A noise-resistant neural network trajectory tracking control with joint angle constraints for a mobile arm

Abstract

The present invention discloses a noise-resistant neural network trajectory tracking control method for a mobile arm with joint angle constraints. The method relates to the field of mobile robots, and in particular to a trajectory tracking control method for a mobile manipulator based on kinematics, joint angle constraints, and a noise-resistant zeroing neural network. The method comprises the following steps: collecting initial angle data and movable angle range of the wheels and arm of the mobile manipulator; designing the desired trajectory to be tracked by the mobile manipulator; establishing an overall kinematic model based on the kinematic characteristics of the mobile manipulator; establishing joint angle inequality constraints and converting them into equality constraints; defining a vector error function for the trajectory tracking problem; and constructing a noise-resistant zeroing neural network controller by combining the kinematic model of the mobile manipulator, the angle constraints, and the noise-resistant zeroing neural network. The method solves the dynamic equations of the noise-resistant zeroing neural network to solve the trajectory tracking problem of a mobile manipulator with joint angle constraints under noise disturbances.

Description

Technical Field

[0001] The present invention relates to the field of mobile robots, and in particular to a trajectory tracking control method for a mobile robot arm based on kinematics, joint angle constraints and a noise-resistant return-to-zero neural network. Background Art

[0002] To promote a new round of industrial upgrading, it is necessary to vigorously promote the development of the manufacturing industry, of which intelligent manufacturing projects are a key component. To achieve the goal of industrial intelligence, the development and application of mobile robotic arms are particularly important. Current research on trajectory tracking control is largely based on experiments conducted under ideal conditions. Under non-ideal conditions, the operation of mobile robotic arms inevitably involves internal and external interference factors, which can affect trajectory tracking performance. Summary of the Invention

[0003] In view of the shortcomings of the existing technology, the present invention discloses a noise-resistant neural network trajectory tracking control method with joint angle constraints of a mobile arm, which uses a noise-resistant zeroing neural network to solve the trajectory tracking control strategy.

[0004] The present invention is achieved through the following technical solutions:

[0005] A noise-resistant neural network trajectory tracking control method for mobile arm joint angle constraints, the control method is specifically as follows:

[0006] S1: Collect the initial angles of the four-degree-of-freedom manipulator joints, the initial angles of the four wheels of the omnidirectional mobile platform, the movable angle range of the manipulator joints, and the movable angle range of the wheels;

[0007] S2: Design the desired trajectory equation for the mobile manipulator;

[0008] S3: The kinematic equations of the four-degree-of-freedom manipulator in the base coordinate system are obtained through spatial coordinate transformation. The kinematic equations of the omnidirectional mobile platform are obtained based on the motion characteristics of the Mecanum wheel. The kinematic equations of the manipulator are combined with the kinematic equations of the omnidirectional mobile platform. The overall kinematic equations of the mobile manipulator in the world coordinate system are obtained through coordinate transformation.

[0009] S4: Design joint angle inequality constraints based on the joint constraint range of step S1, and convert the inequality constraints into equality constraints by adding time-varying non-negative vectors.

[0010] S5: Design a vector error function as the difference between the desired trajectory and the overall kinematic equation of the mobile manipulator, and construct a noise-resistant return-to-zero neural network controller by combining the error function, the equality constraint in step S4, and the noise-resistant return-to-zero neural network model;

[0011] S6: Based on the noise-resistant return-to-zero neural network controller in step S5, the noise-resistant return-to-zero neural network dynamic equation is solved to solve the trajectory tracking problem of the mobile robotic arm.

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

[0013] This invention establishes an overall kinematic model for a mobile manipulator. By adding a time-varying nonnegative vector, it converts joint angle inequality constraints into equality constraints, and introduces an integral term to eliminate noise. The following are some key features of this method: First, while traditional mobile manipulator control requires establishing a system dynamics model and separately controlling the omnidirectional mobile platform and each joint of the manipulator, this invention avoids complex dynamics modeling by separately modeling the omnidirectional mobile platform and the four-degree-of-freedom manipulator. Through spatial coordinate transformation, the two are integrated into a single system, achieving coordinated control of the mobile manipulator. Second, this invention constructs joint angle inequality constraints and converts them into equality constraints, adding them to the system. Adding these inequality constraints to the system allows the joints of the mobile manipulator to move within a certain range. Compared to adding fixed-value equality constraints, inequality constraints increase the range of motion of the mobile manipulator. Compared to not adding joint constraints, inequality constraints ensure that the output value is within the reachable range of the mobile manipulator's joints, enabling better trajectory tracking. Third, this invention designs a noise-resistant return-to-zero neural network control algorithm to solve the trajectory tracking problem of the mobile manipulator, addressing the control of the mobile manipulator in the presence of external noise interference. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 Schematic diagram of the noise-resistant return-to-zero neural network model for suppressing external time-varying disturbances according to the present invention;

