Regularization method for singularity-avoiding control of mobile manipulators

Abstract

This invention discloses a regularized singularity avoidance control method for a mobile robotic arm, relating to the field of mobile robotic arm control technology. It includes: establishing a kinematic model of an omnidirectional redundant robotic arm; constructing trajectory tracking constraints for the end effector; constructing an operability index and its gradient term; constructing a regularized approximate null space projection matrix; constructing a regularized orthogonal operability maximization optimization problem; designing a non-convex projection function; designing a fuzzy adaptive pseudo-inverse recurrent neural network solver; and applying the generalized joint velocity control quantity output by the fuzzy adaptive pseudo-inverse recurrent neural network to the omnidirectional redundant robotic arm, enabling coordinated movement of the mobile platform and the robotic arm joints. This invention can achieve high-precision trajectory tracking and singularity avoidance while satisfying non-convex velocity constraints, balancing convergence speed, control smoothness, and computational efficiency.

Description

Technical Field

[0001] This invention relates to the field of mobile robotic arm control technology, and in particular to a regularized singularity avoidance control method for mobile robotic arms. Background Technology

[0002] The omnidirectional redundant robotic arm consists of an omnidirectional mobile platform and a redundant robotic arm. It combines the wide-range mobility of the mobile platform with the high dexterity of the redundant robotic arm, enabling it to perform large-scale, highly dexterous, and multi-constraint tasks in complex environments. Compared to a fixed-base robotic arm, the omnidirectional redundant robotic arm can expand its workspace and improve its task execution capabilities through coordinated movement between the mobile platform and the robotic arm. However, the increased redundancy also creates stronger coupling between trajectory tracking, singular configuration avoidance, joint speed limits, and actuator constraints.

[0003] In the control of omnidirectional redundant robotic arms, singularity avoidance is a key issue in ensuring system safety, stability, and operational flexibility. When the robotic arm approaches a singular configuration, the end effector's motion capability in certain directions significantly decreases, easily leading to sudden joint velocity changes, control oscillations, and reduced trajectory tracking accuracy. Maneuverability characterizes the degree to which the robotic arm configuration moves away from singular regions, and is therefore often used for redundant robotic arm configuration optimization and motion planning. By improving or maintaining maneuverability during task execution, the system's dexterity, singularity avoidance capability, and motion stability can be enhanced.

[0004] Existing operability optimization methods are mostly based on gradient projection, pseudo-inverse, or generalized inverse frameworks, mapping the end-effector task to joint space and utilizing redundant degrees of freedom to optimize the operability index. However, these methods still have the following shortcomings: First, operability is usually a nonlinear, non-convex function of the joint configuration, and direct optimization at the joint position level is prone to getting trapped in local extrema; Second, traditional gradient-based methods usually directly superimpose the operability gradient term into the joint velocity solution, which can easily lead to coupling between the operability optimization term and the end-effector position error adjustment, thereby limiting the trajectory tracking accuracy; Third, when approaching singular configurations, pseudo-inverse or generalized inverse operations are prone to numerical amplification, leading to sudden changes in joint velocity, system oscillations, or even solution stagnation.

[0005] Furthermore, the joint velocities, actuator operating modes, and physical limits in real-world omnidirectional redundant robotic arms often exhibit non-convex characteristics, making them difficult to accurately describe using simple convex constraints or linear velocity boundaries. While some existing neurodynamic solution methods can achieve online optimization, they often require the introduction of Lagrange multipliers, relaxation variables, or penalty functions when dealing with non-convex constraints, leading to increased problem dimensionality and computational burden. If explicit pseudo-inverse operations are still involved in the solution process, numerical instability near singular regions cannot be fundamentally avoided.

[0006] Meanwhile, the convergence performance of the neurodynamic model is significantly affected by the selection of parameters. Fixed parameters facilitate theoretical analysis, but when the end-effector tracking error is large, the error changes rapidly, or the system is close to steady state, fixed parameters cannot simultaneously take into account error convergence speed, control smoothness, and computational efficiency. Therefore, a singular configuration avoidance method for omnidirectional redundant manipulators is needed that can weaken the coupling between operability optimization and end-effector position error adjustment, avoid explicit pseudo-inverse calculations, adapt to non-convex velocity constraints, and adaptively adjust convergence parameters according to the tracking error state.

[0007] Therefore, proposing a regularized singularity avoidance control method for mobile robotic arms to solve the difficulties existing in the prior art is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0008] In view of this, the present invention provides a regularized singularity avoidance control method for mobile robotic arms, which weakens the coupling between operability optimization and end-effector position error adjustment, avoids numerical amplification caused by pseudo-inverse operations near singular regions, and can achieve high-precision trajectory tracking and singular configuration avoidance while satisfying non-convex velocity constraints, taking into account convergence speed, control smoothness and computational efficiency.

