A method, system and robot for implementing redundant robotic arm path tracking and obstacle avoidance

Abstract

The application provides a redundant robot arm position layer path tracking and obstacle avoidance method and system, and a robot, and steps include: (1) determining a safe distance between the robot arm and an obstacle; (2) constructing a coupling problem equation of the robot arm position layer path tracking and obstacle avoidance; (3) introducing a mode switcher, and designing a variable structure ZNN solver according to a zero neural network (ZNN) evolution law to solve the coupling problem in step (2); and (4) transmitting the solution in step (3) to a lower machine controller to drive the robot arm to complete a specified end task. The application designs a new variable structure neural network, so that the robot arm can realize path tracking of the robot arm on the position layer, and can avoid obstacles without affecting the end task, and physical damage of the robot arm is avoided.

Description

Technical Field

[0001] This invention relates to the field of robotics, and more specifically to a method, system, and robot for achieving redundant robotic arm path tracking and obstacle avoidance. Background Technology

[0002] A robotic arm is a common type of industrial robot, typically consisting of multiple joints, connected rigid links, and an end effector. It can move in three-dimensional space and perform various tasks, such as grasping, assembly, welding, and drawing. Based on their kinematic structure, robotic arms are classified as redundant or non-redundant. Redundant robotic arms possess additional degrees of freedom, allowing them to meet additional objectives while performing a specific task, such as obstacle avoidance, joint limit avoidance, and energy optimization. Because redundant robotic arms can be more flexible in task execution, they have significant application potential in fields such as space exploration, surgical robotics, aircraft maintenance, and artistic creation.

[0003] Redundancy analysis is a fundamental problem in the motion control of redundant robotic arms. It refers to the need to generate corresponding joint angles in real time given the three-dimensional trajectory of the end effector. Redundancy analysis problems often have multiple or even infinitely many solutions, requiring complex mathematical methods such as optimization algorithms, inverse kinematics, and trajectory planning to determine the optimal joint trajectory or control strategy. Zeroing Neural Networks (ZNNs), by designing a vector-valued error function, can monitor the solution process and progressively set each element of the error function to zero, leading to system convergence. ZNNs offer advantages such as high accuracy, computational efficiency, and the elimination of the need for training and iterative calculations, effectively solving the redundancy analysis problem.

[0004] In practical applications, without obstacle avoidance, robotic arms are prone to collisions and damage from environmental obstacles. Currently, most obstacle avoidance functions are implemented at the velocity level, resulting in joint angular velocities as the resolution of the redundancy problem. This is insufficient for some position-controlled robotic arms. This invention, based on a variable structure neural network, designs a position-level path tracking and obstacle avoidance scheme for redundant robotic arms. This scheme outputs joint angular positions to the robotic arm to drive it to complete given tasks and objectives, and its positioning accuracy surpasses that of velocity-level obstacle avoidance schemes. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method, system and robot for achieving redundant robotic arm path tracking and obstacle avoidance. This invention can output joint angle positions to the robotic arm while achieving obstacle avoidance, and has high positioning accuracy, fast solution speed and no need for training and iterative calculation.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] In a first aspect, the present invention provides a method for implementing redundant robotic arm path tracking and obstacle avoidance, comprising the following steps:

[0008] Step 1: Determine the safe distance d between the robotic arm and the obstacle;

[0009] Step 2: Based on the specific robotic arm, construct its position-level path tracking and obstacle avoidance coupled problem, and realize the equality constraint for path tracking as f. E (θ)=r d The inequality constraint for obstacle avoidance is (p C -p O ) T (p C -p O )≥d 2 Where θ represents the joint angle position of the robotic arm, f E (θ) represents the three-dimensional coordinates of the end effector of the robotic arm at the joint angle position θ, r d p represents the desired end effector motion trajectory. C and p O Let p represent the coordinates of key point C and obstacle point O, respectively. C By constructing the kinematic equation f of the robotic arm C (θ) is obtained, representing the three-dimensional coordinates of key point C at the joint angle position θ;

