Joint-limited redundant robot arm position layer repetitive motion and obstacle avoidance method, system and robot

Abstract

The application provides a joint-restricted redundant robot arm position layer repetitive motion and obstacle avoidance method and system, and a robot. The method comprises the following steps: (1) determining a safe distance between the robot arm and the obstacle; (2) constructing a multi-task optimization scheme for the robot arm position layer repetitive motion and obstacle avoidance based on a quadratic programming (QP); (3) converting the QP problem in step (2) into a nonlinear equation set based on a nonlinear complementarity problem (NCP) function; (4) designing a zero neural network (ZNN) solver to solve the nonlinear equation set according to a ZNN evolution law; and (5) transmitting the solution in step (4) to a lower machine controller to drive the robot arm to complete a specified end task. The application designs a multi-task optimization scheme in the position layer, so that the robot arm can realize repetitive motion, obstacle avoidance and joint limit avoidance in the position layer, and can avoid physical damage of the robot arm without affecting the end task.

Description

Methods, systems, and robots for repetitive motion and obstacle avoidance at the position layer of a joint-constrained redundant robotic arm. Technical Field

[0001] This invention relates to the field of robotics, specifically to a method, system, and robot for position-layer repetitive motion and obstacle avoidance in a joint-constrained redundant robotic arm. Background Technology

[0002] A robotic arm is a mechanical device composed of rigid bodies connected by joints, and it is currently widely used in industrial manufacturing, space exploration, agricultural production, construction, and other fields. Based on their kinematic structure, robotic arms can be divided into redundant robotic arms and non-redundant robotic arms. A redundant robotic arm is one whose degrees of freedom exceed those required to perform a specified task. Due to its extra degrees of freedom, a redundant robotic arm can fulfill some secondary objectives while achieving the primary task at the end effector, such as obstacle avoidance, joint-limit avoidance, and avoidance of unusual configurations.

[0003] Repetitive motion performance indicators ensure that the joint angles of the robotic arm return to their initial positions after completing a closed path, avoiding joint angle drift. In actual operation, without obstacle avoidance, the robotic arm is prone to collisions with obstacles in the environment, leading to damage. Furthermore, when the robotic arm joints approach their joint limits, the robotic arm may suddenly stop operating due to the triggering of safety devices. Therefore, obstacle avoidance and joint limit avoidance functions ensure the continuous, safe, and reliable operation of the redundant robotic arm.

[0004] The redundancy analysis problem is a fundamental problem in the motion planning and control of redundant robotic arms. It refers to solving for the corresponding joint angles of the robotic arm given the desired trajectory of the end effector. In practical applications, the redundancy analysis problem may have multiple or even infinitely many solutions. Therefore, determining the optimal solution to the redundancy analysis problem is one of the fundamental yet challenging difficulties in redundant robotic arms. The zero-form neural network (ZNN) solver offers advantages such as high accuracy, fast solution speed, and no need for training or iterative computation, effectively solving time-varying optimization problems such as the redundancy analysis problem.

[0005] Currently, obstacle avoidance and joint limit avoidance functions are mostly implemented at the velocity level. The result of the corresponding redundancy analysis problem is the joint angular velocity, which cannot meet the needs of some robotic arms using position control. This invention designs a position-level repetitive motion and obstacle avoidance scheme for a joint-constrained redundant robotic arm. This scheme can output the joint angular position to the robotic arm to drive it to complete a given task and target, and its positioning accuracy is superior to that of the velocity-level obstacle avoidance scheme. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method, system and robot for position-layer repetitive motion and obstacle avoidance of a joint-constrained redundant robotic arm. This invention can output the joint angle position to the robotic arm under the premise of achieving obstacle avoidance and joint limit avoidance, and has high positioning accuracy, fast solution speed and no need for training and iterative calculation.