[0009] To achieve the above objectives, the present invention adopts the following technical solution: A method for regularized singularity avoidance control of a mobile robotic arm includes: S1. Obtain the joint states, end-effector desired trajectory, and desired velocity of the omnidirectional redundant manipulator. Unify the wheel system coordinates of the mobile platform and the joint angles of the manipulator to form generalized joint variables, and establish the kinematic model of the omnidirectional redundant manipulator. S2. Construct end effector trajectory tracking constraints; S3. Construct the operability index of the omnidirectional mobile redundant manipulator using the Jacobian matrix, and calculate the gradient vector of operability with respect to the generalized joint variables as the driving term for singular configuration avoidance and posture optimization. S4. Construct a regularized approximate null space projection matrix; S5. Apply the regularized approximate null space projection matrix to the gradient vector, and combine it with the non-convex feasible region obtained by modeling the end effector trajectory tracking constraints to construct a regularized orthogonal operability maximization optimization problem. S6. For the non-convex feasible region, construct a piecewise non-convex projection function to limit the generalized joint velocity within the preset non-convex feasible range. S7. Design a fuzzy adaptive pseudo-free inverse recurrent neural network solver; S8. Apply the generalized joint speed control quantity output by the fuzzy adaptive pseudo-inverse recurrent neural network to the omnidirectional mobile redundant manipulator to control the coordinated motion of the mobile platform and the manipulator joints, thereby achieving end effector trajectory tracking, operability maintenance and singular configuration avoidance.

[0010] Optionally, in the above method, in S1, a kinematic model of the omnidirectional redundant robotic arm is established, specifically as follows: Based on the geometric relationship of the omnidirectional mobile platform and the DH parameters of the robotic arm, a nonlinear kinematic mapping between the end effector pose and generalized joint variables is established, and the derivative of the nonlinear kinematic mapping is obtained to obtain the kinematic model at the velocity level.

[0011] Optionally, in S2 of the above method, the end effector trajectory tracking constraints are constructed as follows: Based on the desired trajectory and speed of the end effector of the omnidirectional redundant manipulator, a velocity-layer trajectory tracking equation constraint is established, which is satisfied by the Jacobian matrix of the omnidirectional redundant manipulator and the generalized joint speed, so that the end effector can track the preset desired trajectory.

[0012] Optionally, in S4 of the above method, a regularized approximate null space projection matrix is ​​constructed, specifically as follows: The regularization approximate null space projection matrix contains a regularization parameter, which is adaptively adjusted according to the magnitude of the operability index. When the operability index decreases, the regularization parameter increases.

[0013] Optionally, in S5, the above method involves constructing a regularized orthogonal operability maximization optimization problem, specifically: Apply the regularized approximate null space projection matrix to the operability gradient term, so that the operability optimization objective is embedded into the approximate orthogonal subspace of the task constraints; The joint velocity constraints of the omnidirectional redundant robotic arm are modeled as a non-convex feasible region, forming a regularized orthogonal operability maximization optimization problem that includes end-effector trajectory tracking equality constraints and non-convex velocity constraints.

[0014] The above method, optionally, constructs the non-convex feasible region as follows: For each component of the generalized joint velocity, an external saturation value and an internal threshold are set. The internal threshold is less than the external saturation value. The value range of each component is such that the absolute value does not exceed the external saturation value, and the preset non-convex gap interval centered at zero and determined by the internal threshold is excluded.

[0015] Optionally, in S6 of the above method, for the non-convex feasible region, a piecewise non-convex projection function is constructed to limit the generalized joint velocity within a preset non-convex feasible range, specifically as follows: The piecewise non-convex projection function maps input variables into segments according to their intervals to the boundaries of the non-convex feasible region or within the non-convex feasible region. This includes limiting the amplitude of components that exceed the external saturation value and mapping components that fall into the preset non-convex gap interval to the nearest feasible boundary.

[0016] Optionally, in S7, a fuzzy adaptive pseudo-free inverse recurrent neural network solver is designed as follows: Based on the gradient descent principle, velocity compensation mechanism, and the structure of the optimization problem maximizing regularized orthogonal operability, a recursive neural dynamics model is constructed that does not require explicit computation of the pseudo-inverse of the Jacobian matrix model. The position error and its rate of change of the end effector are used as the input of the fuzzy logic system, and the convergence parameter adjustment is used as the output of the fuzzy logic system. The convergence parameter of the recursive neural dynamics model is adaptively adjusted to obtain a fuzzy adaptive pseudo-inverse-free recursive neural network.

[0017] Optionally, the above method can be used to construct a recursive neurodynamic model that does not require explicit computation of the pseudo-inverse of the Jacobian matrix model, specifically as follows: Define the end effector position error: , in, w The desired pose of the end effector. w A This represents the actual pose of the end effector; Construct the error energy function: ; The initial neural dynamics update form is obtained by evolving along the negative gradient direction of the error energy function, and then the initial neural dynamics update form is embedded into the piecewise non-convex projection function. According to the gradient descent principle, the initial neural dynamics update form can be obtained by evolving along the negative gradient direction of the error energy function: ; in, q For the generalized joint variables of the omnidirectional redundant robotic arm, Represents generalized joint velocity; Error energy function E For generalized joint variables q The partial derivatives, For convergence parameters, The Jacobian matrix of the omnidirectional redundant robotic arm. for Transpose of; Embedding the initial neurodynamic update form into a non-convex projection function, we obtain: ; in, For is defined in a nonconvex feasible region Ξ Piecewise nonconvex projection operator on; Ξ For the nonconvex feasible region of generalized joint velocities; By introducing a velocity compensation term and combining it with a regularized orthogonal operability optimization term, a fuzzy adaptive pseudo-free inverse recurrent neural network is constructed.

[0018] ; in, β For the internal state variables of the neural network, τ >0 represents the time constant. γ >0 represents the position error feedback coefficient. This refers to the adjustment amount of the convergence parameter output by the fuzzy logic system. Optimize weights for operability. This is the regularized approximate null space projection matrix. Let the gradient vector of operability with respect to the generalized joint variables be denoted as . The desired speed for the end effector.

