planning; the second kind is to regard the motion planning of two subsystems as two optimization problems, and to obtain approximate optimal solutions by separately optimizing two problems with different cost functions to solve the problems; and the third kind is to comprehensively consider the mobile platform and the manipulator as a whole. Among them, the third kind of coordination scheme adds the degrees of freedom of the mobile platform to the system of the manipulator, and plans the motion of the manipulator and the mobile platform as a comprehensive redundant system, which is more easy to realize the cooperative control of the two subsystems to complete the task. Multiple mobile manipulators can complete the work that a single manipulator cannot complete, and make up for the performance deficiency of a single manipulator.

[0003] Multiple mobile manipulators have been widely used in industrial manufacturing, defense equipment processing and other fields, and play a very big role in major equipment. The biggest difference between multiple mobile manipulators and single manipulators is group learning, and the biggest challenge it faces is communication. The first aspect is how to cooperatively perceive; the second aspect is how to cooperatively plan; and the third aspect is how to form a better cooperative control system. Therefore, the present application establishes the kinematic model of the mobile platform and the manipulator, integrates them through spatial coordinate transformation, obtains the position of the end effector in the world coordinate system, and proposes a multi-mobile manipulator distributed cooperative control scheme based on recurrent neural network, to realize the cooperative control of multiple mobile manipulators to complete the specified task. SUMMARY

[0004] The present application discloses a multi-mobile arm distributed cooperative control method based on recurrent neural network, which uses recurrent neural network to solve the cooperative control strategy in real time.

[0005] The present application is implemented by the following technical solutions:

[0006] A multi-mobile arm distributed cooperative control method based on recurrent neural network, the control method is as follows:

[0007] S1: measuring the hardware parameters of the mobile platform and the manipulator of the mobile manipulator;

[0008] S2: designing the expected trajectory function of the cooperative motion of multiple mobile manipulators according to the requirements;

[0009] S3: Obtain the kinematics equation of the end effector of the mechanical arm in the base coordinate system by the D-H parameter method, analyze the motion characteristics of the Mecanum wheel to establish the kinematics equation of the mobile platform, and combine the mobile platform and the mechanical arm model to obtain the kinematics equation of the end effector in the world coordinate system;

[0010] S4: Real-time position information is transmitted between adjacent mobile manipulators in the group by using a distributed communication scheme, and a repetitive motion optimization index is further introduced, so that the objective function of repetitive motion and the equality constraint of distributed collaborative control are converted into a quadratic programming problem;

[0011] S5: A neural dynamics controller for collaborative control of all mobile manipulators in the group is constructed by combining the distributed collaborative control scheme for repetitive motion with the recurrent neural network model, and the multiple mobile manipulators are controlled to collaboratively move to complete the specified task.

[0012] Compared with the prior art, the advantages of the present application are:

[0013] The present application establishes the kinematics model of the whole mobile manipulator, transmits the position information for collaborative control between adjacent mobile manipulators in the group by using a distributed communication scheme, introduces a repetitive motion optimization index, and converts the objective function of repetitive motion and the equality constraint of distributed collaborative control into a quadratic programming scheme. The characteristics are as follows: first, the control scheme of the traditional mobile manipulator needs to establish the dynamic model of the system, and complex dynamic analysis needs to be performed on the mobile platform and the mechanical arm two subsystems respectively. However, the kinematics models of the two subsystems are integrated into one by space coordinate transformation in the present application, the kinematics model of the whole is obtained, and the collaborative control of the mobile manipulator is realized; second, the communication topology of the multiple mobile manipulators in the present application adopts a distributed scheme, mainly relies on communication between adjacent mobile manipulators, and is a limited communication scheme without a unified superior communication control center. Therefore, the distributed communication scheme greatly reduces the overall communication burden, and the work can be well completed even when some mobile manipulators fail to communicate; third, a recurrent neural network control algorithm is designed in the present application to solve the distributed collaborative control problem of multiple mobile manipulators. BRIEF DESCRIPTION OF DRAWINGS

[0014] Figure 1 An image for tracking the trajectory of the end effector of the multiple mobile manipulators controlled based on the recurrent neural network model according to the present application;

[0015] Figure 2 A top view for tracking the desired trajectory of the end effector of the multiple mobile manipulators controlled based on the recurrent neural network model according to the present application;

[0016] Figure 3 An error image for tracking the desired trajectory of the end effector of the multiple mobile manipulators controlled based on the recurrent neural network model according to the present application;