[0015] Figure 2 An image of the end effector tracking the desired trajectory of the noise-resistant neural network under the joint angle constraint of the mobile arm described in the present invention;

[0016] Figure 3 A top view of the end effector of the noise-resistant neural network tracking the desired trajectory under the joint angle constraint of the mobile arm according to the present invention;

[0017] Figure 4 The error image of the end effector tracking the desired trajectory of the noise-resistant neural network under the joint angle constraint of the mobile arm described in the present invention;

[0018] Figure 5 An image of the error change rate of the end effector tracking the desired trajectory of the anti-noise neural network under the joint angle constraint of the mobile arm described in the present invention;

[0019] Figure 6An image of the change in joint angles of each manipulator arm when the end effector of the anti-noise neural network tracks a desired trajectory under the joint angle constraint of the mobile arm as described in the present invention;

[0020] Figure 7 An image of the angular velocity changes of each manipulator arm joint when the end effector of the anti-noise neural network tracks a desired trajectory under the joint angle constraint of the mobile arm as described in the present invention;

[0021] Figure 8 An image of the angle changes of each wheel of the end effector tracking the desired trajectory of the anti-noise neural network under the joint angle constraint of the mobile arm described in the present invention;

[0022] Figure 9 An image of the angular velocity changes of each wheel of the end effector of the anti-noise neural network tracking the desired trajectory under the joint angle constraint of the mobile arm described in the present invention; DETAILED DESCRIPTION

[0023] The following is a clear and complete description of the technical solutions in the embodiments of the present invention, in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts are within the scope of protection of the present invention.

[0024] The embodiment of the present invention discloses a noise-resistant neural network trajectory tracking control method for mobile arm joint angle constraints. The mobile manipulator consists of a four-degree-of-freedom manipulator and an omnidirectional mobile platform. The overall kinematic equation of the mobile manipulator is established based on the world coordinate system, and the angle constraints of the manipulator and wheel joints are constructed as inequality constraints. The inequality constraints are converted into equality constraints by introducing a time-varying non-negative vector κ(t). The expected trajectory is designed within the reachable space of the mobile manipulator, and a vector error function is defined based on the difference between the expected trajectory function and the actual motion trajectory function. The smaller the absolute value of the error function, the better the trajectory tracking effect. The differential equation for constructing the error function satisfies the convergence design formula Φ(·) represents the activation function, and the trajectory tracking control strategy is solved using a noise-resistant zeroing neural network.

[0025] The present invention is achieved through the following technical solutions:

[0026] A noise-resistant neural network trajectory tracking control method for mobile arm joint angle constraints, the control method is specifically as follows:

[0027] S1: Collect the initial angles of the four-degree-of-freedom manipulator joints, the initial angles of the four wheels of the omnidirectional mobile platform, the movable angle range of the manipulator joints, and the movable angle range of the wheels;

[0028] S2: Design the desired trajectory equation for the mobile manipulator;

[0029] S3: The kinematic equations of the four-degree-of-freedom manipulator in the base coordinate system are obtained through spatial coordinate transformation. The kinematic equations of the omnidirectional mobile platform are obtained based on the kinematic characteristics of the Mecanum wheel. The kinematic equations of the manipulator and the omnidirectional mobile platform are combined to obtain the overall kinematic equations of the mobile manipulator in the world coordinate system through coordinate transformation.

[0030] S4: Design joint angle inequality constraints based on the joint constraint range of step S1, and convert the inequality constraints into equality constraints by adding time-varying non-negative vectors.

[0031] S5: Design a vector error function as the difference between the desired trajectory and the overall kinematic equation of the mobile manipulator, and construct a noise-resistant return-to-zero neural network controller by combining the error function, the equality constraints in step S4, and the noise-resistant return-to-zero neural network model;

[0032] S6: Based on the noise-resistant return-to-zero neural network controller in step S5, the noise-resistant return-to-zero neural network dynamic equation is solved to solve the trajectory tracking problem of the mobile robot arm with joint angle constraints under noise interference.

