Multi-constraint unknown redundant manipulator obstacle avoidance and path tracking method

Abstract

The embodiment of the present disclosure provides a multi-constraint unknown redundant robot arm obstacle avoidance and path tracking method, which belongs to the technical field of control and specifically comprises: establishing a forward kinematics model and a path tracking error model of the redundant robot arm; constructing an online identifier based on regularized zero dynamics to identify unknown physical parameters in real time and update the Jacobian matrix; constructing a velocity layer smooth obstacle avoidance constraint; unifying the path tracking, obstacle avoidance, joint speed boundary and joint acceleration boundary into a multi-constraint quadratic programming problem; using a multi-task quadruple projection neural network online solver based on the Karush-Kuhn-Tucker condition to output joint speed control instructions that satisfy all constraints in real time. Through the scheme of the present disclosure, high-precision collision-free path tracking can be realized when the physical parameters of the robot arm are unknown or drift, while strictly meeting the joint speed and acceleration hard constraints, and good engineering adaptability is achieved.

Description

Technical Field

[0001] This disclosure relates to the field of control technology, and in particular to a method for obstacle avoidance and path tracking of a multi-constraint, unknown, redundant robotic arm. Background Technology

[0002] Currently, although existing technologies can achieve obstacle avoidance and path tracking control of redundant robotic arms to a certain extent, they still have the following shortcomings in engineering scenarios with unknown physical parameters, multiple constraints, and complex environmental coupling: 1) Some learning-based obstacle avoidance methods rely on offline data collection and training in specific scenarios. When the environmental layout, obstacle position, or working state of the robotic arm changes, it is often necessary to resample, retrain, or re-adapt, resulting in high deployment costs and difficulty in meeting the requirements for online real-time response.

[0003] 2) Many real-time obstacle avoidance or path adjustment methods rely on accurate prior information of the physical structure parameters of the robotic arm or the Jacobian matrix. However, in reality, the relevant parameters may deviate from the calibration values ​​due to factors such as manufacturing errors, long-term wear, load changes, or maintenance and reconstruction. This results in a deviation between the task mapping relationship established based on an inaccurate model and the real system, thereby affecting the obstacle avoidance accuracy and path tracking effect.

[0004] 3) While some existing methods can handle path tracking or obstacle avoidance tasks, they fail to explicitly handle multiple physical boundaries such as obstacle avoidance constraints, path tracking constraints, joint velocity, and joint acceleration within a unified framework. In particular, they do not adequately consider joint acceleration constraints, which can easily lead to overly aggressive online control quantities, affecting the smoothness of the robotic arm's motion and engineering safety.

[0005] 4) Under unknown physical parameters, some “learning + control” or “identification + control” methods require high accuracy in parameter estimation. However, under actual conditions such as insufficient excitation, measurement errors or environmental changes, the accuracy of parameter identification and the effectiveness of online updates are prone to decline, which in turn affects the accuracy and stability of multi-task coupled control.

[0006] It is evident that there is an urgent need for a method for obstacle avoidance and path tracking of multi-constrained, unknown, redundant robotic arms with high control precision and adaptability. Summary of the Invention

[0007] In view of this, the present disclosure provides a method for obstacle avoidance and path tracking of a multi-constraint, unknown, redundant robotic arm, which at least partially solves the problems of poor control accuracy and adaptability in the prior art.

[0008] This disclosure provides a method for obstacle avoidance and path tracking of a multi-constraint, unknown, redundant robotic arm, including: Step 1: Establish the forward kinematics model and path tracking error model of the redundant robotic arm. The forward kinematics model is used to describe the mapping relationship between the joint space and the task space to calculate the actual position of the robotic arm end effector. The path tracking error model is used to define the deviation between the expected path of the end effector and the actual position. Step 2: Based on the forward kinematics model, construct an online identifier based on regularized null neurodynamics. Utilize the real-time joint state of the robotic arm and the actual end position calculated by the forward kinematics model to identify the unknown physical parameters of the robotic arm online. Update the end Jacobian matrix and the local Jacobian matrix of key points of the robotic arm in real time according to the identification results. Step 3: Based on the local Jacobian matrix of the key points, construct the velocity layer obstacle avoidance inequality constraint between the key points of the robotic arm and the obstacle, and smooth the velocity layer obstacle avoidance inequality constraint to generate smooth obstacle avoidance constraint. Step 4: In each control cycle, construct the equality constraints for path tracking based on the path tracking error model, and combine them with the smooth obstacle avoidance constraints, joint velocity boundary constraints, and joint acceleration boundary constraints to uniformly construct a multi-constraint quadratic programming problem with joint velocity as the optimization variable. Step 5: Based on the Caro-Kuhn-Tucker conditions, construct a multi-task quadruple projection neural network online solver to solve the multi-constraint quadratic programming problem online, and output joint speed control commands that satisfy all constraints to the robot arm's underlying controller for execution.