[0010] Inequality constraints for obstacle avoidance (p) C -p O ) T (p C -p O )≥d 2 Transformed into equality constraints (p) using the projection operator P(·). C -p O ) T (p C -p O )-d 2 =Ρ((p C -p O ) T (p C -p O )-d 2 ), where the projection operator is defined as:

[0011]

[0012] Step 3: Define the error monitoring function e(t) as follows:

[0013]

[0014] Introducing the upper right Dini derivative, based on the evolutionary rules of the ZNN (Zero Neural Network)... After designing and simplifying, a ZNN solver was obtained:

[0015]

[0016] Where γ > 0 is the convergence parameter, J E (θ) represents the Jacobian matrix of the robotic arm's end effector, J C (θ) represents the Jacobian matrix of the key point C of the robotic arm. Indicates joint angular velocity, S is the velocity of the obstacle, and S is the mode switcher matrix consisting of the identity matrix I and the derivative Δ of the projection operator, defined as:

[0017]

[0018] Because the projection operator P(·) is continuous but not everywhere differentiable, it is not possible to directly differentiate the error e(t) with respect to P(z(t)). By introducing the upper right Dini derivative, the derivatives Δ of the projection operators in each row can be obtained. i for:

[0019]

[0020] Where z i (t)=[(p C -p O ) T (p C -p O )] i -d, the solution to the coupled problem is obtained through this ZNN solver, and then the joint angle position θ of the robotic arm is obtained;

[0021] Step 4: Pass the solution θ from Step 3 to the lower-level controller to drive the robotic arm to complete the specified end-effector task.

[0022] As a preferred technical solution, the key point C is the point on a certain link of the robotic arm that is closest to the obstacle point O.

[0023] As a preferred technical solution, the robotic arm consists of an end effector and seven drive joints θ1…θ7, and the kinematic equation of the robotic arm is f E (θ)=r d The inequality constraint equation is (p C -p O ) T (p C -p O )≥d2 ,in f E (θ) represents the three-dimensional coordinates of the robotic arm's end effector at the joint angle θ, r d f represents the desired motion trajectory of the robotic arm's end effector. E (θ)=r d Used to consider path tracing constraints, (p C -p O ) T (p C -p O )≥d 2 Used to account for obstacle avoidance constraints.

[0024] As a preferred technical solution, the designed obstacle avoidance constraint (p C -p O ) T (p C -p O )≥d 2 By transforming the problem into an equality constraint using a projection operator, the hybrid constraint problem of position-layer path tracking and obstacle avoidance for the redundant robotic arm is transformed into an equality constraint problem. Ultimately, the motion of the redundant robotic arm is constrained by the following constraints:

[0025]

[0026] As a preferred technical solution, after introducing the upper right Dini derivative, the non-differentiable part is transformed into a differentiable part, so that the equation with the projection operator P(·) can be differentiated.

[0027] As a preferred technical solution, for the coupling problem of equality constraints and inequality constraints in robotic arms, the inequality constraints are transformed into equality constraints, and then based on the evolutionary law... A variable structure ZNN solver was designed and simplified.

[0028] Secondly, the present invention also provides a system for realizing redundant robotic arm path tracking and obstacle avoidance, including a safety distance module, an obstacle avoidance planning module, a robotic arm joint angle solving module, and a robotic arm drive module.

[0029] The safety distance module is used to determine the safety distance d between the robotic arm and the obstacle;

[0030] The obstacle avoidance planning module is used to construct a coupled problem of position-level path tracking and obstacle avoidance for a specific robotic arm, realizing the equality constraint of path tracking as f. E (θ)=r d The inequality constraint for obstacle avoidance is (p C -p O )T (p C -p O )≥d 2 Where θ represents the joint angle position of the robotic arm, f E (θ) represents the three-dimensional coordinates of the end effector of the robotic arm at the joint angle position θ, r d p represents the desired end effector motion trajectory. C and p O Let p represent the coordinates of key point C and obstacle point O, respectively. C By constructing the kinematic equation f of the robotic arm C (θ) is obtained, representing the three-dimensional coordinates of key point C at the joint angle position θ;