[0017] Figure 4 an error rate of change image of the multi-mobile manipulator end effector tracking the desired trajectory based on the recursive neural network model described in the present application;

[0018] Figure 5 an angle change image of each joint angle of the multi-mobile manipulator end effector tracking the desired trajectory based on the recursive neural network model described in the present application;

[0019] Figure 6 an angular velocity change image of each joint angle of the multi-mobile manipulator end effector tracking the desired trajectory based on the recursive neural network model described in the present application;

[0020] Figure 7 an angle change image of each wheel rotation angle of the multi-mobile manipulator end effector tracking the desired trajectory based on the recursive neural network model described in the present application;

[0021] Figure 8 an angular velocity change image of each wheel angle of the multi-mobile manipulator end effector tracking the desired trajectory based on the recursive neural network model described in the present application; DETAILED DESCRIPTION

[0022] The technical solutions in the embodiments of the present application will be apparently and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative labor fall within the scope of protection of the present application.

[0023] The present application discloses a multi-mobile manipulator distributed cooperative control method based on a recursive neural network. A whole kinematics equation of the mobile manipulator is established based on a world coordinate system, and a desired trajectory is designed within a workspace range of an end effector of the mobile manipulator. A distributed communication scheme is adopted to transmit position information in the system. A mobile manipulator at a command center directly receives desired trajectory information, and the remaining mobile manipulators acquire position information by communicating with adjacent mobile manipulators. A vector type error function is defined by a position difference value of the cooperative motion of adjacent mobile manipulators and a position difference value of the command center mobile manipulator and the desired trajectory. The smaller the absolute value of the error function is, the better the cooperative control effect is. A differential equation of the error function is constructed to satisfy an exponential convergence design formula Φ(·) represents an activation function, and a linear activation function Φ(ξ(t)) = ξ(t) is selected. A recursive neural network is used to solve the cooperative control strategy in real time.

[0024] The present application is implemented by the following technical solutions:

[0025] A multi-mobile-arm distributed cooperative control method based on a recurrent neural network, the control method being specifically as follows:

[0026] S1: measuring hardware parameters of a mobile platform and a mechanical arm of a mobile mechanical arm;

[0027] S2: designing a desired trajectory function of cooperative movement of multiple mobile mechanical arms according to requirements;

[0028] S3: obtaining a kinematics equation of an end effector of the mechanical arm in a base coordinate system through a D-H parameter method, analyzing movement characteristics of a Mecanum wheel to establish a kinematics equation of the mobile platform, and combining the mobile platform and the mechanical arm model to obtain a kinematics equation of the end effector in a world coordinate system;

[0029] S4: using a distributed communication scheme to transmit real-time position information between adjacent mobile mechanical arms in a group, further introducing a repetitive motion optimization index, and converting a target function of repetitive motion and an equality constraint of the distributed cooperative control into a quadratic programming problem;

[0030] S5: combining the repetitive motion-oriented distributed cooperative control scheme and a recurrent neural network model to construct a neural dynamics controller of cooperative control of all mobile mechanical arms in the group, and controlling cooperative movement of the multiple mobile mechanical arms to complete a specified task.

[0031] The specific process of step S1 is as follows:

[0032] A measurement tool is used to measure hardware parameters required in the modeling process, including the mobile platform height, the Mecanum wheel radius, the distance between the front and rear Mecanum wheel hub shaft centers, the distance between the left and right Mecanum wheel hub shaft centers, the mechanical arm link length, and the workspace range of the end effector of the mobile mechanical arm under the condition of power-off.

[0033] The specific process of step S2 is as follows:

[0034] According to the measurement data in step S1 and actual task requirements, a desired trajectory is designed to make the end effector of the mobile mechanical arm within the reachable space range. The mathematical expression of the desired trajectory is as follows:

[0035] r x = 0.2*cos(0.2*t)

[0036] r y = 0.2*sin(0.4*t)

[0037] r z = 0.4+0.05*sin(0.2*t)

[0038] r d = [r x ; ry z ]

[0039] The specific process of step S3 is as follows:

[0040] S301: When the working task described by the Cartesian space coordinates of step S2 is given, the space coordinates must be converted into a series of time-varying postures of the mechanical arm, that is, the joint angle size of the mechanical arm is solved through the kinematics equation. To obtain the kinematics equation of the end effector of the mechanical arm, the mechanical arm is regarded as a series of connecting rods connected by joints, a coordinate system is established for each connecting rod of the mechanical arm, the relative positions and postures between the coordinate systems are described by homogeneous transformation, and the position of the end effector of the mechanical arm in the base coordinate system is obtained. The homogeneous transformation formula between the connecting rods is as follows:

[0041] i-1 i = Rot(x, a i-1 ) Trans(x, a i-1 ) Rot(z, ψ i ) Trans(z, d i )

[0042] The expansion is as follows:

[0043]

[0044] The above formula represents the homogeneous transformation of the connecting rod coordinate system {i} relative to {i-1} as i-1 i , by solving the torsion angle a i-1 , the connecting rod length a i-1 , the connecting rod offset d i , and the joint angle ψ i of each connecting rod coordinate system, and substituting the D-H parameter table, the homogeneous transformation matrix of each connecting rod can be obtained. Taking a four-degree-of-freedom mechanical arm as an example, the homogeneous transformation matrices are multiplied in sequence to obtain the coordinate transformation relationship of the origin of the coordinate system of the end effector of the mechanical arm relative to the base coordinate system {0} as follows:

[0045] 0 0 1 2 3

[0046] The position equation of the end effector of the mechanical arm in the base coordinate system {0} obtained by coordinate transformation is as follows:

[0047]

[0048] ​​​​​​​​Wherein, l1, l2, l3, l4 are the length of the connecting rod 1, connecting rod 2, connecting rod 3, connecting rod 4 respectively; c1 = cos(ψ1), s1 = sin(ψ1), c 23 = cos(ψ2+ψ3), s 23 = sin(ψ2+ψ3).

[0049] S302: The mobile platform wheel adopts a Mecanum wheel that can realize omnidirectional movement, and power is output in a four-wheel all-drive manner. The motion of the mobile platform can be described by three independent variables: X-axis translation, Y-axis translation, and yaw-axis rotation. The inverse kinematics model of the mobile platform is calculated according to the motion state of the chassis to obtain the speed of the four Mecanum wheels. The forward kinematics model equation group can be obtained by inverse operation of the inverse kinematics model equation group as follows:

[0050]

[0051] In the formula, α represents the rotation angle of the omnidirectional mobile platform around the yaw axis, also called the yaw angle, and the counterclockwise direction is defined as positive; d x , d y represent the displacement distances of the geometric center of the omnidirectional mobile platform along the X-axis and the Y-axis, respectively, and are defined as positive along the positive direction of the X-axis and the Y-axis, respectively; r is the wheel radius of the Mecanum wheel; a and b represent half of the distance between the front and rear Mecanum wheel hub shafts and half of the distance between the left and right Mecanum wheel hub shafts, respectively; represents the rotation angle of the nth Mecanum wheel.

[0052] S303: Through the conversion matrix of the base coordinate system to the world coordinate system {0}, the overall kinematics equation of the mobile manipulator end effector with respect to the world coordinate system can be obtained as follows:

[0053]

[0054] Based on the kinematics characteristics of the mobile manipulator, the overall kinematics model of the end effector velocity level is constructed, and the specific mathematical expression is as follows:

[0055]

[0056] Wherein, J(θ(t)) is the Jacobian matrix of the overall kinematics model, is the differential of the actual position of the end effector of the mobile manipulator with respect to time t. is the differential of the angle variables of the four wheels of the mobile platform and the four joints of the manipulator with respect to time t.

[0057] The specific process of step S4 is as follows:

[0058] A distributed communication scheme is adopted in the system, all mobile manipulators in the system can complete the task under the limited communication condition between each other, the distributed communication scheme for the ith mobile manipulator in the group is designed as follows:

[0059]

[0060] In the formula, W(i) represents the neighborhood set of the ith mobile manipulator on the communication graph, W(0) represents the neighborhood set of the command center on the communication graph; T ij represents the connection weight between the ith and jth mobile manipulators; O i (t) is the actual position of the end effector r i (t) minus a constant distance vector between the end effector and the reference point; y i 1 for the mobile manipulator in the neighborhood set of the command center, otherwise 0; r d (t) is the desired path.

[0061] Rewrite the above formula into a compact form containing each mobile manipulator in the group, get the distributed communication scheme of the whole system, and write it in the form of the following error function:

[0062]

[0063] In the formula, is the Laplace matrix, L = diag(T1 p )-T; The ijth element of T ij ; is the Kronecker product operator of matrix; is a p-dimensional column vector with all elements being 1, and p is the number of mobile manipulators in the system; is a p-dimensional square matrix, its element H ij = 1, if and only if i = j and i ∈ W(0), otherwise H ij = 0; is an n-dimensional unit matrix, n is the dimension of the workspace of the mobile manipulator; The superscript “ T ” is the transpose operation of the matrix.