[0009] According to a specific implementation of an embodiment of this disclosure, the step of constructing an online identifier based on regularized null neural dynamics includes: Construct velocity layer error equations and position layer error equations, wherein the velocity layer error consists of the difference between the actual end velocity measured by the sensor and the end velocity estimated based on the Jacobian matrix to be identified, and the position layer error consists of the difference between the actual end position calculated by the positive kinematics model and the end position estimated based on the linear regression form. Based on the principle of nullification neurodynamics, the velocity layer error and the position layer error are made to decay exponentially, and a Tikhonov regularization term is introduced. By combining the attenuated velocity layer error equation and the position layer error equation, the identification law for online updating of the physical parameter vector to be identified is derived.

[0010] According to a specific implementation of this disclosure, the step of constructing velocity layer obstacle avoidance inequality constraints between key points of the robotic arm and obstacles based on the local Jacobian matrix of key points includes: Based on the relative displacement direction between the collision-prone key points of the robotic arm and the nearest point of the obstacle, and combined with the local Jacobian matrix of the key points, a system is constructed that satisfies... Inequality constraints of the form, where, The coefficient matrix represents the velocity-layer obstacle avoidance inequality constraints, used to characterize the motion constraint relationship of the robot arm's key points relative to the nearest point of the obstacle. Indicates that the robotic arm is in The joint velocity vector at time t.

[0011] According to a specific implementation of an embodiment of this disclosure, the step of smoothing the velocity layer obstacle avoidance inequality constraints includes: By using a piecewise smooth function, based on the real-time minimum distance between the robotic arm's key points and obstacles, the right-hand vector of the obstacle avoidance inequality constraint in the velocity layer is dynamically modulated, generating a vector of the form: The smooth obstacle avoidance constraint, in which, Indicates the smoothed velocity layer avoidance The right-hand vector of the obstacle inequality constraint is used to dynamically adjust the obstacle avoidance constraint strength based on the real-time minimum distance between the key points of the robotic arm and the obstacle.

[0012] According to a specific implementation of this disclosure, the expression for the multi-constraint quadratic programming problem is:

[0013]

[0014]

[0015]

[0016]

[0017] in, , This is the vector of coefficients of the linear terms in the objective function. For error feedback gain; This is the set of upper and lower bounds for joint velocities. This is the set of upper and lower bounds for joint acceleration.

[0018] According to a specific implementation of this disclosure, the dynamic equations of the multi-task quadruple projection neural network online solver are constructed by introducing Lagrange multipliers and setting corresponding projection operators for the joint velocity boundary, joint acceleration boundary, Lagrange multiplier rate of change boundary, and obstacle avoidance multiplier non-negative boundary, respectively.

[0019] According to a specific implementation of this disclosure, the dynamic equation of the multi-task quad projection neural network online solver is:

[0020]

[0021]

[0022] in, Adjustable gain; for The upper and lower bound sets, To avoid obstacles, the multipliers are a non-negative set; These are the projection operators on the corresponding sets, used to ensure that the acceleration boundary, velocity boundary, multiplier rate of change boundary, and obstacle avoidance multiplier non-negativity are always satisfied during the solution process.

[0023] According to a specific implementation of this disclosure, the following sub-steps are executed sequentially in each control cycle: Step a, execute step 2, update the physical parameters online using the joint state and end state of the current cycle, and update the end Jacobian matrix and the local Jacobian matrix of the key points in real time; Step b: Based on the updated local Jacobian matrix of key points in step a, execute step 3 to generate the smooth obstacle avoidance constraint for the current cycle. Step c: Based on the updated terminal Jacobian matrix in step a and the smooth obstacle avoidance constraints generated in step b, combined with the path tracking error model, execute step 4 to construct the multi-constraint quadratic programming problem for the current cycle. Step d: Execute step 5 to solve the multi-constraint quadratic programming problem constructed in step c, obtain the joint speed control command for the current cycle, and output it to the underlying controller. Step e: Repeat steps a through d in the next control cycle.

[0024] According to a specific implementation of this disclosure, the joint velocity boundary constraint and the joint acceleration boundary constraint are hard constraints, and the multi-task quadruple projection neural network online solver ensures through its projection operator mechanism that the solved joint velocity and joint acceleration commands do not exceed the preset physical upper and lower limits at any time.