[0019] Optionally, in S7, the fuzzy logic system uses the end effector position error norm as described above. and its rate of change As an antecedent variable, the convergence parameter adjustment amount As a consequent variable; The linguistic variables of the positional error norm ε include: zero region, moderately positive region, and large positive region; Error change rate The language variables include: zero region, medium positive region, and large positive region; Convergence parameter adjustment The linguistic variables include: zero, positive small, positive medium, positive large, and positive large; The fuzzy logic system employs a Mamdani-type fuzzy inference mechanism. The activation strength of the rules is determined using the minimum operator, and the aggregated fuzzy output is defuzzified using the centroid method to obtain the convergence parameter adjustment. Clarity value; When the position error norm ε of the end effector is in the zero region, and the convergence parameter adjustment amount When the region is zero, the convergence parameter adjustment amount It is zero; When the position error norm ε of the end effector is in the zero region, and the convergence parameter adjustment amount When the region is in the medium positive region, the convergence parameter adjustment amount It is in the center; When the position error norm ε of the end effector is in the moderately positive region, and the convergence parameter adjustment amount When the region is zero, the convergence parameter adjustment amount It is in the center; When the position error norm ε of the end effector is in the zero region, and the convergence parameter adjustment amount When the positive region is large, the convergence parameter adjustment amount For the sake of righteousness; When the position error norm ε of the end effector is in a large positive region, and the convergence parameter adjustment amount When the region is zero, the convergence parameter adjustment amount For the sake of righteousness; When the position error norm ε of the end effector is in the medium or large positive region, and the convergence parameter adjustment amount When the positive region is medium or large, the convergence parameter adjustment amount The value is relatively large.

[0020] As can be seen from the above technical solutions, compared with the prior art, the present invention provides a regularized singularity avoidance control method for mobile robotic arms, which has the following beneficial effects: The present invention embeds the operability gradient term into the approximate orthogonal subspace of the task constraint by regularizing the approximate null space projection matrix, weakening the coupling relationship between end-position error adjustment and operability improvement, and improving the system's ability to avoid singular configurations while maintaining trajectory tracking accuracy; The present invention adaptively adjusts the regularization parameter according to the operability magnitude, and enhances the regularization strength when the operability decreases, thereby suppressing the numerical amplification caused by pseudo-inverse or generalized inverse operations near singular configurations, and improving the motion stability of the omnidirectional mobile redundant robotic arm near singular regions; The present invention constructs a fuzzy adaptive pseudo-inverse-free recurrent neural network solver, avoiding explicit calculation of matrix pseudo-inverses during online solving, reducing computational complexity, and suppressing the lag error of traditional neurodynamic methods in time-varying trajectory tracking through a speed compensation mechanism. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0022] Figure 1 A flowchart of a regularized singularity avoidance control method for a mobile robotic arm provided by the present invention; Figure 2This invention provides a block diagram of a fuzzy adaptive pseudo-inverse recurrent neural network solver in a regularized singularity avoidance control method for a mobile robotic arm. Figure 3 A schematic diagram of the membership function of the input error of the fuzzy logic system in a regularized singularity avoidance control method for a mobile robotic arm provided by the present invention; Figure 4 A schematic diagram of the membership function of the input error change rate of a fuzzy logic system in a regularized singularity avoidance control method for a mobile robotic arm provided by the present invention; Figure 5 This invention provides a schematic diagram of the membership function of the fuzzy logic system output convergence parameter adjustment quantity in a regularized singularity avoidance control method for a mobile robotic arm. Figure 6 This invention provides a fuzzy inference system input-output relationship and fuzzy rule representation for a regularized singularity avoidance control method for a mobile robotic arm. Figure 7 A schematic diagram of the end effector motion process under the Lisa Ru trajectory task, which is a regularized singularity avoidance control method for a mobile robotic arm provided by the present invention. Figure 8 A schematic diagram illustrating the changes in joint angles and wheel variables of a mobile robotic arm under a Lisza trajectory task, based on a regularized singularity avoidance control method for a mobile robotic arm provided by this invention. Figure 9 A schematic diagram illustrating the changes in joint velocity and wheel velocity of the mobile platform under a Lisaru trajectory task, illustrating the regularized singularity avoidance control method for a mobile robotic arm provided by this invention. Figure 10 A schematic diagram illustrating the change in end effector tracking error under a Lisa Ru trajectory task, illustrating the regularized singularity avoidance control method for a mobile robotic arm provided by this invention. Figure 11 A schematic diagram illustrating the input-output relationship of a fuzzy logic system under a Lisaru trajectory task, illustrating a regularized singularity avoidance control method for a mobile robotic arm provided by this invention. Figure 12 This is a schematic diagram illustrating the change in operability index of a regularized singularity avoidance control method for a mobile robotic arm provided by the present invention under the Lisa Ru trajectory task; Figure 13 This is a three-dimensional simulation diagram of the end-effector trajectory tracking of a mobile robotic arm implemented in the CoppeliaSim platform in a specific embodiment of the present invention. Detailed Implementation