[0007] To achieve the above-mentioned objectives, the technical solution adopted is as follows:

[0008] In a first aspect, the present invention provides a method for repetitive position-layer motion and obstacle avoidance of a joint-constrained redundant robotic arm, comprising the following steps:

[0009] Step 1: Determine the safe distance d between the robotic arm and the obstacle;

[0010] Step 2: Based on the specific robotic arm, construct a multi-task optimization scheme for repetitive motion and obstacle avoidance at the position layer using quadratic programming (QP). The designed minimization objective function is the repetitive motion performance index φ(θ) = ||θ - θ0|| / 2, constrained by the Jacobian equality constraint f(θ) = r E Considering the inequality constraints for obstacle avoidance ||p C -p O ||≥d and considering the two-end constraint θ of the joint limit - ≤θ≤θ + Where θ represents the joint angle position, θ0 represents the initial joint angle position, f(θ) represents the three-dimensional coordinates of the robotic arm end effector at joint angle position θ, and r E p represents the motion trajectory of the end effector of the robotic arm. C and p O Let θ represent the coordinates of the criterion point C and the obstacle point O, respectively. + and θ - These represent the upper and lower limits of the joint angle position, respectively.

[0011] Through equivalent transformation, the above inequality constraints and double-ended constraints can be rearranged into a single inequality constraint g(θ)≤r. I This is used to consider obstacle avoidance constraints and joint limit constraints, where g(θ)=[-||p C -p O ||,θ T ,-θ T ] T r I =[-d,θ +T ,-θ -T ] T superscript T Represents the transpose of a matrix and a vector;

[0012] Step 3: Based on the nonlinear complementarity problem NCP function and KKT conditions, the QP problem in Step 2 is equivalently transformed into a nonlinear equation system h(t,y)=0, where the specific expression of the NCP function is defined as follows: δ→0 + It is the perturbation term that makes the NCP function continuously differentiable, with the symbol... It is the Hadamard product, where λ and μ are the equality constraints f(θ) = r E and the inequality constraint g(θ)≤r I The corresponding Lagrange multipliers are:

[0013]

[0014] Among them, J E J represents the Jacobian matrix of the robotic arm's end effector. C Let J be the Jacobian matrix of the criterion point C. I This indicates the inequality constraint g(θ)≤r. I The Jacobian matrix is ​​defined as:

[0015]

[0016] Where I represents the identity matrix of appropriate dimensions;

[0017] Step 4: Define the error monitoring function e(t):=h(t,y). The error monitoring function is the nonlinear equation system obtained in Step 3, and is defined according to the evolution rule of the ZNN (Zero Neural Network). A ZNN solver was designed, where γ > 0 is the convergence parameter. The optimal solution to the QP problem was obtained through the ZNN solver, and then the joint angle position θ of the robot arm was obtained.

[0018] 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.

[0019] As a preferred technical solution, the criterion point C is located on a link of a robotic arm and is closest to the obstacle point O.

[0020] 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(θ)=r E The inequality constraint equation is g(θ)≤r I , where θ = [θ1, θ2,…, θ7] T ∈R 7 f(θ) represents the three-dimensional coordinates of the robotic arm's end effector at the joint angle θ, and r EDescribes the motion trajectory of the end effector of the robotic arm, g(θ)≤r I Used to consider obstacle avoidance constraints and joint limit constraints.

[0021] As a preferred technical solution, in the position layer kinematic equation of the robotic arm, the performance index ||θ-θ0|| / 2 is designed to be minimized, and obstacle avoidance constraints and joint limit constraints are considered to establish a position layer repetitive motion and obstacle avoidance scheme for the joint-constrained redundant robotic arm.

[0022] After equivalent transformation, the position-level repetitive motion and obstacle avoidance scheme of the aforementioned joint-constrained redundant robotic arm can be uniformly represented as a general QP problem, where the objective function is to minimize the repetitive motion performance index ||θ-θ0|| / 2, constrained by the equality constraint f(θ)=r E and the inequality constraint g(θ)≤r I ;

[0023] Based on the NCP function and KKT conditions, the QP problem is equivalently transformed into a nonlinear system of equations h(t,y)=0.

[0024] As a preferred technical solution, the NCP function is continuously differentiable.