[0025] The obstacle avoidance and path tracking scheme for a multi-constraint, unknown, redundant robotic arm in this embodiment includes: Step 1, establishing a forward kinematics model and a path tracking error model for the redundant robotic arm, wherein the forward kinematics model is used to describe the mapping relationship between the joint space and the task space to calculate the actual position of the robotic arm's end effector, and the path tracking error model is used to define the deviation between the expected path of the end effector and the actual position; Step 2, based on the forward kinematics model, constructing an online identifier based on regularized nullable neurodynamics, using the real-time joint states of the robotic arm and the actual position of the end effector calculated by the forward kinematics model to identify the unknown physical parameters of the robotic arm online, and updating the end effector Jacobian matrix and the local Jacobian matrix of key points of the robotic arm in real time according to the identification results; Step 3, ... Step 3: Based on the local Jacobian matrix of key points, construct velocity-layer obstacle avoidance inequality constraints between the key points of the robotic arm and obstacles, and smooth the velocity-layer obstacle avoidance inequality constraints to generate smooth obstacle avoidance constraints; Step 4: In each control cycle, construct equality constraints for path tracking based on the path tracking error model, and combine them with smooth obstacle avoidance constraints, joint velocity boundary constraints, and joint acceleration boundary constraints to uniformly construct a multi-constraint quadratic programming problem with joint velocity as the optimization variable; Step 5: Based on the Cartesian-Kuhn-Tucker conditions, construct a multi-task quadruple projection neural network online solver to solve the multi-constraint quadratic programming problem online, and output joint velocity control commands that satisfy all constraints to the robotic arm's bottom-level controller for execution.

[0026] The beneficial effects of this disclosure are as follows: By establishing an online physical parameter identification and Jacobian matrix real-time update mechanism through the scheme of this disclosure, and combining it with a multi-constraint online solution strategy based on projection operators, the obstacle avoidance task, path tracking task, and physical boundary constraints such as joint velocity and joint acceleration of the redundant robotic arm are uniformly incorporated into the same optimization framework, so that the robotic arm can still achieve safe, stable, and real-time collision-free path tracking control under unknown physical parameter conditions. Attached Figure Description

[0027] To more clearly illustrate the technical solutions of the embodiments of this disclosure, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this disclosure. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0028] Figure 1 A flowchart illustrating a multi-constraint, unknown, redundant robotic arm obstacle avoidance and path tracking method provided in this embodiment of the disclosure; Figure 2 This is a framework diagram corresponding to a multi-constraint unknown redundancy robotic arm obstacle avoidance and path tracking method provided in an embodiment of this disclosure; Figure 3 Numerical experimental results of an MT-QPNN solver for parameter estimation, obstacle avoidance, and path tracking provided in this embodiment of the disclosure are shown in the figure. (a) shows the movement process of the robotic arm, (b) shows the comparison between the expected path and the actual path, (c) shows the path tracking error norm, (d) shows the physical parameter estimation error norm, (e) shows the physical parameter estimation result, (f) shows the end Jacobian matrix estimation error norm, (g) shows the Jacobian matrix estimation error accuracy curve, (h) shows the critical point Jacobian matrix estimation error norm, (i) shows the minimum distance curve between the robotic arm and the obstacle, (j) shows the joint acceleration curve, (k) shows the joint velocity curve, and (l) shows the joint angle curve. Figure 4 A comparison diagram of the method of the present invention and the comparative method provided in the embodiments of this disclosure on the Jacobian matrix recognition task; Figure 5 The following is an experimental result diagram of the method of the present invention performing path tracking and obstacle avoidance tasks in the UR5 robotic arm simulation environment, provided as an embodiment of the present disclosure. (a) is a snapshot of the key moment in the movement process of the robotic arm, (b) is a comparison between the expected path and the actual path, (c) is the path tracking error norm, (d) is the Jacobian matrix estimation error accuracy curve, and (e) is the distance curve between the robotic arm and the obstacle. Figure 6 The figure shows the experimental results of the method of the present invention performing path tracking and obstacle avoidance tasks on the UR7e robotic arm physical platform, which is an embodiment of the present disclosure. (a) is a snapshot of key moments in the movement process of the robotic arm, (b) is the actual end path obtained by OpenCV, (c) is the joint acceleration curve, (d) is the joint velocity curve, and (e) is the joint angle curve. Detailed Implementation

[0029] The embodiments of this disclosure will now be described in detail with reference to the accompanying drawings.

[0030] The following specific examples illustrate the implementation of this disclosure. Those skilled in the art can easily understand other advantages and effects of this disclosure from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this disclosure, and not all of them. This disclosure can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this disclosure. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this disclosure, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this disclosure.

[0031] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this disclosure, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.

[0032] It should also be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of this disclosure. The illustrations only show the components related to this disclosure and are not drawn according to the number, shape and size of the components in actual implementation. In actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0033] Furthermore, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.

[0034] This disclosure provides a method for obstacle avoidance and path tracking of a multi-constraint, unknown, redundant robotic arm. The method can be applied to redundant robotic arm operation processes in scenarios such as industrial manufacturing, collaborative operations, rehabilitation assistance, and complex environment operations.