[0023] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] Reference Figure 1 As shown, this invention discloses a regularized singularity avoidance control method for a mobile robotic arm, comprising: S1. Obtain the joint states, end-effector desired trajectory, and desired velocity of the omnidirectional redundant manipulator. Unify the wheel system coordinates of the mobile platform and the joint angles of the manipulator to form generalized joint variables, and establish the kinematic model of the omnidirectional redundant manipulator. S2. Construct end effector trajectory tracking constraints; S3. Construct the operability index of the omnidirectional mobile redundant manipulator using the Jacobian matrix, and calculate the gradient vector of operability with respect to the generalized joint variables as the driving term for singular configuration avoidance and posture optimization. S4. Construct a regularized approximate null space projection matrix; S5. Apply the regularized approximate null space projection matrix to the gradient vector, and combine it with the non-convex feasible region obtained by modeling the end effector trajectory tracking constraints to construct a regularized orthogonal operability maximization optimization problem. S6. For the non-convex feasible region, construct a piecewise non-convex projection function to limit the generalized joint velocity within the preset non-convex feasible range. S7. Design a fuzzy adaptive pseudo-free inverse recurrent neural network solver; S8. Apply the generalized joint speed control quantity output by the fuzzy adaptive pseudo-inverse recurrent neural network to the omnidirectional mobile redundant manipulator to control the coordinated motion of the mobile platform and the manipulator joints, thereby achieving end effector trajectory tracking, operability maintenance and singular configuration avoidance.

[0025] Furthermore, in S1, a kinematic model of the omnidirectional redundant robotic arm is established, specifically as follows: Based on the geometric relationship of the omnidirectional mobile platform and the DH parameters of the robotic arm, a nonlinear kinematic mapping between the end effector pose and generalized joint variables is established, and the derivative of the nonlinear kinematic mapping is obtained to obtain the kinematic model at the velocity level. Furthermore, the omnidirectional redundant robotic arm can consist of a six-degree-of-freedom robotic arm and an omnidirectional mobile platform. Let the joint angle vector of the robotic arm be: , The coordinate vector of the mobile platform's wheel system is: , Combining the two yields the generalized joint variable: , Where n is the number of robotic arm joints; The pose or position variable of the end effector of an omnidirectional redundant robotic arm in Cartesian space is denoted as w(t) ; Based on the geometric relationships of the mobile platform, the DH parameters of the robotic arm, and the coordinate transformation relationships, the following nonlinear kinematic mapping is established: , in, This represents the nonlinear kinematic mapping determined by the geometry of the omnidirectional redundant manipulator; Differentiating the nonlinear kinematic mapping yields the kinematic model at the velocity level: , in, Represents generalized joint velocity. Let be the Jacobian matrix of the omnidirectional redundant robotic arm. For simplicity, it will be... Abbreviated as .

[0026] Furthermore, in S2, the end effector trajectory tracking constraints are constructed as follows: Based on the desired trajectory and speed of the end effector of the omnidirectional redundant manipulator, a velocity-layer trajectory tracking equation constraint is established, which is satisfied by the Jacobian matrix of the omnidirectional redundant manipulator and the generalized joint speed, so that the end effector can track the preset desired trajectory.

[0027] Furthermore, in S3, the greater the operability, the further the system configuration is from the singular region, and the stronger the flexibility of the end effector's movement. The operability gradient vector is used to indicate the generalized joint velocity direction that can improve operability; unlike the traditional method that directly superimposes it into the joint velocity solution, this invention first performs a regularized approximate null space projection to reduce the coupling between operability optimization and end-point trajectory tracking error. Furthermore, since the operability gradient term directly participates in the solution of generalized joint velocities, it can easily cause mutual interference between operability improvement and end-effector position error adjustment. To enhance numerical stability and weaken the above coupling, this invention constructs a regularized approximate null space projection matrix: Furthermore, in S4, a regularized approximate null space projection matrix is ​​constructed as follows: The regularization approximate null space projection matrix contains a regularization parameter that is adaptively adjusted according to the magnitude of the operability index. When the operability index decreases, the regularization parameter increases to suppress numerical ill-conditioning near singular regions.

[0028] Furthermore, in S5, a regularized orthogonal operability maximization optimization problem is constructed, specifically as follows: Apply the regularized approximate null space projection matrix to the operability gradient term, so that the operability optimization objective is embedded into the approximate orthogonal subspace of the task constraints; To more realistically describe the speed constraints of the omnidirectional redundant robotic arm actuator, this invention models the generalized joint speed constraints as a non-convex feasible region. The joint velocity constraints of the omnidirectional redundant robotic arm are modeled as a non-convex feasible region, forming a regularized orthogonal operability maximization optimization problem that includes end-effector trajectory tracking equality constraints and non-convex velocity constraints.

[0029] Furthermore, the non-convex feasible region is constructed as follows: For each component of the generalized joint velocity, an external saturation value and an internal threshold are set. The internal threshold is less than the external saturation value. The value range of each component is such that the absolute value does not exceed the external saturation value, and the preset non-convex gap interval centered at zero and determined by the internal threshold is excluded.

[0030] Furthermore, in S6, for the non-convex feasible region, a piecewise non-convex projection function is constructed to limit the generalized joint velocity within a preset non-convex feasible range, specifically as follows: The piecewise non-convex projection function maps input variables into segments according to their intervals to the boundaries of the non-convex feasible region or within the non-convex feasible region. This includes limiting the amplitude of components that exceed the external saturation value and mapping components that fall into the preset non-convex gap interval to the nearest feasible boundary.

[0031] Furthermore, in S7, a fuzzy adaptive pseudo-free inverse recurrent neural network solver is designed, specifically as follows: Based on the gradient descent principle, velocity compensation mechanism, and the structure of the optimization problem maximizing regularized orthogonal operability, a recursive neural dynamics model is constructed that does not require explicit computation of the pseudo-inverse of the Jacobian matrix model. The position error and its rate of change of the end effector are used as the input of the fuzzy logic system, and the convergence parameter adjustment is used as the output of the fuzzy logic system. The convergence parameter of the recursive neural dynamics model is adaptively adjusted to obtain a fuzzy adaptive pseudo-inverse-free recursive neural network.