[0031] Inequality constraints for obstacle avoidance (p) C -p O ) T (p C -p O )≥d 2 Transformed into equality constraints (p) using the projection operator P(·). C -p O ) T (p C -p O )-d 2 =Ρ((p C -p O ) T (p C -p O )-d 2 ), where the projection operator is defined as:

[0032]

[0033] The robotic arm joint angle calculation module is used to obtain the desired robotic arm joint angle position, specifically:

[0034] Define the error monitoring function e(t) as:

[0035]

[0036] Introducing the upper right Dini derivative, based on the evolutionary rules of the ZNN (Zero Neural Network)... After designing and simplifying, a ZNN solver was obtained:

[0037]

[0038] Where γ > 0 is the convergence parameter, J E (θ) represents the Jacobian matrix of the robotic arm's end effector, J C(θ) represents the Jacobian matrix of the key point C of the robotic arm. Indicates joint angular velocity, S is the velocity of the obstacle, and S is the mode switcher matrix consisting of the identity matrix I and the derivative Δ of the projection operator, defined as:

[0039] Δ=[Δ1,Δ2,…,Δ p ] T ,

[0040] Because the projection operator P(·) is continuous but not everywhere differentiable, it is not possible to directly differentiate the error e(t) with respect to P(z(t)). By introducing the upper right Dini derivative, the derivatives Δ of the projection operators in each row can be obtained. i for:

[0041]

[0042] Where z i (t)=[(p C -p O ) T (p C -p O )] i -d, the solution to the coupled problem is obtained through this ZNN solver, and then the joint angle position θ of the robotic arm is obtained;

[0043] The robotic arm drive module is used to transmit the solution result θ of the robotic arm joint angle module to the lower-level controller to drive the robotic arm to complete the specified end-effector task.

[0044] Thirdly, the present invention also provides a computer-readable storage medium storing a program, which, when executed by a processor, implements the method for redundant robotic arm path tracking and obstacle avoidance.

[0045] Fourthly, the present invention also provides a robot, the robot comprising:

[0046] At least one processor; and,

[0047] A memory communicatively connected to the at least one processor; wherein,

[0048] The memory stores computer program instructions that can be executed by the at least one processor, which enables the at least one processor to perform the method for implementing redundant robotic arm path tracking and obstacle avoidance.

[0049] Compared with the prior art, the present invention has the following advantages:

[0050] This invention effectively overcomes the shortcomings of conventional techniques by introducing a projection operator and the upper-right Dini derivative, and considering path tracking and obstacle avoidance constraints, to establish a novel position-layer path tracking and obstacle avoidance scheme for redundant robotic arms. This scheme uses the projection operator to transform inequality constraints in the coupled problem into equality constraints, designs a variable-structure neural network based on the ZNN evolution law, and then obtains the solution to the coupled problem. This solution is ultimately used to drive the movement of the robotic arm. This invention can meet the requirements of certain position-controlled robotic arms while achieving obstacle avoidance. Compared to velocity-layer and acceleration-layer schemes, the position-layer scheme avoids error accumulation caused by solving numerical integrals of joint variables, thus achieving higher positioning accuracy. Furthermore, the ZNN solver requires no training or iterative calculation, resulting in a faster solution speed. Attached Figure Description

[0051] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0052] Figure 1 This is a flowchart of the position layer path tracking and obstacle avoidance method for redundant robotic arms according to an embodiment of the present invention.

[0053] Figure 2 This is a model diagram of the simulated Franka Emika robotic arm according to an embodiment of the present invention.

[0054] Figure 3 The image shows the expected and actual trajector trajector trajector trajector trajectories of the simulated Franka Emika robotic arm in an embodiment of the present invention, under obstacle avoidance constraints.

[0055] Figure 4 This is a trajectory error diagram of a simulated Franka Emika robotic arm in an embodiment of the present invention, under obstacle avoidance constraints.