[0035] See Figure 1 This is a flowchart illustrating a multi-constraint, unknown, redundant robotic arm obstacle avoidance and path tracking method provided in an embodiment of this disclosure. Figure 1 and Figure 2 As shown, the method mainly includes the following steps: Step 1: Establish the forward kinematics model and path tracking error model of the redundant robotic arm. The forward kinematics model is used to describe the mapping relationship between the joint space and the task space to calculate the actual position of the robotic arm end effector. The path tracking error model is used to define the deviation between the expected path of the end effector and the actual position. In practice, a positive kinematic mapping from the joint space of the redundant robotic arm to the task space can be established, where the end effector position of the robotic arm satisfies ,here Let be the joint angle vector of the robotic arm. Given the position of the end effector of the robotic arm, the redundant robotic arm satisfies... Differentiating the above forward kinematics relationship, we can obtain the relationship between the end effector velocity and the joint velocity of the robotic arm as follows: ,in Let be the Jacobian matrix of the robotic arm.

[0036] Furthermore, the end-path tracing error is defined as... The corresponding speed error is ,in These represent the desired position and speed of the robotic arm's end effector.

[0037] Step 2: Based on the forward kinematics model, construct an online identifier based on regularized null neurodynamics. Utilize the real-time joint state of the robotic arm and the actual end position calculated by the forward kinematics model to identify the unknown physical parameters of the robotic arm online. Update the end Jacobian matrix and the local Jacobian matrix of key points of the robotic arm in real time according to the identification results. In practice, the specific process of constructing the Regularized Zero-Nearest Neurodynamic Physical Parameter Identification Method (RZND) and updating the Jacobian matrix in real time is as follows: When physical parameters are unknown, the Jacobian matrix cannot be obtained directly and accurately. Let the final Jacobian matrix to be estimated be... It also introduces the "true speed" of the end effector based on sensor measurements. Then the velocity layer error can be constructed as Furthermore, the terminal position is written in linear regression form. in For the corresponding regression matrix, Let be the vector of physical parameters to be identified. Then, the Jacobian is vectorized and decomposed, denoted as […]. And construct the mapping matrix (Kronecker product). .

[0038] Next, the position information and velocity information are combined as two types of error terms, where the position error term is: The speed error term is Based on the concept of nullification neurodynamics, the error is made to satisfy the law of exponential decay. To avoid matrix invertibility due to weak excitations, a Tikhonov regularization term is introduced, ultimately yielding the RZND online identification law as follows: ,in This is the gain parameter.

[0039] Through online output This allows for real-time updates of the end-effector Jacobian matrix. When subsequent obstacle avoidance constraints require local velocity mapping of key points on the robotic arm, the identified parameters can be used to construct the corresponding local Jacobian matrix for subsequent control solutions.

[0040] Step 3: Based on the local Jacobian matrix of the key points, construct the velocity layer obstacle avoidance inequality constraint between the key points of the robotic arm and the obstacle, and smooth the velocity layer obstacle avoidance inequality constraint to generate smooth obstacle avoidance constraint. In specific implementation, based on the identification parameters obtained in step 2 and the further construction of the local Jacobian matrix of the key points of the robotic arm, in order to avoid collisions between the robotic arm and obstacles, a velocity layer obstacle avoidance inequality constraint is constructed based on the relative relationship between the "collision-prone key point" C of the robotic arm and the nearest point O of the obstacle: in The relative displacement direction of the key point and the local Jacobian of the key point The combination yields the result, and the relative displacement vector between the keypoint and the obstacle point is defined as follows: When the structure is unknown, keypoint C can be obtained by minimum distance geometric detection, and the local Jacobian of the keypoint can be calculated from the identification parameters obtained in step 2. .

[0041] To avoid velocity discontinuities caused by obstacle avoidance constraints at activation or deactivation boundaries, the above constraints are further smoothed out as follows: .in, By distance After piecewise smoothing function Modulation (gradually weakening or disabling obstacle avoidance constraints outside the safe zone), thereby gradually weakening or disabling obstacle avoidance constraints outside the safe zone, and employing... (Safe distance) and (Effective distance) controls the obstacle avoidance activation range. This step outputs the velocity layer smooth obstacle avoidance constraints, which are used for subsequent construction and online solving of multi-constraint QP models.

[0042] Step 4: In each control cycle, construct the equality constraints for path tracking based on the path tracking error model, and combine them with the smooth obstacle avoidance constraints, joint velocity boundary constraints, and joint acceleration boundary constraints to uniformly construct a multi-constraint quadratic programming problem with joint velocity as the optimization variable. In specific implementation, based on the real-time updating of the end Jacobian matrix in step 2 and the construction of smooth obstacle avoidance constraints in the velocity layer in step 3, within each control cycle, "path tracking + obstacle avoidance + joint velocity boundary + joint acceleration boundary" is uniformly written as a multi-constraint QP problem in the joint velocity space, that is, using... To optimize the variables, construct the objective function and the constraints it satisfies:

[0043]

[0044]

[0045]