[0032] Furthermore, a recursive neural dynamics model is constructed that does not require explicit computation of the pseudo-inverse of the Jacobian matrix model, specifically as follows: Define the end effector position error: , in, w The desired pose of the end effector. w A This represents the actual pose of the end effector; Construct the error energy function: ; The initial neural dynamics update form is obtained by evolving along the negative gradient direction of the error energy function, and then the initial neural dynamics update form is embedded into the piecewise non-convex projection function. According to the gradient descent principle, the initial neural dynamics update form can be obtained by evolving along the negative gradient direction of the error energy function: ; in, q For the generalized joint variables of the omnidirectional redundant robotic arm, Represents generalized joint velocity; Error energy function E For generalized joint variables q The partial derivatives, For convergence parameters, The Jacobian matrix of the omnidirectional redundant robotic arm. for Transpose of; Embedding the initial neurodynamic update form into a non-convex projection function, we obtain: ; in, For is defined in a nonconvex feasible region Ξ Piecewise nonconvex projection operator on; Ξ For the nonconvex feasible region of generalized joint velocities; To suppress the lag error present in traditional recurrent neural networks for time-varying trajectory tracking, this invention introduces a velocity compensation term and combines it with a regularized orthogonal operability optimization term to construct a fuzzy adaptive pseudo-free inverse recurrent neural network:

[0033] ; in, β For the internal state variables of the neural network, τ >0 represents the time constant. γ >0 represents the position error feedback coefficient. This refers to the adjustment amount of the convergence parameter output by the fuzzy logic system. Optimize weights for operability. This is the regularized approximate null space projection matrix. Let the gradient vector of operability with respect to the generalized joint variables be denoted as . The desired speed of the end effector; the fuzzy adaptive pseudo-inverse recurrent neural network does not require explicit computation of the pseudo-inverse of the Jacobian matrix, thus reducing the complexity of online solution and improving the numerical stability near the singular configuration; Furthermore, refer to Figure 2 As shown, the composition and signal transmission relationship of the fuzzy adaptive pseudo-inverse recurrent neural network solver are shown. The desired pose of the end effector and the actual pose form a position error. The fuzzy logic system outputs the convergence parameter adjustment amount according to the position error and its rate of change. This adjustment amount works together with the velocity compensation term, the regularized orthogonal operability optimization term and the non-convex projection operator to generate a generalized joint velocity control amount that satisfies trajectory tracking and non-convex velocity constraints. Furthermore, in S7, the fuzzy logic system uses the end effector position error norm. and its rate of change As an antecedent variable, the convergence parameter adjustment amount As a consequent variable; Reference Figure 3 and Figure 4 As shown, Figure 3 Used to illustrate the membership distribution of the location error norm in the zero region, the moderately positive region, and the large positive region. Figure 4 Used to illustrate the membership degree distribution of the error change rate on the corresponding linguistic variables; the two sets of input membership functions map the continuous error signal into fuzzy linguistic variables, serving as the basis for online adjustment of fuzzy rule activation and convergence parameters; The linguistic variables of the positional error norm ε include: zero region, moderately positive region, and large positive region; Error change rate The language variables include: zero region, medium positive region, and large positive region; Convergence parameter adjustment The linguistic variables include: zero, positive small, positive medium, positive large, and positive large; Reference Figure 5 As shown, the membership distribution of the convergence parameter adjustment amount on five linguistic variables: zero, small, medium, large, and large. The output membership function is used to convert the fuzzy inference results into convergence parameter adjustment amounts of different magnitudes. The fuzzy logic system employs a Mamdani-type fuzzy inference mechanism. The activation strength of the rules is determined using the minimum operator, and the aggregated fuzzy output is defuzzified using the centroid method to obtain the convergence parameter adjustment. Clarity value; Reference Figure 6 As shown, Figure 6 The left-side surface represents the convergence parameter adjustment result under the combined effect of the position error norm and the error change rate, while the right-side fuzzy rule table illustrates the correspondence between each combination of input linguistic variables and the output linguistic variables, thereby achieving online adaptive adjustment of the convergence speed of the neurodynamic solver. When the position error norm ε of the end effector is in the zero region, and the convergence parameter adjustment amount When the region is zero, the convergence parameter adjustment amount It is zero; When the position error norm ε of the end effector is in the zero region, and the convergence parameter adjustment amount When the region is in the medium positive region, the convergence parameter adjustment amount It is in the center; When the position error norm ε of the end effector is in the moderately positive region, and the convergence parameter adjustment amount When the region is zero, the convergence parameter adjustment amount It is in the center; When the position error norm ε of the end effector is in the zero region, and the convergence parameter adjustment amount When the positive region is large, the convergence parameter adjustment amount For the sake of righteousness; When the position error norm ε of the end effector is in a large positive region, and the convergence parameter adjustment amount When the region is zero, the convergence parameter adjustment amount For the sake of righteousness; When the position error norm ε of the end effector is in the medium or large positive region, and the convergence parameter adjustment amount When the positive region is medium or large, the convergence parameter adjustment amount The positive value is relatively large to avoid over-adjustment and improve control smoothness. This invention can dynamically adjust the convergence parameters of the neurodynamic solver according to the real-time tracking error state, so that the system can balance rapid error decay, smooth speed output, and low computational burden in different motion stages.