[0056] Figure 5 This is a graph showing the change in the shortest distance between the simulated Franka Emika robotic arm and the obstacle under obstacle avoidance constraints, as per an embodiment of the present invention.

[0057] Figure 6 This is a diagram showing the change in joint angle position of the simulated Franka Emika robotic arm according to an embodiment of the present invention.

[0058] Figure 7 This is a schematic diagram of the system for implementing redundant robotic arm path tracking and obstacle avoidance in an embodiment of the present invention.

[0059] Figure 8 This is a schematic diagram of the robot according to an embodiment of the present invention. Detailed Implementation

[0060] To enable those skilled in the art to better understand the present application, the technical solution of the present invention will be clearly and completely described below with reference to the embodiments and accompanying drawings. It should be understood that the accompanying drawings are for illustrative purposes only and should not be construed as limiting the present patent. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present application.

[0061] In this application, the reference to "embodiment" means that a specific feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a mutually exclusive, independent, or alternative embodiment. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described in this application can be combined with other embodiments.

[0062] Example

[0063] like Figure 1 As shown, this embodiment is a method for position-layer path tracking and obstacle avoidance of a redundant robotic arm. The method includes the following steps:

[0064] Step 1: Determine the safe distance d between the robotic arm and the obstacle;

[0065] In step one, the safe distance between the robotic arm and the obstacle is set as d;

[0066] Step 2: Based on the specific robotic arm, construct its position-level path tracking and obstacle avoidance coupled problem, and design the equality constraint as f. E (θ)=r d Inequality constraints for obstacle avoidance (p) C -p O ) T (p C -p O )≥d 2 Inequality constraints can be transformed into equality constraints (p) using the projection operator P(·). C -p O ) T (p C -p O )-d 2 =Ρ((p C -pO ) T (p C -p O )-d 2 ).

[0067] In step two, f is constrained by this equation. E (θ)=r d The desired path of the end effector can be linked to its joint angular position θ, thereby enabling path planning and control of the end effector. This can be achieved through inequality constraints (p... C -p O ) T (p C -p O )≥d 2 It can handle obstacle avoidance constraints on the robotic arm's drive rods, using f C (θ) represents p C This allows the obstacle avoidance constraint of the robotic arm to be linked to its joint angle position θ.

[0068] Step 3: Define the error monitoring function e(t) as follows:

[0069]

[0070] According to the evolutionary rules of the ZNN (Zero Neural Network) After designing and simplifying, a ZNN solver was obtained:

[0071]

[0072] In step three, the mode switcher matrix S is subject to inequality constraints (p C -p O ) T (p C -p O )≥d 2 When the conditions are not met, the obstacle avoidance part of the ZNN solver is activated, generating an escape velocity away from the obstacle. When the inequality constraints are met, the ZNN solver only performs the path tracing task.

[0073] Step 5: Pass the solution θ from Step 4 to the lower-level controller to drive the robotic arm to complete the specified end-effector task.

[0074] like Figure 2 As shown, the robotic arm model consists of a first drive link 1, a second drive link 2, a third drive link 3, a fourth drive link 4, a fifth drive link 5, a sixth drive link 6, and a seventh drive link 7. The kinematic relationship of the position layer of the robotic arm is f. E (θ)=r d , where f E(θ) represents the three-dimensional coordinates of the robotic arm's end effector at the joint angle θ, r d Let θ represent the desired motion trajectory of the robotic arm's end effector, θ = [θ1, θ2, ..., θ7]. T ∈R 7 .

[0075] like Figure 3 As shown in the figure, the solid line represents the expected trajectory of the simulated Franka Emika robotic arm end effector, and the dashed line represents the actual trajectory of the simulated Franka Emika robotic arm end effector. The figure shows that the expected trajectory and the actual trajectory almost overlap, indicating that this method can achieve precise control of the robotic arm's movement with minimal error.