[0046]

[0047] in , This is the vector of coefficients of the linear terms in the objective function. For error feedback gain; This is the set of upper and lower bounds for joint velocities. Let this be the set of upper and lower bounds for joint acceleration. In the QP problem described above, equality constraints are used to achieve end-point path tracking, inequality constraints are used to achieve velocity-layer obstacle avoidance, and set constraints are used to limit the physical boundaries of joint velocity and joint acceleration, respectively; simultaneously, through... The online updates ensure that the QP problem maintains the correct task mapping even when the physical parameters are unknown or drift occurs. This step outputs a multi-constraint QP model containing path tracing constraints, smooth obstacle avoidance constraints, joint velocity constraints, and joint acceleration constraints, for subsequent online solution use.

[0048] Step 5: Based on the Caro-Kuhn-Tucker conditions, construct a multi-task quadruple projection neural network online solver to solve the multi-constraint quadratic programming problem online, and output joint speed control commands that satisfy all constraints to the robot arm's underlying controller for execution.

[0049] In practice, based on the multi-constraint QP problem constructed in step 4, Lagrange multipliers are introduced to solve the QP problem online. And construct the Lagrange function .

[0050] Furthermore, based on the KKT equivalence conditions, the optimal solution is written in the form of a projection operator to handle the velocity boundary, acceleration boundary, and non-negativity constraint of the obstacle avoidance multiplier.

[0051] Building upon this, inspired by the concept of multiple projection, a continuous-time online solver for a multi-task quadruple projection neural network (MT-QPNN) is constructed, with its dynamic update equation being:

[0052]

[0053]

[0054] in Adjustable gain; for The upper and lower bound sets, To avoid obstacles, the multipliers are a non-negative set; These are the projection operators on the corresponding sets, used to ensure that the acceleration boundary, velocity boundary, multiplier rate of change boundary, and obstacle avoidance multiplier non-negativity are always satisfied during the solution process. In actual online execution, RZND first updates... Then update and Then, the minimum distance to the key point—the obstacle—is calculated using geometric detection. and generate Then, the MT-QPNN solver was run to obtain... and satisfying constraints The resulting control commands are then output to the underlying controller for execution, thereby achieving real-time obstacle avoidance path tracking under hard constraints of speed and acceleration. This step outputs feasible joint speed control commands that satisfy multiple constraints for the robotic arm to execute online.

[0055] This embodiment provides a multi-constraint, unknown, redundant robotic arm obstacle avoidance and path tracking method. Within a unified quadratic programming (QP) framework, it models the collision-free path tracking problem of a redundant robotic arm as a multi-constraint real-time QP. Within the same control cycle, it simultaneously characterizes the path tracking task, obstacle avoidance task, and motion boundary constraints such as joint velocity and acceleration, thus providing a unified optimization carrier for online generation of feasible control variables. It proposes an RZND online physical parameter identification method based on "regularization + nullification neurodynamics," utilizing information such as robotic arm joint states, end-effector position, and velocity to achieve online identification of physical parameters. Based on the identification results, it updates the end-effector Jacobian matrix and keypoint local Jacobian matrices in real time, thereby maintaining the correct task mapping relationship under unknown or drifting physical parameter conditions. Finally, it addresses the minimum distance relationship between the robotic arm and obstacles. A velocity-layer obstacle avoidance constraint is constructed, and smoothing is used to avoid control discontinuities caused by the activation and deactivation boundaries of the obstacle avoidance constraint, thereby improving the stability and safety of the robotic arm when performing obstacle avoidance path tracking tasks in complex environments. A multi-task quadruple projection neural network (MT-QPNN) online solution method based on projection operators is proposed. Four types of projection mechanisms are used to handle joint velocity constraints, joint acceleration constraints, and the boundaries of auxiliary variables and obstacle-related variables in the solution process, so that the online solution process always evolves within the feasible region. The RZND online identification method, Jacobian matrix real-time update, smooth obstacle avoidance constraint construction, and MT-QPNN online solution method are coupled to enable the robotic arm to achieve stable and executable collision-free path tracking control under conditions of unknown physical parameters, multiple constraints, and obstacle environments.

[0056] This invention addresses obstacle avoidance path tracking scenarios for redundant robotic arms with unknown physical parameters and multiple constraints such as joint velocity and acceleration. By unifying obstacle avoidance, tracking, and joint motion boundaries into a QP problem that can be solved online, and introducing RZND online physical parameter identification (including real-time Jacobian matrix updates) and MT-QPNN quadruple projection online solution mechanism, the robotic arm can achieve stable collision-free path tracking under the premise of satisfying physical constraints, and improve the parameter identification accuracy, control stability, and engineering adaptability under unknown physical parameter conditions.

[0057] The method provided by this invention has at least the following effects and advantages: 1. It can achieve online identification of unknown physical parameters and real-time updating of the Jacobian matrix.