[0034] In one specific embodiment, the omnidirectional redundant robotic arm in this embodiment can be composed of a six-degree-of-freedom robotic arm and an omnidirectional mobile platform. Let the joint angle vector of the robotic arm be... The coordinate vector of the mobile platform's wheel system is: , Combining the two yields the generalized joint variable: , Where n is the number of joints in the robotic arm.

[0035] In this embodiment, n=6, therefore the generalized joint variable q(t) Let w(t) be a 10-dimensional vector; the pose or position variable of the omnidirectional redundant manipulator end effector in Cartesian space is denoted as w(t); based on the geometric relationship of the mobile platform, the DH parameters of the manipulator, and the coordinate transformation relationship, the following nonlinear kinematic mapping is established: ; in, The nonlinear kinematic mapping, defined by the geometry of the omnidirectional redundant robotic arm, can be differentiated to obtain the kinematic model at the velocity level: ; in, Represents generalized joint velocity. Let be the Jacobian matrix of the omnidirectional redundant robotic arm; for simplicity, the following will... Abbreviated as .

[0036] When the end effector expects the trajectory to be At that time, its expected speed is To achieve end effector trajectory tracking, the following velocity layer equality constraint is constructed: , In one specific embodiment, the wheel radius of the omnidirectional mobile platform It is 76.2mm, half the length of the platform. It is 306mm thick, half the width of the platform. The velocity is 305mm. The velocities of the four Mecanum wheels of the mobile platform satisfy the inverse and forward kinematic relationships of the omnidirectional mobile platform with respect to the platform's center velocity. Therefore, the motion of the mobile platform and the joint motion of the robotic arm can be unified into a generalized joint variable. middle.

[0037] To measure the ability of an omnidirectional redundant robotic arm to move away from singular configurations, a maneuverability index is constructed based on the Jacobian matrix. Maneuverability is defined as: ; Here, det(·) represents the matrix determinant; it calculates the operability with respect to the generalized joint variables. gradient components: ; The operability gradient vector is composed of each gradient component: ; Traditional gradient-based operability maximization optimization methods can typically be written in the following form: ;

[0038] Where Θ is a positive definite weighting matrix, Optimize weights for operability; Construct the regularized approximate null space projection matrix: ; in, For regularization parameters, The identity matrix is ​​used; to enable the regularization parameter to adapt to the singularity of the system, this invention further... Designed as follows: ; in, , and All are relatively small positive numbers. When operability... When it decreases, It automatically increases, thereby improving the regularization strength near singular configurations and suppressing numerical ill-conditioning caused by matrix inversion.

[0039] Construct a regularized orthogonal operability maximization optimization problem: ; ; in, The nonconvex feasible region representing the generalized joint velocity.

[0040] From the regularized approximate null space projection matrix, we can obtain: ; Therefore, when When it approaches 0, Approaching the standard null space projection matrix; when When positive, the strict null space property is moderately relaxed, and a bounded projective leakage term is formed; this treatment improves the numerical robustness near the singular configuration at the cost of a smaller approximation error. Let z be the variable to be projected, then the nonconvex feasible region can be written as: ; in, Representing vectors The One portion, This is the external saturation value. The internal threshold is close to zero and satisfies... and ; For a nonconvex feasible region, construct the following piecewise nonconvex projection function: ; in, The representation is defined in a non-convex feasible region. The projection operator on the surface; through this projection function, the generalized joint velocity generated by the neurodynamics solver can be limited to a preset non-convex velocity range, so as to avoid the output velocity violating the physical constraints of the mobile platform and the robotic arm.

[0041] In actual control, this invention can be implemented according to the following process: (1) Input the structural parameters, DH parameters, geometric parameters of the mobile platform, and regularization parameters of the omnidirectional redundant manipulator. , , Operability weight Neurodynamic parameters γ and non-convex velocity constraint parameters , , and .

[0042] (2) Obtain generalized joint variables at each sampling time. And calculate the actual pose of the end effector based on the kinematic mapping. And Jacobi matrix .

[0043] (3) Based on the expected trajectory and expected speed Calculate position error Error norm and error change rate .

[0044] (4) Calculate the operability based on the Jacobian matrix. and its gradient vector Update regularization parameters Furthermore, the regularized approximate null space projection matrix is ​​obtained. .

[0045] (5) and The convergence parameter adjustment Δδ is obtained by using a 2-norm input fuzzy logic system through membership degree calculation, fuzzy inference, and centroid method to defuzzify.

[0046] (6) Update the internal state of the neural network And calculate the generalized joint velocity. .

[0047] (7) Through non-convex projection function The generalized joint velocity is limited and projected to ensure that the output velocity meets the non-convex physical constraints.

[0048] (8) Input the projected generalized joint velocity control quantity into the omnidirectional redundant manipulator to drive the mobile platform and the manipulator joints to move in coordination. Repeat the above steps at the next sampling time until the trajectory tracking task ends.

[0049] In another specific embodiment, the initial state of the omnidirectional redundant robotic arm is set as follows: ; The neurodynamic parameters can be set to The geometric parameters of the mobile platform can be set to... Wheel radius End height related parameters .