[0025] As a preferred technical solution, the NCP function is used. And define the error monitoring function e(t):=h(t,y), based on the evolutionary law. A ZNN solver was designed. Among them are:

[0026]

[0027]

[0028] And there are M, N, D1 and Both represent matrices. Both D1 and D2 represent vectors, K1 = diag{(r I -g(θ))⊙S}, K2=diag{μ⊙S} are both diagonal matrices. The symbol ⊙ represents Hadamard division, and the element μ1 in the M matrix is ​​the first row element of the μ vector. elements in a vector These are the time derivatives of θ, λ, and μ, respectively, and the elements of the N matrix. J E r E The derivative with respect to time, the D2 vector and Elements in the matrix It is the trajectory of the obstacle's movement speed, the stated In the matrix It is J C The derivative with respect to time.

[0029] Secondly, the present invention provides a method for repetitive motion of position layer and obstacle avoidance of a joint-constrained redundant robotic arm, including an obstacle avoidance task setting module, a multi-task optimization scheme construction module, an equivalent transformation module, a quadratic programming problem solving module, and a robotic arm driving module.

[0030] The obstacle avoidance task setting module is used to determine the safe distance d between the robotic arm and the obstacle;

[0031] The multi-task optimization scheme construction module is used to construct a multi-task optimization scheme for the position-level repetitive motion and obstacle avoidance based on quadratic programming (QP) for a specific robotic arm. The designed minimization objective function is the repetitive motion performance index φ(θ)=||θ-θ0|| / 2, constrained by the Jacobian equality constraint f(θ=r E Considering the inequality constraints for obstacle avoidance ||p C -p O ||≥d and considering the two-end constraint θ of the joint limit - ≤θ≤θ + Where θ represents the joint angle position, θ0 represents the initial joint angle position, f(θ) represents the three-dimensional coordinates of the robotic arm end effector at joint angle position θ, and r E p represents the motion trajectory of the end effector of the robotic arm. C and p O Let θ represent the coordinates of the criterion point C and the obstacle point O, respectively. + and θ - These represent the upper and lower limits of the joint angle position, respectively.

[0032] Through equivalent transformation, the above inequality constraints and double-ended constraints are rearranged into a single inequality constraint g(θ)≤r. I This is used to consider obstacle avoidance constraints and joint limit constraints, where g(θ)=[-||p C -p O || T ,θ T ,-θ T ] T r I =[-d,θ +T ,-θ -T ] T superscript T Represents the transpose of a matrix and a vector;

[0033] The equivalent transformation module is used to convert the QP problem in the multi-task optimization scheme construction module into a nonlinear equation system h(t,y)=0 based on the nonlinear complementarity problem NCP function and KKT conditions, where the specific expression of the NCP function is defined as follows: δ→0 + It is the perturbation term that makes the NCP function continuously differentiable, with the symbol... It is the Hadamard product, where λ and μ are the equality constraints f(θ) = r E and the inequality constraint g(θ)≤r I The corresponding Lagrange multipliers are:

[0034]

[0035] Among them, J E J represents the Jacobian matrix of the robotic arm's end effector. C Let J be the Jacobian matrix of the criterion point C. I This indicates the inequality constraint g(θ)≤r. I The Jacobian matrix is ​​defined as:

[0036]

[0037] Where I represents the identity matrix of appropriate dimensions;

[0038] The quadratic programming problem-solving module is used to solve the optimal solution to the QP problem. First, an error monitoring function e(t) := h(t,y) is defined. This error monitoring function is a system of nonlinear equations obtained from the equivalent transformation module. Then, the evolution rule of the zero-form neural network ZNN is applied. A ZNN solver was designed, where γ > 0 is the convergence parameter. The optimal solution to the QP problem was finally obtained through the ZNN solver, and then the joint angle position θ of the robot arm was obtained.

[0039] The robotic arm drive module is used to transmit the solution result θ from the quadratic programming problem solving module to the lower-level controller, driving the robotic arm to complete the specified end-effector task.

[0040] Thirdly, the present invention provides a robot including at least one processor; and,

[0041] A memory communicatively connected to the at least one processor; wherein,

[0042] 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 the position-layer repetitive motion and obstacle avoidance method of the joint-constrained redundant robotic arm.