[0064] The formula is designed by using recurrent neural dynamics, where γ > 0, the error function is substituted into the above formula to get the equality constraint of the distributed cooperative control as follows:

[0065]

[0066] In the formula, m is the number of wheels of the mobile platform of the mobile manipulator and the joint angle of the manipulator; is the differential with respect to time t; is a compound diagonal matrix containing Jacobian matrices of p mobile manipulators in the system. The equality constraint is equivalent to i (t) = r d (t); i = 1,..., p, that is, each mobile manipulator in the system can receive the desired trajectory information from the command center.

[0067] The repetitive motion optimization index is introduced, and the objective function containing the repetitive motion optimization index and the equality constraint of the distributed collaborative control are converted into the following quadratic programming.

[0068]

[0069] where θ i (0) is the initial value of the chassis wheel and the joint angle of the manipulator of the i-th mobile manipulator.

[0070] The specific process of step S5 is as follows:

[0071] The Lagrange function is constructed to convert the time-varying quadratic programming problem with equality constraints into the extreme value problem of the Lagrange function, and the Karush-Kuhn-Tucker condition is used to obtain the following equation:

[0072] υ(t)x(t) = η(t)

[0073] where

[0074] According to the recursive neural network model design formula, the vector-valued error function of the system is defined as follows:

[0075] ζ(t) = υ(t)x(t) - η(t)

[0076] In order to make ζ(t) approach 0 over time, the recursive neural dynamics design formula is used to construct the neural dynamics equation of the multi-mobile manipulator collaborative control with noise interference term, and the mathematical expression is as follows:

[0077]

[0078] where, are the differentials of x(t), υ(t), and η(t) with respect to time t, is the state variable to be solved; represents the vector form noise caused by communication noise, calculation error, disturbance, or their superposition. Under the control of the model, the multi-mobile manipulator can cooperatively move to complete the specified task.

[0079] The angles of the wheels of the mobile platform and the angles of the joints of the arms are solved by the above kinematic equations, and the solutions are applied to the motors to adjust the variables. Figure 1 、 Figure 2 Fig. 8 shows the three-dimensional view and the top view of the trajectories of the end effectors of the eight mobile arms in cooperative motion, Figure 3 Fig. 9 shows the position error of the trajectory tracking of the end effectors of each mobile arm, and the simulation results show that the multiple mobile arms complete the cooperative repetitive motion task with a very small error. Figure 5 、 Figure 7 Fig. 10 shows the angle changes of the wheels of the mobile platform and the angles of the joints of the arms, and the results show that each angle returns to the desired initial value. That is, under the control of the distributed model based on the recurrent neural network, the trajectories and postures of the end effectors of the multiple mobile arms meet the requirements of cooperative control.

[0080] Although the embodiments of the present application have been shown and described, it is to be understood that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the present application, and the scope of the present application is defined by the appended claims and their equivalents.

Claims

1. A distributed cooperative control method for multiple moving arms based on recurrent neural networks, characterized in that, The control method steps are as follows: S1: Measure the hardware parameters of the mobile platform and the robotic arm of the mobile robotic arm; S2: Design the desired trajectory function for the coordinated motion of multiple mobile robotic arms according to requirements; S3: Obtain the kinematic equations of the end effector of the robotic arm in the base coordinate system through the DH parameter method, analyze the motion characteristics of the Mecanum wheel to establish the kinematic equations of the mobile platform, and combine the mobile platform and robotic arm models to obtain the kinematic equations of the end effector in the world coordinate system. S4: A distributed communication scheme is adopted to transmit real-time position information between adjacent mobile robotic arms within the group. A repetitive motion optimization index is introduced, transforming the objective function of the repetitive motion and the equality constraints of the distributed cooperative control into a quadratic programming problem; the expression for the quadratic programming problem is: In the formula, m is the number of wheels and joint angles of the mobile robotic arm platform; yes Differentiate with respect to time t; θ i (0) is the initial value of the chassis wheel and the joint angle of the i-th moving robotic arm; It is the Laplace matrix, L = diag(T1) p -T; the ij-th element of T is T ij ;T ij This represents the connection weight between the i-th and j-th mobile robotic arms; It is a p-dimensional square matrix with elements H ij =1, if and only if i = j and i ∈ W(0), otherwise H ij =0; It is the Kronecker product operator for matrices; It is an n-dimensional identity matrix, where n is the workspace dimension of the mobile robotic arm; It is a composite diagonal matrix containing the Jacobian matrices corresponding to the p mobile robotic arms in the system; It is a p-dimensional column vector with all elements equal to 1, where p is the number of mobile robotic arms in the system; r d (t) represents the desired path; convergence parameter γ>0; O i (t) represents the actual position r of the end effector. i (t) minus a constant distance vector between the end effector and the reference point; superscript T " is the matrix transpose operation; S5: Combining a distributed cooperative control scheme for repetitive motion with a recurrent neural network model, a neurodynamic controller is constructed to coordinate the control of all mobile robotic arms within a group, controlling the coordinated movement of multiple mobile robotic arms to complete a specified task; wherein, the neurodynamic controller uses 10 -5 The system completes collaborative repetitive motion tasks with an error of orders of magnitude. After the task is completed, the various angles of the wheels of the mobile platform and the joints of the robotic arm return to the expected initial values, thus realizing the collaborative control of the trajectory and attitude of the ends of multiple mobile arms.