[0076] like Figure 4 As shown, the dotted line ζ x dashed line ζ y solid line ζ z These figures represent the errors of the simulated Franka Emika robotic arm end effector in the X, Y, and Z directions, respectively. During the end effector's task execution, the errors in all three directions were less than 3 × 10⁻⁶. -6 Meters, with positioning accuracy exceeding sub-millimeter level requirements.

[0077] like Figure 5 As shown, the dashed line d represents the safe distance between the robotic arm and the obstacle, and the solid line l represents the shortest distance between the key point C and the obstacle O. During the robotic arm's task execution, if the shortest distance between the robotic arm and the obstacle is always greater than the set safe distance d, it indicates that the robotic arm does not collide with the obstacle, demonstrating that this invention can achieve obstacle avoidance.

[0078] like Figure 6 As shown, θ1, θ2, θ3, θ4, θ5, θ6, and θ7 represent the joint angle positions of the first drive link 1, the second drive link 2, the third drive link 3, the fourth drive link 4, the fifth drive link 5, the sixth drive link 6, and the seventh drive link 7 of the simulated Franka Emika robotic arm, respectively. During the robotic arm's task execution, the joint angle positions of each drive link continuously change, corresponding to various joint configurations and end effector poses of the robotic arm. The changes in the joint angle positions are continuous, with no solution failures, indicating that the position-layer control scheme of this invention can maintain smooth robotic arm movement and ensure successful solution of the coupled problem of path tracking and obstacle avoidance.

[0079] like Figure 7 As shown, this embodiment also provides a system 100 for implementing redundant robotic arm path tracking and obstacle avoidance, including a safety distance module 101, an obstacle avoidance planning module 102, a robotic arm joint angle solving module 103, and a robotic arm drive module 104.

[0080] The safety distance module 101 is used to determine the safety distance d between the robotic arm and the obstacle;

[0081] The obstacle avoidance planning module 102 is used to construct a coupled problem of position-level path tracking and obstacle avoidance for the specific robotic arm, realizing the equality constraint of path tracking as f. E (θ)=r d The inequality constraint for obstacle avoidance is (p C -p O ) T (p C -p O )≥d 2 Where θ represents the joint angle position of the robotic arm, f E (θ) represents the three-dimensional coordinates of the end effector of the robotic arm at the joint angle position θ, r d p represents the desired end effector motion trajectory. C and p O Let p represent the coordinates of key point C and obstacle point O, respectively. C By constructing the kinematic equation f of the robotic arm C (θ) is obtained, representing the three-dimensional coordinates of key point C at the joint angle position θ;

[0082] Inequality constraints for obstacle avoidance (p) C -p O ) T (p C -p O )≥d 2 Transformed into equality constraints (p) using the projection operator P(·). C -p O ) T (p C -p O )-d 2 =Ρ((p C -p O ) T (p C -p O )-d 2 ), where the projection operator is defined as:

[0083]

[0084] The robotic arm joint angle solving module 103 is used to obtain the desired robotic arm joint angle position, specifically:

[0085] Define the error monitoring function e(t) as:

[0086]

[0087] Introducing the upper right Dini derivative, based on the evolutionary rules of the ZNN (Zero Neural Network)... After designing and simplifying, a ZNN solver was obtained:

[0088]

[0089] Where γ > 0 is the convergence parameter, J E (θ) represents the Jacobian matrix of the robotic arm's end effector, J C (θ) represents the Jacobian matrix of the key point C of the robotic arm. Indicates joint angular velocity, S is the velocity of the obstacle, and S is the mode switcher matrix consisting of the identity matrix I and the derivative Δ of the projection operator, defined as:

[0090] Δ=[Δ1,Δ2,…,Δ p ] T ,

[0091] Because the projection operator P(·) is continuous but not everywhere differentiable, it is not possible to directly differentiate the error e(t) with respect to P(z(t)). By introducing the upper right Dini derivative, the derivatives Δ of the projection operators in each row can be obtained. i for:

[0092]

[0093] Where z i (t)=[(p C -p O ) T (p C -p O )] i -d, the solution to the coupled problem is obtained through this ZNN solver, and then the joint angle position θ of the robotic arm is obtained;

[0094] The robotic arm drive module 104 is used to transmit the solution result θ of the robotic arm joint angle module to the lower-level controller to drive the robotic arm to complete the specified end-effector task.