[0043] Compared with the prior art, the present invention has the following advantages:

[0044] This invention effectively overcomes the shortcomings of conventional techniques by minimizing repetitive motion performance indicators and considering obstacle avoidance and joint limit constraints to establish a novel position-layer repetitive motion and obstacle avoidance scheme for a joint-constrained redundant robotic arm. Mathematically, this scheme can be characterized as a QP problem with a general form and constraints containing equality and inequality equations. Based on the NCP function, the QP problem is transformed into a system of nonlinear equations. A ZNN solver is designed according to the ZNN evolution rule to obtain the optimal solution to the QP problem, which is then used to drive the robotic arm's motion. This invention can meet the requirements of certain position-controlled robotic arms while achieving obstacle avoidance and joint limit 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 calculations, resulting in faster solution speed. Attached Figure Description

[0045] 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.

[0046] Figure 1 is a flowchart of the position layer repetitive motion and obstacle avoidance method of the joint-constrained redundant robotic arm according to an embodiment of the present invention.

[0047] Figure 2 is a model diagram of the simulated Franka Emika robotic arm according to an embodiment of the present invention.

[0048] Figure 3 shows the expected and actual trajectories of the end effector of the simulated Franka Emika robotic arm in an embodiment of the present invention under constrained joint angle positions.

[0049] Figure 4 shows the trajectory error of the simulated Franka Emika robotic arm in an embodiment of the present invention under constrained joint angle positions.

[0050] Figure 5 shows the variation of the shortest distance between the simulated Franka Emika robotic arm and the obstacle under constrained joint angle positions according to an embodiment of the present invention.

[0051] Figure 6 shows the change in the joint angle position of the simulated Franka Emika robotic arm under constrained joint angle position according to an embodiment of the present invention.

[0052] Figure 7 shows the change in the angular velocity of the driven joint under constrained joint angular position in the simulation of the Franka Emika robotic arm according to an embodiment of the present invention.

[0053] Figure 8 is a schematic diagram of the position layer repetitive motion and obstacle avoidance system of the joint-constrained redundant robotic arm according to an embodiment of the present invention.

[0054] Figure 9 is a schematic diagram of the structure of the robot according to an embodiment of the present invention. Detailed Implementation

[0055] 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.

[0056] 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.

[0057] Example

[0058] As shown in Figure 1, this embodiment is a method for repetitive motion of the position layer and obstacle avoidance of a joint-constrained redundant robotic arm. The method includes the following steps:

[0059] Step 1: Determine the safe distance d between the robotic arm and the obstacle;

[0060] In step one, the safe distance between the robotic arm and the obstacle is set as d.

[0061] Step 2: Based on the specific robotic arm, construct a multi-task optimization scheme for position-layer repetitive motion and obstacle avoidance using quadratic programming (QP). The final QP scheme minimizes the objective function φ(θ) = ||θ - θ0|| / 2, with Jacobi equality constraints f(θ) = r EConsidering the inequality constraint for obstacle avoidance and joint limit avoidance, g(θ)≤r I .

[0062] In step two, the equation constrains f(θ) = r. E The desired motion trajectory of the end effector can be linked to its joint angle position θ, thereby enabling motion planning and control of the end effector. This is achieved through the inequality constraint g(θ)≤r. I It can handle obstacle avoidance constraints and joint limit constraints on the robotic arm drive rod.

[0063] Step 3: Based on the NCP function and KKT conditions of the nonlinear complementary problem, the QP problem in Step 2 is equivalently transformed into a system of nonlinear equations.

[0064] In step three, corresponding Lagrangian functions are defined for the equality and inequality constraints in the QP problem, and the KKT conditions are obtained by differentiation. The NCP function is then introduced. By transforming the inequality constraints in the KKT conditions into equality constraints, the QP problem in step two is equivalently transformed into the nonlinear system of equations h(t,y)=0.

[0065] Step 4: For the nonlinear equations in Step 3, design a nullification neural network (ZNN) solver using the error monitoring function to obtain the optimal solution of the nonlinear equations in Step 3, which is also the QP problem in Step 2.