[0058] The RZND online physical parameter identification method can perform parameter estimation and Jacobian matrix update in real time under the condition that the physical parameters of the robotic arm are unknown or drifting, thereby reducing the impact of model uncertainty on control accuracy and providing reliable model support for online obstacle avoidance and path tracking control.

[0059] 2. It enables stable, collision-free path tracking in obstacle-prone environments. This invention integrates obstacle avoidance and path tracking tasks into the same QP framework, effectively avoiding obstacles while the robotic arm performs the predetermined path tracking task, thereby improving the safety and continuity of path execution in complex environments.

[0060] 3. It can simultaneously satisfy multiple physical constraints and maintain smooth and executable motion. This invention unifies the handling of joint velocity constraints, joint acceleration constraints, and obstacle avoidance constraints, avoiding control conflicts caused by the separation of constraints or insufficient consideration of constraints in traditional methods. This allows the robotic arm to maintain continuous, smooth motion and conform to the actual execution boundaries even under multiple constraint conditions.

[0061] 4. It can improve the feasibility and stability of the online solution process. MT-QPNN constrains the boundaries of joint velocity, joint acceleration and related auxiliary variables through a quadruple projection mechanism, so that the online iteration process can evolve within the feasible domain. Thus, even under the conditions of unknown physical parameters and obstacle environment, it can still effectively complete the integrated control of obstacle avoidance and path tracking.

[0062] 5. It possesses good real-time performance, stability, and engineering application value. The RZND online identification method proposed in this invention, combined with the MT-QPNN online solution method, can effectively improve the overall performance of redundant robotic arm obstacle avoidance path tracking control under unknown parameter conditions. This can be verified through numerical experiments, simulations, and physical platform testing, demonstrating promising engineering application prospects.

[0063] The method of the present invention will be further described below with reference to several embodiments: Example 1: Numerical Experiment and Comparative Verification of the UR5 Robotic Arm 1) Experimental Object, Platform, and Scenario Setup: The UR5 six-DOF redundant robotic arm was selected as the experimental object, and numerical experiments were conducted on the MATLAB R2022a platform. The total experimental time was set to... The experiment required the UR5 robotic arm to simultaneously avoid vertically placed regular triangular prism obstacles in real time, track the desired path of a four-leaf clover, identify the physical parameters of each physical link of the robotic arm online, and update the end-effector Jacobian matrix in real time. In this experiment, the end-effector task dimension of the Universal Robots (UR) robotic arm was taken as... Joint number .

[0064] 2) Initial value and constraint parameter settings: The initial joint angles of the UR5 robotic arm are set to... Initial joint velocity and initial joint acceleration are both set to 0. The upper and lower bounds of the joint velocity are set to... , The upper and lower bounds of joint acceleration are set to... , In MT-QPNN, the Lagrange multiplier derivative boundary is set to... , For the RZND online identification method, its parameters are set to... , For the MT-QPNN online solver, its parameters are set to... , , The initial values ​​of the physical parameters to be identified are set to... .

[0065] 3) Obstacle and Scene Geometry Setup: Obstacles are modeled as regular triangular prisms, with their three vertices set as follows: , and Obstacle height set to In this scenario, the robotic arm executes online according to the process described in Part 5 of this invention. First, the RZND identifies the physical parameters and updates the end-effector Jacobian matrix and the local Jacobian matrix at key points. Then, a multi-constraint QP problem of "path tracking + obstacle avoidance + velocity boundary + acceleration boundary" is constructed uniformly. The MT-QPNN solves this problem online to obtain control commands, achieving obstacle avoidance and path tracking. Numerical experimental results of the RZND and MT-QPNN solvers for parameter estimation, obstacle avoidance, and path tracking are shown in the figure. Figure 3 As shown.

[0066] 4) Comparison settings and result recording: such as Figure 4As shown, to verify the identification accuracy and overall performance of this invention under unknown physical parameter conditions, the Jacobian matrix obtained by this invention under RZND is compared with comparative methods, including the HCL method, IJM method, and DDLE method. The focus is on comparing the differences between different methods in terms of Jacobian matrix error norm convergence speed, steady-state accuracy, and whether they simultaneously possess parameter identification, obstacle avoidance, and explicit acceleration constraint processing capabilities. The experiment records and displays the robotic arm motion process, the comparison between the desired end-effector path and the actual path, the path error norm, the physical parameter identification results, the end-effector Jacobian matrix error, the local Jacobian matrix error at key points, the change in the minimum distance between the robotic arm and obstacles, and the curves showing the changes in joint angles, joint velocities, and joint accelerations. The results show that this invention can achieve high-precision physical parameter identification and stable collision-free path tracking, where the Jacobian matrix error can converge to approximately [value missing]. Magnitude.