[0095] It should be noted that the system for achieving redundant robotic arm path tracking and obstacle avoidance of the present invention corresponds one-to-one with the method for achieving redundant robotic arm path tracking and obstacle avoidance of the present invention. The technical features and beneficial effects described in the embodiments of the method for achieving redundant robotic arm path tracking and obstacle avoidance described above are applicable to the system embodiments for achieving redundant robotic arm path tracking and obstacle avoidance. For details, please refer to the description in the embodiments of the method of the present invention, which will not be repeated here.

[0096] Furthermore, in the implementation of the system for redundant robotic arm path tracking and obstacle avoidance in the above embodiments, the logical division of each program module is only an example. In actual applications, the above functions can be assigned to different program modules as needed, for example, for the sake of corresponding hardware configuration requirements or the convenience of software implementation. That is, the internal structure of the system for redundant robotic arm path tracking and obstacle avoidance is divided into different program modules to complete all or part of the functions described above.

[0097] like Figure 8 As shown, in one embodiment, a robot 200 is provided. The robot 200 may include a first processor 201, a first memory 202 and a bus, and may also include a computer program stored in the first memory 202 and executable on the first processor 201, such as a program 203 for implementing redundant robotic arm path tracking and obstacle avoidance.

[0098] The first memory 202 includes at least one type of readable storage medium, including flash memory, portable hard drive, multimedia card, card-type memory (e.g., SD or DX memory), magnetic memory, magnetic disk, optical disk, etc. In some embodiments, the first memory 202 can be an internal storage unit of the robot 200, such as the robot 200's portable hard drive. In other embodiments, the first memory 202 can also be an external storage device of the robot 200, such as a plug-in portable hard drive, smart media card (SMC), secure digital (SD) card, flash card, etc., equipped on the robot 200. Furthermore, the first memory 202 can include both internal storage units and external storage devices of the robot 200. The first memory 202 can be used not only to store application software and various types of data installed on the robot 200, such as the code of program 203 for redundant robotic arm path tracking and obstacle avoidance, but also to temporarily store data that has been output or will be output.

[0099] In some embodiments, the first processor 201 may be composed of integrated circuits, such as a single packaged integrated circuit or multiple integrated circuits packaged with the same or different functions, including combinations of one or more central processing units (CPUs), microprocessors, digital processing chips, graphics processors, and various control chips. The first processor 201 is the control unit of the electronic device, connecting various components of the entire electronic device through various interfaces and lines. It executes programs or modules stored in the first memory 202 and calls data stored in the first memory 202 to perform various functions of the robot 200 and process data.

[0100] Figure 8 Only a robot with parts is shown; those skilled in the art will understand that... Figure 8 The structure shown does not constitute a limitation on the robot 200, and may include fewer or more parts than shown, or combine certain parts, or have different part arrangements.

[0101] The program 203 stored in the first memory 202 of the robot 200, which implements redundant robotic arm path tracking and obstacle avoidance, is a combination of multiple instructions. When run in the first processor 201, it can achieve the following:

[0102] Step 1: Determine the safe distance d between the robotic arm and the obstacle;

[0103] Step 2: Based on the specific robotic arm, construct its position-level path tracking and obstacle avoidance coupled problem, and realize the equality constraint for path tracking as f. E (θ)=r d The inequality constraint for obstacle avoidance is (p C -p O ) T (p C -p O )≥d 2 Where θ represents the joint angle position of the robotic arm, f E (θ) represents the three-dimensional coordinates of the end effector of the robotic arm at the joint angle position θ, r d p represents the desired end effector motion trajectory. C and p O Let p represent the coordinates of key point C and obstacle point O, respectively. C By constructing the kinematic equation f of the robotic arm C (θ) is obtained, representing the three-dimensional coordinates of key point C at the joint angle position θ;