[0050] The desired trajectory of the end effector can be selected as a Lissajous type trajectory, let... Its expression is: ; in, ; Reference Figure 7 As shown, the spatial motion path of the end effector and the coordinated motion process of the mobile platform and the robot arm are demonstrated when the omnidirectional mobile redundant robot arm performs the Lisa Ru trajectory task. The end effector moves along a preset spatial curve, and the mobile platform and the robot arm adjust their configuration synchronously, indicating that the control method can drive the system to complete the predetermined trajectory task. Reference Figure 8 As shown, the time-domain changes of the joint angles of the six robotic arms and the wheel variables of the four mobile platforms are displayed during the task execution. The state variables change continuously without any obvious jumps, indicating that the mobile platform and the robotic arms can achieve coordinated movement within a unified generalized joint space. Reference Figure 9 As shown, the changes in the joint speed of the robotic arm and the wheel speed of the mobile platform are illustrated, as well as the effect of the non-convex speed constraint. Each speed component remains bounded after the initial adjustment and is limited to the preset feasible range, indicating that the piecewise non-convex projection function can avoid the control output from violating the speed constraint of the actuator. Reference Figure 10 As shown, the trajectory tracking error of the end effector in each Cartesian direction is illustrated. The error in each direction decays rapidly in a short time and converges to a small neighborhood near zero, indicating that the present invention can achieve high-precision end effector trajectory tracking. Reference Figure 11 As shown, the corresponding changes of the position error norm, error rate of change, and convergence parameter adjustment over time are illustrated. When the error is large in the initial stage of the task, the convergence parameter adjustment takes a large value; after the error tends to stabilize, the convergence parameter adjustment decreases rapidly, indicating that the fuzzy logic system can adjust the convergence parameters of the neurodynamic solver online according to the real-time error state. Reference Figure 12 As shown, the change in the operability index under the Lisa trajectory task is illustrated. The operability index remains positive throughout the task and does not show a trend close to zero, indicating that regularized orthogonal operability optimization can improve the system's ability to stay away from singular configurations. comprehensive Figures 7 to 12The results show that, compared with the regularized orthogonal operability optimization method of this invention, the traditional method can complete the basic trajectory tracking task, but there is still coupling between operability optimization and end-position error adjustment, and the steady-state error suppression capability is limited. The method of this invention can make the actual trajectory highly coincide with the expected trajectory, make the end-position error converge quickly, and maintain a high operability level while satisfying the non-convex velocity constraint, thereby taking into account trajectory tracking accuracy, motion smoothness and singular configuration avoidance capability.

[0051] Furthermore, referring to Figure 13 As shown, the method described in this invention was deployed on the CoppeliaSim 3D simulation platform for verification. Simulation results show that the omnidirectional redundant manipulator can stably track a given trajectory while the mobile platform and the manipulator joints move in coordination. The posture changes of each joint are smooth, and no obvious motion conflicts or discontinuities occur, indicating that the method described in this invention has good executability and engineering application potential.

[0052] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, for system or system embodiments, since they are basically similar to method embodiments, the description is relatively simple, and relevant parts can be referred to the descriptions in the method embodiments. The systems and system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0053] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A regularized singularity avoidance control method for a mobile robotic arm, characterized in that, include: S1. Obtain the joint states, end-effector desired trajectory, and desired velocity of the omnidirectional redundant manipulator. Unify the wheel system coordinates of the mobile platform and the joint angles of the manipulator to form generalized joint variables, and establish the kinematic model of the omnidirectional redundant manipulator. S2. Construct end effector trajectory tracking constraints; S3. Construct the operability index of the omnidirectional mobile redundant manipulator using the Jacobian matrix, and calculate the gradient vector of operability with respect to the generalized joint variables as the driving term for singular configuration avoidance and posture optimization. S4. Construct a regularized approximate null space projection matrix; S5. Apply the regularized approximate null space projection matrix to the gradient vector, and combine it with the non-convex feasible region obtained by modeling the end effector trajectory tracking constraints to construct a regularized orthogonal operability maximization optimization problem. S6. For the non-convex feasible region, construct a piecewise non-convex projection function to limit the generalized joint velocity within the preset non-convex feasible range. S7. Design a fuzzy adaptive pseudo-free inverse recurrent neural network solver; S8. Apply the generalized joint speed control quantity output by the fuzzy adaptive pseudo-inverse recurrent neural network to the omnidirectional mobile redundant manipulator to control the coordinated motion of the mobile platform and the manipulator joints, thereby achieving end effector trajectory tracking, operability maintenance and singular configuration avoidance.

2. The method for regularized singularity avoidance control of a mobile robotic arm according to claim 1, characterized in that, In S1, the kinematic model of the omnidirectional redundant robotic arm is established, specifically as follows: Based on the geometric relationship of the omnidirectional mobile platform and the DH parameters of the robotic arm, a nonlinear kinematic mapping between the end effector pose and generalized joint variables is established, and the derivative of the nonlinear kinematic mapping is obtained to obtain the kinematic model at the velocity level.

3. The method for regularized singularity avoidance control of a mobile robotic arm according to claim 2, characterized in that, In S2, the trajectory tracking constraints for the end effector are constructed as follows: Based on the desired trajectory and speed of the end effector of the omnidirectional redundant manipulator, a velocity-layer trajectory tracking equation constraint is established, which is satisfied by the Jacobian matrix of the omnidirectional redundant manipulator and the generalized joint speed, so that the end effector can track the preset desired trajectory.

4. The method for regularized singularity avoidance control of a mobile robotic arm according to claim 3, characterized in that, In S4, the regularized approximate null space projection matrix is ​​constructed as follows: The regularization approximate null space projection matrix contains a regularization parameter, which is adaptively adjusted according to the magnitude of the operability index. When the operability index decreases, the regularization parameter increases.