[0067] Example 2: Validation of obstacle avoidance path tracking for the UR5 robotic arm using the MATLAB–CoppeliaSim co-simulation platform 1) such as Figure 5 As shown, the experimental object and platform settings are as follows: A UR5 six-DOF redundant robotic arm was selected as the object, and a MATLAB R2022a and CoppeliaSim 4.1.0 co-simulation platform was built. The desired path was set as a toothed path to verify the path tracking and obstacle avoidance capabilities of this invention in the co-simulation environment.

[0068] 2) Initial value and constraint parameter settings: The initial joint angles of the UR5 robotic arm are set to... The initial joint velocity and initial joint acceleration are both set to 0. The upper and lower bounds of the joint acceleration are set to... and The upper and lower bounds of joint velocity are set to , The boundary value of the Lagrange multiplier derivative is set as follows: , The relevant parameters of this invention are respectively set as follows: , , , , , .

[0069] 3) Obstacle and Scene Geometry Setup: The obstacle is set as a thick wooden board with a length of [length missing]. Width is The height is The coordinates of the UR5 robotic arm base are set to... The object's center coordinates are set to During the co-simulation process, following the procedure described in Part 5 of this invention, the physical parameters are updated online using RZND and the Jacobian matrix is ​​updated in real time. Based on this, a multi-constraint QP problem is constructed, and the control commands that satisfy the constraints are obtained by online solving using MT-QPNN, enabling UR5 to complete path tracking and obstacle avoidance in the simulation environment.

[0070] 4) Results Recording and Presentation: The system records snapshots of key moments in the robotic arm's motion, compares the expected and actual paths, shows the path error norm convergence curve, the Jacobian matrix error accuracy curve, and the minimum distance variation curve between the robotic arm and obstacles. The results demonstrate that the robotic arm can stably avoid obstacles and accurately track the toothed path in the co-simulation environment, with the path error converging rapidly to... The Jacobian matrix error can still converge to the order of magnitude. The scale is significant, and the robotic arm maintains a safe distance from obstacles throughout its operation.

[0071] Example 3: Obstacle Avoidance Path Tracking Verification on the UR7e Robotic Arm Physical Platform 1) such as Figure 6 As shown, the experimental object and scenario settings are as follows: A physical experiment was conducted using the UR7e six-DOF redundant robotic arm to further verify the feasibility, stability, and engineering application capabilities of this invention in a real system. The desired path is still set as a toothed path, with a maximum radius of [missing information]. .

[0072] 2) Constraint and Algorithm Parameter Settings: The obstacle is set as a thick wooden board with a length of [missing information]. Width is The height is The upper and lower bounds of joint acceleration are set to... , Parameters in MT-QPNN Set as The remaining parameters are consistent with the settings in Example 2.

[0073] 3) Method Execution and Data Acquisition: Within the physical control cycle, RZND is first used to identify physical parameters online and update the Jacobian matrix synchronously. Then, a multi-constraint QP problem is constructed based on the updated model, and the control commands are obtained by MT-QPNN online to drive the UR7e to complete path tracking and obstacle avoidance tasks. Simultaneously, PyCharm 2023.3.4 combined with OpenCV is used to collect data on the motion process of the robotic arm's end effector, and the actual path is obtained for result comparison and analysis.

[0074] 4) Results Recording and Display: The system displays snapshots of the actual motion process, the actual end-effector path captured by OpenCV, joint acceleration curves, joint velocity curves, and joint angle variation curves. The results show that the UR7e can accurately complete path tracking and obstacle avoidance tasks. Joint velocity and acceleration consistently meet preset constraints and quickly stabilize after brief transient peaks. Joint angles are smooth and continuous throughout the entire process, demonstrating that the invention has good executability and stability on a real platform.

[0075] It should be understood that the various parts of this disclosure can be implemented in hardware, software, firmware, or a combination thereof.

[0076] The above description is merely a specific embodiment of this disclosure, but the scope of protection of this disclosure is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this disclosure should be included within the scope of protection of this disclosure. Therefore, the scope of protection of this disclosure should be determined by the scope of the claims.

Claims

1. A method for obstacle avoidance and path tracking of a multi-constraint, unknown, redundant robotic arm, characterized in that, include: Step 1: Establish the forward kinematics model and path tracking error model of the redundant robotic arm. The forward kinematics model is used to describe the mapping relationship between the joint space and the task space to calculate the actual position of the robotic arm end effector. The path tracking error model is used to define the deviation between the expected path of the end effector and the actual position. Step 2: Based on the forward kinematics model, construct an online identifier based on regularized null neurodynamics. Utilize the real-time joint state of the robotic arm and the actual end position calculated by the forward kinematics model to identify the unknown physical parameters of the robotic arm online. Update the end Jacobian matrix and the local Jacobian matrix of key points of the robotic arm in real time according to the identification results. Step 3: Based on the local Jacobian matrix of the key points, construct the velocity layer obstacle avoidance inequality constraint between the key points of the robotic arm and the obstacle, and smooth the velocity layer obstacle avoidance inequality constraint to generate smooth obstacle avoidance constraint. Step 4: In each control cycle, construct the equality constraints for path tracking based on the path tracking error model, and combine them with the smooth obstacle avoidance constraints, joint velocity boundary constraints, and joint acceleration boundary constraints to uniformly construct a multi-constraint quadratic programming problem with joint velocity as the optimization variable. Step 5: Based on the Caro-Kuhn-Tucker conditions, construct a multi-task quadruple projection neural network online solver to solve the multi-constraint quadratic programming problem online, and output joint speed control commands that satisfy all constraints to the robot arm's underlying controller for execution.