2. The distributed cooperative control method for multiple moving arms based on recurrent neural networks as described in claim 1, characterized in that, The specific process of step S3 is as follows: Based on the kinematic characteristics of the mobile robotic arm, a global kinematic model of its end effector speed level is constructed, and the specific mathematical expression is as follows: Where J(θ(t)) is the Jacobian matrix of the overall kinematic model. Let be the derivative of the actual position of the end effector of the mobile robotic arm with respect to time t. It is the derivative of the angle variables of the four wheels of the mobile platform and the four joints of the robotic arm with respect to time t.

3. The distributed cooperative control method for multiple moving arms based on recurrent neural networks as described in claim 1, characterized in that, The specific process of step S4 is as follows: A distributed communication scheme is adopted within the system, enabling all mobile robotic arms within the system to complete tasks under limited communication conditions. The distributed communication scheme design for the i-th mobile robotic arm in the group is as follows: Where W(i) represents the neighborhood set of the i-th mobile robotic arm on the communication graph, and T ij O represents the connection weight between the i-th and j-th mobile robotic arms; i (t) represents the actual position r of the end effector. i (t) minus a constant distance vector between the end effector and the reference point; y i The value is 1 for mobile robotic arms within the command center's neighborhood set, and 0 otherwise; d (t) represents the desired path; Rewriting the above equation into a compact form that includes each mobile robotic arm within the group yields the overall distributed communication scheme for the system, which can be expressed as the following error function: In the formula It is the Laplace matrix, L = diag(T1) p -T; the ij-th element of T is T ij ; It is the Kronecker product operator for matrices; It is a p-dimensional column vector with all elements being 1, where p is the number of moving robotic arms in the system; It is an n-dimensional identity matrix, where n is the workspace dimension of the mobile robotic arm; superscript T " is the matrix transpose operation; It is a p-dimensional square matrix with elements H ij =1, if and only if i = j and i ∈ W(0), otherwise H ij =0; Using recursive neurodynamic design formula Where γ>0, substituting the error function in the above equation yields the following equality constraints for distributed collaborative control: In the formula m is the number of wheels and joint angles of the mobile robotic arm platform; yes Differentiate with respect to time t; It is a composite diagonal matrix containing the Jacobian matrices corresponding to the p mobile robotic arms in the system; this equality constraint is equivalent to O. i (t)=r d (t); i = 1,...,p, meaning that each mobile robotic arm in the system can receive the desired trajectory information from the command center.

4. The distributed cooperative control method for multiple moving arms based on recurrent neural networks as described in claim 1, characterized in that... The specific process of step S5 is as follows: By constructing the Lagrangian function, solving the time-varying quadratic programming problem with equality constraints is transformed into solving the extremum problem of the Lagrangian function. Using the Karush-Kuhn-Tucker conditions, the following equation is obtained: υ(t)x(t)=η(t) In the formula Based on the recurrent neural network model design formula, the system's vector value error function is defined as follows: ζ(t)=υ(t)x(t)-η(t) To make ζ(t) approach 0 over time, a recursive neurodynamic design formula is used to construct the neurodynamic equation for the collaborative control of multiple moving robotic arms with noise interference terms. The mathematical expression is as follows: In the formula, Let x(t), υ(t), and η(t) be the derivatives of x(t), υ(t), and η(t) with respect to time t, respectively. Let these be the state variables to be solved; This represents vector noise caused by communication noise, computational errors, disturbances, or their superposition; under the control of this model, multiple mobile robotic arms can work together to complete a specified task.

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