5. The method for regularized singularity avoidance control of a mobile robotic arm according to claim 4, characterized in that, In S5, a regularized orthogonal operability maximization optimization problem is constructed, specifically: Apply the regularized approximate null space projection matrix to the operability gradient term, so that the operability optimization objective is embedded into the approximate orthogonal subspace of the task constraints; The joint velocity constraints of the omnidirectional redundant manipulator are modeled as a non-convex feasible region, forming a regularized orthogonal operability maximization optimization problem that includes end-effector trajectory tracking equality constraints and non-convex velocity constraints.

6. The method for regularized singularity avoidance control of a mobile robotic arm according to claim 5, characterized in that, The construction method for non-convex feasible regions is as follows: For each component of the generalized joint velocity, an external saturation value and an internal threshold are set. The internal threshold is less than the external saturation value. The value range of each component is such that the absolute value does not exceed the external saturation value, and the preset non-convex gap interval centered at zero and determined by the internal threshold is excluded.

7. A regularized singularity avoidance control method for a mobile robotic arm according to claim 6, characterized in that, In S6, for the non-convex feasible region, a piecewise non-convex projection function is constructed to limit the generalized joint velocity within a preset non-convex feasible range, specifically as follows: The piecewise non-convex projection function maps input variables into segments according to their intervals to the boundaries of the non-convex feasible region or within the non-convex feasible region. This includes limiting the amplitude of components that exceed the external saturation value and mapping components that fall into the preset non-convex gap interval to the nearest feasible boundary.

8. A regularized singularity avoidance control method for a mobile robotic arm according to claim 7, characterized in that, In S7, a fuzzy adaptive pseudo-free inverse recurrent neural network solver is designed, specifically as follows: Based on the gradient descent principle, velocity compensation mechanism, and the structure of the optimization problem maximizing regularized orthogonal operability, a recursive neural dynamics model is constructed that does not require explicit computation of the pseudo-inverse of the Jacobian matrix model. The position error and its rate of change of the end effector are used as the input of the fuzzy logic system, and the convergence parameter adjustment is used as the output of the fuzzy logic system. The convergence parameter of the recursive neural dynamics model is adaptively adjusted to obtain a fuzzy adaptive pseudo-inverse-free recursive neural network.

9. A regularized singularity avoidance control method for a mobile robotic arm according to claim 8, characterized in that, A recursive neurodynamic model is constructed that does not require explicit computation of the pseudo-inverse of the Jacobian matrix model, specifically as follows: Define the end effector position error: ， in, w The desired pose of the end effector. w A This represents the actual pose of the end effector; Construct the error energy function: ； The initial neural dynamics update form is obtained by evolving along the negative gradient direction of the error energy function, and then the initial neural dynamics update form is embedded into the piecewise non-convex projection function. According to the gradient descent principle, the initial neural dynamics update form can be obtained by evolving along the negative gradient direction of the error energy function: ； in, q For the generalized joint variables of the omnidirectional redundant robotic arm, Represents generalized joint velocity; Error energy function E For generalized joint variables q The partial derivatives, For convergence parameters, The Jacobian matrix of the omnidirectional redundant robotic arm. for Transpose of; Embedding the initial neurodynamic update form into a non-convex projection function, we obtain: ； in, For is defined in a nonconvex feasible region Ξ Piecewise nonconvex projection operator on; Ξ For the nonconvex feasible region of generalized joint velocities; By introducing a velocity compensation term and combining it with a regularized orthogonal operability optimization term, a fuzzy adaptive pseudo-free inverse recurrent neural network is constructed. ； in, β For the internal state variables of the neural network, τ >0 represents the time constant. γ >0 represents the position error feedback coefficient. This refers to the adjustment amount of the convergence parameter output by the fuzzy logic system. Optimize weights for operability. This is the regularized approximate null space projection matrix. Let the gradient vector of operability with respect to the generalized joint variables be denoted as . The desired speed for the end effector.

10. A regularized singularity avoidance control method for a mobile robotic arm according to claim 9, characterized in that, In S7, the fuzzy logic system uses the end effector position error norm. and its rate of change As an antecedent variable, the convergence parameter adjustment amount As a consequent variable; The linguistic variables of the positional error norm ε include: zero region, moderately positive region, and large positive region; Error change rate The language variables include: zero region, medium positive region, and large positive region; Convergence parameter adjustment The linguistic variables include: zero, positive small, positive medium, positive large, and positive large; The fuzzy logic system employs a Mamdani-type fuzzy inference mechanism. The activation strength of the rules is determined using the minimum operator, and the aggregated fuzzy output is defuzzified using the centroid method to obtain the convergence parameter adjustment. Clarity value; When the position error norm ε of the end effector is in the zero region, and the convergence parameter adjustment amount When the region is zero, the convergence parameter adjustment amount It is zero; When the position error norm ε of the end effector is in the zero region, and the convergence parameter adjustment amount When the region is in the medium positive region, the convergence parameter adjustment amount It is in the center; When the position error norm ε of the end effector is in the moderately positive region, and the convergence parameter adjustment amount When the region is zero, the convergence parameter adjustment amount It is in the center; When the position error norm ε of the end effector is in the zero region, and the convergence parameter adjustment amount When the positive region is large, the convergence parameter adjustment amount For the sake of righteousness; When the position error norm ε of the end effector is in a large positive region, and the convergence parameter adjustment amount When the region is zero, the convergence parameter adjustment amount For the sake of righteousness; When the position error norm ε of the end effector is in the medium or large positive region, and the convergence parameter adjustment amount When the positive region is medium or large, the convergence parameter adjustment amount The value is relatively large.

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