2. The method according to claim 1, characterized in that, The steps for constructing an online identifier based on regularized null neural dynamics include: Construct velocity layer error equations and position layer error equations, wherein the velocity layer error consists of the difference between the actual end velocity measured by the sensor and the end velocity estimated based on the Jacobian matrix to be identified, and the position layer error consists of the difference between the actual end position calculated by the positive kinematics model and the end position estimated based on the linear regression form. Based on the principle of nullification neurodynamics, the velocity layer error and the position layer error are made to decay exponentially, and a Tikhonov regularization term is introduced. By combining the attenuated velocity layer error equation and the position layer error equation, the identification law for online updating of the physical parameter vector to be identified is derived.

3. The method according to claim 1, characterized in that, The step of constructing the velocity layer obstacle avoidance inequality constraint between the key points of the robotic arm and the obstacle based on the local Jacobian matrix of the key points includes: Based on the relative displacement direction between the collision-prone key points of the robotic arm and the nearest point of the obstacle, and combined with the local Jacobian matrix of the key points, a system is constructed that satisfies... Inequality constraints of the form, where, The coefficient matrix represents the velocity-layer obstacle avoidance inequality constraints, used to characterize the motion constraint relationship of the robot arm's key points relative to the nearest point of the obstacle. Indicates that the robotic arm is in The joint velocity vector at time t.

4. The method according to claim 3, characterized in that, The step of smoothing the velocity layer obstacle avoidance inequality constraints includes: By using a piecewise smooth function, based on the real-time minimum distance between the robotic arm's key points and obstacles, the right-hand vector of the obstacle avoidance inequality constraint in the velocity layer is dynamically modulated, generating a vector of the form: The smooth obstacle avoidance constraint, in which, The vector on the right side of the smoothed velocity layer obstacle avoidance inequality constraint is used to dynamically adjust the obstacle avoidance constraint strength based on the real-time minimum distance between the key points of the robotic arm and the obstacle.

5. The method according to claim 4, characterized in that, The expression for the multi-constraint quadratic programming problem is: in, , This is the vector of coefficients of the linear terms in the objective function. For error feedback gain; This is the set of upper and lower bounds for joint velocities. This is the set of upper and lower bounds for joint acceleration.

6. The method according to claim 5, characterized in that, The dynamic equations of the multi-task quadruple projection neural network online solver are constructed by introducing Lagrange multipliers and setting corresponding projection operators for the joint velocity boundary, joint acceleration boundary, Lagrange multiplier rate of change boundary, and obstacle avoidance multiplier non-negative boundary, respectively.

7. The method according to claim 6, characterized in that, The dynamic equation of the online solver of the multi-task quad projection neural network is: in, Adjustable gain; for The upper and lower bound sets, To avoid obstacles, the multipliers are a non-negative set; These are the projection operators on the corresponding sets, used to ensure that the acceleration boundary, velocity boundary, multiplier rate of change boundary, and obstacle avoidance multiplier non-negativity are always satisfied during the solution process.

8. The method according to claim 1, characterized in that, Within each control cycle, the following sub-steps are executed sequentially: Step a, execute step 2, update the physical parameters online using the joint state and end state of the current cycle, and update the end Jacobian matrix and the local Jacobian matrix of the key points in real time; Step b: Based on the updated local Jacobian matrix of key points in step a, execute step 3 to generate the smooth obstacle avoidance constraint for the current cycle. Step c: Based on the updated terminal Jacobian matrix in step a and the smooth obstacle avoidance constraints generated in step b, combined with the path tracking error model, execute step 4 to construct the multi-constraint quadratic programming problem for the current cycle. Step d: Execute step 5 to solve the multi-constraint quadratic programming problem constructed in step c, obtain the joint speed control command for the current cycle, and output it to the underlying controller. Step e: Repeat steps a through d in the next control cycle.

9. The method according to claim 1, characterized in that, The joint velocity boundary constraints and joint acceleration boundary constraints are hard constraints. The multi-task quadruple projection neural network online solver ensures through its projection operator mechanism that the solved joint velocity and joint acceleration commands do not exceed the preset physical upper and lower limits at any time.

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