[0104] Inequality constraints for obstacle avoidance (p) C -p O ) T (p C -p O )≥d 2 Transformed into equality constraints (p) using the projection operator P(·). C -p O ) T (p C -p O )-d 2 =Ρ((p C -p O ) T (p C -p O )-d 2 ), where the projection operator is defined as:

[0105]

[0106] Step 3: Define the error monitoring function e(t) as follows:

[0107]

[0108] Introducing the upper right Dini derivative, based on the evolutionary rules of the ZNN (Zero Neural Network)... After designing and simplifying, a ZNN solver was obtained:

[0109]

[0110] Where γ > 0 is the convergence parameter, J E (θ) represents the Jacobian matrix of the robotic arm's end effector, J C (θ) represents the Jacobian matrix of the key point C of the robotic arm. Indicates joint angular velocity, S is the velocity of the obstacle, and S is the mode switcher matrix consisting of the identity matrix I and the derivative Δ of the projection operator, defined as:

[0111] Δ=[Δ1,Δ2,…,Δ p ] T ,

[0112] Because the projection operator P(·) is continuous but not everywhere differentiable, it is not possible to directly differentiate the error e(t) with respect to P(z(t)). By introducing the upper right Dini derivative, the derivatives Δ of the projection operators in each row can be obtained. i for:

[0113]

[0114] Where z i (t)=[(p C -p O ) T (p C -p O )] i -d, the solution to the coupled problem is obtained through this ZNN solver, and then the joint angle position θ of the robotic arm is obtained;

[0115] Step 4: Pass the solution θ from Step 3 to the lower-level controller to drive the robotic arm to complete the specified end-effector task.

[0116] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0117] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0118] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A method for implementing path tracking and obstacle avoidance with a redundant robotic arm, characterized in that, Includes the following steps: Step 1: Determine the safe distance d between the robotic arm and the obstacle; Step 2: Based on the specific robotic arm, construct its position-level path tracking and obstacle avoidance coupled problem, and realize the equality constraint for path tracking as f. E (θ)=r d The inequality constraint for obstacle avoidance is (p C -p O ) T (p C -p O )≥d 2 Where θ represents the joint angle position of the robotic arm, f E (θ) represents the three-dimensional coordinates of the end effector of the robotic arm at the joint angle position θ, r d p represents the desired end effector motion trajectory. C and p O Let p represent the coordinates of key point C and obstacle point O, respectively. C By constructing the kinematic equation f of the robotic arm C (θ) is obtained, representing the three-dimensional coordinates of key point C at the joint angle position θ; Inequality constraints for obstacle avoidance (p) C -p O ) T (p C -p O )≥d 2 Transformed into equality constraints (p) using the projection operator P(·). C -p O ) T (p C -p O )-d 2 =Ρ((p C -p O ) T (p C -p O )-d 2 ), where the projection operator is defined as: Step 3: Define the error monitoring function e(t) as follows: Introducing the upper right Dini derivative, based on the evolutionary rules of the ZNN (Zero Neural Network)... After designing and simplifying, a ZNN solver was obtained: Where γ > 0 is the convergence parameter, J E (θ) represents the Jacobian matrix of the robotic arm's end effector, J C (θ) represents the Jacobian matrix of the key point C of the robotic arm. Indicates joint angular velocity, S is the velocity of the obstacle, and S is the mode switcher matrix consisting of the identity matrix I and the derivative Δ of the projection operator, defined as: Δ=[Δ1,Δ2,…,Δ p ] T , Because the projection operator P(·) is continuous but not everywhere differentiable, it is not possible to directly differentiate the error e(t) with respect to P(z(t)). By introducing the upper right Dini derivative, the derivatives Δ of the projection operators in each row can be obtained. i for: Where z i (t)=[(p C -p O ) T (p C -p O )] i -d, the solution to the coupled problem is obtained through this ZNN solver, and then the joint angle position θ of the robotic arm is obtained; Step 4: Pass the solution θ from Step 3 to the lower-level controller to drive the robotic arm to complete the specified end-effector task.