[0033] The specific process of step S1 is:

[0034] The experiment requires reference to the hardware parameters of the mobile robot arm. Use a ruler to measure the length and width of the omnidirectional mobile platform, and measure the working range of each robot arm when the power is off. The parameters of each joint are as follows:

[0035] Axis 1 base Working range +15 to +180 Maximum speed 320 / s Axis 2 boom Working range +10 to +70 Maximum speed 320 / s Axis 3 arm Working range +15 to +60 Maximum speed 320 / s Axis 4 rotation Working range +90 to -90 Maximum speed 480 / s

[0036] The specific process of step S2 is:

[0037] Based on the measurement data in step S1, the desired trajectory of the end effector of the mobile robot arm is designed so that each joint of the mobile robot arm does not exceed the corresponding reachable angle range. The mathematical expression of the desired trajectory is as follows:

[0038]

[0039] r zd =0.4289

[0040] r d =[r xd ; r yd ; r zd ]

[0041] The specific process of step S3 is:

[0042] S301: To describe the relative position and orientation of the links of the mobile robot, a coordinate system needs to be established on each link based on the joint structure of the robot as follows:

[0043] i-1 T i =Rot(x,α i-1 )Trans(x,a i-1 )Rot(z,θ i )Trans(z,d i )

[0044] The DH method is used to establish the kinematic model of the robot arm, and the homogeneous transformation of the link coordinate system {i} relative to {i-1} i-1 T i It is called the connecting rod transformation, which involves the axis angle α i-1 , connecting rod length a i-1 , connecting rod offset d i , joint variables θ i , so it can be decomposed into a sub-transformation problem of coordinate system {i}, each sub-transformation depends on only one link parameter.

[0045] Transformation formula between connected links:

[0046]

[0047] The kinematic equation of the manipulator in the base coordinate system is obtained through coordinate transformation as follows:

[0048]

[0049] Where h1 is the length of connecting rod 1, h2 is the length of connecting rod 2, h3 is the length of connecting rod 3, and h4 is the length of connecting rod 4; c1 = cos(θ1), s1 = sin(θ1), c 23 =cos(θ2+θ3),s 23 =sin(θ2+θ3).

[0050] S302: The omnidirectional mobile platform uses Mecanum wheels as its drive wheels and adopts a four-wheel all-wheel drive mode for power output. The kinematics of the Mecanum wheel chassis of the omnidirectional mobile platform are decomposed into three independent variables: first, the speed of each wheel axis position is calculated, second, the speed of the roller where the wheel contacts the ground is calculated, and finally, the true rotational speed of the wheel is calculated. This results in the inverse kinematics equation of the omnidirectional mobile platform. After inverse solution, the forward kinematics equation of the omnidirectional mobile platform is obtained as follows:

[0051]

[0052] Where a represents the distance between the front and rear wheel midpoints, and b represents the distance between the front and rear wheel midpoints and the geometric center of the omnidirectional mobile platform. x It represents the displacement of the geometric center of the omnidirectional mobile platform along the X-axis, that is, the displacement in the left and right directions, with rightward displacement being positive; P y It represents the displacement of the geometric center of the omnidirectional mobile platform along the Y axis, that is, the displacement in the front-back direction, and the forward direction is defined as positive; ψ represents the rotation angle of the geometric center of the omnidirectional mobile platform along the yaw axis, and the counterclockwise direction is defined as positive. n (n=1, 2, 3, 4) represents the rotation angle of the nth wheel, and r represents the radius of each wheel.

[0053] S303: Through the transformation matrix from the base coordinate system to the world coordinate system, the overall kinematic equation of the mobile manipulator with respect to the world coordinate system can be obtained as follows:

[0054]

[0055] The specific process of step S4 is:

[0056] Based on step S1, the joint angle constraint inequality of the mobile manipulator is obtained as follows:

[0057] x - ≤x(t)≤x +

[0058] Among them, x(t) is the joint angle, x - 、x + are the lower and upper bounds of the joint angle constraints respectively. The above formula can be further simplified as:

[0059] Cx(t)≤d

[0060] Where C=[-I;I],d=[-x - ;x + By adding the time-varying non-negative vector κ(t), the inequality constraint is transformed into an equality constraint as follows:

[0061] Cx(t)+κ(t)=d

[0062]

[0063] Where n is the number of joint angles, is the adaptive variable, D(t)=diag{y1(t),y2(t),...,y 2n (t)}, is the transpose symbol. The joint angle constraint equation is:

[0064] Cx(t)+D(t)y(t)-d=0

[0065] The specific process of step S5 is:

[0066] In actual operation, the mobile manipulator is subject to various types of disturbances. In order to reduce the impact of disturbances and reduce the error during the operation of the mobile manipulator, the vector error function is defined based on the design formula of the noise-resistant zeroing neural network model:

[0067] f(x(t),t)=R w (t)-r f

[0068] Among them, R w (t) and r f They represent the desired trajectory and actual trajectory of the mobile manipulator, respectively. In order to obtain an accurate solution to the time-varying inverse kinematics, the differential equation of the error function must be constructed to converge to zero. Combined with the joint angle constraint equation, the noise-resistant zeroing neural network dynamics equation is obtained based on the convergence design formula as follows:

[0069]

[0070] Here, Φ(·) represents the activation function of the neural network. A simple linear activation function Φ(e(t)) = e(t) is chosen. δ>0 and μ>0 are adjustable parameters that can change the convergence speed of the system. The dynamic equation of the noise-resistant zeroing neural network with interference terms is constructed as follows:

[0071]

[0072] in, is the noise interference term. In the actual operation of a mobile robot, there are always external interferences that affect the normal operation of the robot, such as constant external force and transient attenuation external force.

[0073] Figure 1 (See attached figure) The composition and basic principles of neurodynamics are presented. A noise-resistant zeroing neural network algorithm based on time derivative information, neural network activation functions, and integral terms can effectively solve the time-varying inverse kinematics problem of a mobile robotic arm with external disturbances. This model can be viewed as a typical closed-loop control system in classical control theory, consisting of a generalized system of proportional, integral, and differential controllers.

[0074] The specific process of step S6 is:

[0075] By solving the noise-resistant zero-return neural network dynamic equation in step S5, the rotation angles of the omnidirectional mobile platform wheels and the rotation angles of each robotic arm joint are obtained during the mobile robotic arm's tracking of the desired trajectory. The obtained parameters are applied to each motor to enable the end effector of the mobile robotic arm to track the trajectory.

[0076] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A noise-resistant neural network trajectory tracking control method for mobile arm joint angle constraints, characterized in that: The control method steps are as follows: S1: Given the initial rotation angle of each wheel of the mobile robot and the initial angle of the four-degree-of-freedom robot, measure the movable angle range of the wheels and robot joints, and the length and width of the omnidirectional mobile platform; S2: Design the desired trajectory equation for the mobile manipulator; S3: Construct the overall kinematic model of the mobile manipulator; S4: Convert joint angle inequality constraints into equality constraints; S5: Combine the equality constraints of step S4, the overall kinematic model of the mobile manipulator, and the neural network model to construct a noise-resistant zeroing neural network controller. Complete the trajectory tracking task of the mobile robot arm, is the derivative of the error function, δ>0, μ>0 are adjustable parameters, is the noise considered in the system.

2. The noise-resistant neural network trajectory tracking control method for mobile arm joint angle constraint according to claim 1, characterized in that: The specific process of step S4 is as follows: According to step S1, the joint angle constraint inequality is: x - ≤x(t)≤x + Where x(t) is the joint angle, x - 、x + are the lower and upper bounds of the joint angle constraints respectively; the inequality constraints are written in matrix form as follows: Cx(t)≤d Where, C=[-I;I], d=[-x - ;x + ], I is the identity matrix; by adding the time-varying non-negative vector κ(t), the inequality constraint is transformed into an equality constraint: Cx(t)+D(t)y(t)-d=0 Where n is the number of joint angles, is the adaptive variable, D(t)=diag{y1(t),y2(t),...,y 2n (t)}, is the transpose symbol.

3. The noise-resistant neural network trajectory tracking control method for mobile arm joint angle constraint according to claim 1, characterized in that: The specific process of step S5 is as follows: Based on the kinematic characteristics of the mobile manipulator, a speed-level overall kinematic model of the mobile manipulator is constructed. The specific mathematical expression is as follows: Where M is the coefficient matrix of the overall kinematic model; The differential of the actual trajectory derived from the kinematic model with respect to time t; is the differential of the four wheels and four joint variables of the mobile robot with respect to time t; according to the design formula of the noise-resistant zero-return neural network model, the error function of the system is: f(x(t),t)=R w (t)-r f Among them, R w (t) and r f They represent the expected trajectory and actual trajectory of the mobile robot respectively; the overall error function is constructed by combining the joint angle constraint equation as follows: Based on the design formula of the noise-resistant return-to-zero neural network, the mathematical expression of the noise-resistant return-to-zero neural network dynamic equation is as follows: Among them, δ>0 and μ>0 are adjustable parameters. is the noise considered in the system.

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