2. The method for achieving redundant robotic arm path tracking and obstacle avoidance according to claim 1, characterized in that, The key point C is the point on a link of the robotic arm that is closest to the obstacle point O.

3. The method for achieving redundant robotic arm path tracking and obstacle avoidance according to claim 1, characterized in that, The robotic arm consists of an end effector and seven drive joints θ1…θ7. The kinematic equation of the robotic arm is f. E (θ)=r d The inequality constraint equation is (p C -p O ) T (p C -p O )≥d 2 ,in f E (θ) represents the three-dimensional coordinates of the robotic arm's end effector at the joint angle θ, r d f represents the desired motion trajectory of the robotic arm's end effector. E (θ)=r d Used to consider path tracing constraints, (p C -p O ) T (p C -p O )≥d 2 Used to account for obstacle avoidance constraints.

4. A system for achieving redundant robotic arm path tracking and obstacle avoidance, characterized in that, It includes a safety distance module, an obstacle avoidance planning module, a robotic arm joint angle calculation module, and a robotic arm drive module; The safety distance module is used to determine the safety distance d between the robotic arm and the obstacle; The obstacle avoidance planning module is used to construct a coupled problem of position-level path tracking and obstacle avoidance for a specific robotic arm, realizing the equality constraint of path tracking as f. E (θ)=r d The inequality constraint for obstacle avoidance is (p C -p O ) T (p C -p O )≥d 2 Where θ represents the joint angle position of the robotic arm, f E (θ) represents the three-dimensional coordinates of the end effector of the robotic arm at the joint angle position θ, r d p represents the desired end effector motion trajectory. C and p O Let p represent the coordinates of key point C and obstacle point O, respectively. C By constructing the kinematic equation f of the robotic arm C (θ) is obtained, representing the three-dimensional coordinates of key point C at the joint angle position θ; Inequality constraints for obstacle avoidance (p) C -p O ) T (p C -p O )≥d 2 Transformed into equality constraints (p) using the projection operator P(·). C -p O ) T (p C -p O )-d 2 =Ρ((p C -p O ) T (p C -p O )-d 2 ), where the projection operator is defined as: The robotic arm joint angle calculation module is used to obtain the desired robotic arm joint angle position, specifically: Define the error monitoring function e(t) as: Introducing the upper right Dini derivative, based on the evolutionary rules of the ZNN (Zero Neural Network)... After designing and simplifying, a ZNN solver was obtained: Where γ > 0 is the convergence parameter, J E (θ) represents the Jacobian matrix of the robotic arm's end effector, J C (θ) represents the Jacobian matrix of the key point C of the robotic arm. Indicates joint angular velocity, S is the velocity of the obstacle, and S is the mode switcher matrix consisting of the identity matrix I and the derivative Δ of the projection operator, defined as: Δ=[Δ1,Δ2,…,Δ p ] T , Because the projection operator P(·) is continuous but not everywhere differentiable, it is not possible to directly differentiate the error e(t) with respect to P(z(t)). By introducing the upper right Dini derivative, the derivatives Δ of the projection operators in each row can be obtained. i for: Where z i (t)=[(p C -p O ) T (p C -p O )] i -d, the solution to the coupled problem is obtained through this ZNN solver, and then the joint angle position θ of the robotic arm is obtained; The robotic arm drive module is used to transmit the solution result θ of the robotic arm joint angle module to the lower-level controller to drive the robotic arm to complete the specified end-effector task.

5. A computer-readable storage medium storing a program, characterized in that, When the program is executed by the processor, it implements the method for redundant robotic arm path tracking and obstacle avoidance as described in any one of claims 1-3.

6. A robot, characterized in that, The robot includes: At least one processor; and, A memory communicatively connected to the at least one processor; wherein, The memory stores computer program instructions that can be executed by the at least one processor, which, when executed by the at least one processor, enables the at least one processor to perform a method for implementing redundant robotic arm path tracking and obstacle avoidance as described in any one of claims 1-3.

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