[0066] In step four, based on the nonlinear equation system h(t,y)=0 from step three, an error monitoring function e(t):=h(t,y) is defined, and the evolutionary rule is used. A ZNN solver was designed. This ZNN solver can be used to solve the nonlinear equations in step three, which is also the optimal solution θ of the QP problem in step two.

[0067] Step 5: Pass the solution θ obtained in Step 4 to the lower-level controller to drive the robotic arm to complete the specified end-effector task.

[0068] As shown in Figure 2, 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(θ) = r E Where f(θ) represents the three-dimensional coordinates of the robotic arm's end effector at the joint angle θ, and r E The motion trajectory of the robotic arm's end effector is represented by θ = [θ1, θ2, ..., θ7]. T ∈R 7 .

[0069] As shown in Figure 3, the solid line represents the expected trajectory of the simulated Franka Emika robotic arm end effector, while the dashed line represents the actual trajectory. The figure shows that the expected and actual trajectories almost perfectly overlap, indicating that this approach can achieve precise control of the robotic arm's movement with minimal error.

[0070] As shown in Figure 4, the dashed line e x dotted line e y solid line e 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, an obstacle avoidance scheme with positioning accuracy higher than that of the speed layer.

[0071] As shown in Figure 5, 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 criterion 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, it indicates that the robotic arm has not collided with the obstacle, demonstrating that the present invention can achieve obstacle avoidance.

[0072] As shown in Figure 6, 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. The upper limit of the joint angle position of the fourth drive link is set to -1.75 radians, and the lower limit of the joint angle position of the sixth drive link is set to 2.13 radians. 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 joint angle position of the fourth drive link is always no greater than -1.75 radians, and the joint angle position of the sixth drive link is always no less than 2.13 radians, indicating that the present invention can achieve joint limit avoidance functionality.

[0073] As shown in Figure 7, These represent the joint angular velocities of the first drive link 1, second drive link 2, third drive link 3, fourth drive link 4, fifth drive link 5, sixth drive link 6, and seventh drive link 7 of the simulated Franka Emika robotic arm, respectively. The upper limit of the joint angular velocity is set to... Radius / second, lower limit of joint angular velocity set to Radius per second. During task execution, the joint angular velocity of each drive link can be guaranteed to vary within a set range, demonstrating the effectiveness of this invention in handling inequality constraints and joint limit avoidance in QP problems.

[0074] This invention establishes a novel position-layer repetitive motion and obstacle avoidance scheme for a joint-constrained redundant robotic arm by minimizing the repetitive motion performance index and considering obstacle avoidance and joint limit constraints. Mathematically, this scheme can be characterized as a QP problem with a general form and constraints containing equality and inequality equations. Based on the NCP function, the QP problem is transformed into a system of nonlinear equations. A ZNN solver is designed according to the ZNN evolution rule to obtain the optimal solution to the QP problem, which is then used to drive the robotic arm's motion.

[0075] It should be noted that, for the sake of simplicity, the aforementioned method embodiments are all described as a series of actions. However, those skilled in the art should understand that the present invention is not limited to the described order of actions, because according to the present invention, some steps can be performed in other orders or simultaneously.

[0076] Based on the same concept as the position-level repetitive motion and obstacle avoidance method of the joint-constrained redundant manipulator in the above embodiments, the present invention also provides a position-level repetitive motion and obstacle avoidance system for a joint-constrained redundant manipulator. This system can be used to execute the above-described position-level repetitive motion and obstacle avoidance method for a joint-constrained redundant manipulator. For ease of explanation, the structural schematic diagram of the embodiment of the position-level repetitive motion and obstacle avoidance system for the joint-constrained redundant manipulator only shows the parts related to the embodiments of the present invention. Those skilled in the art will understand that the illustrated structure does not constitute a limitation on the device, and may include more or fewer components than illustrated, or combine certain components, or have different component arrangements.

[0077] As shown in Figure 8, in another embodiment of this application, a position-layer repetitive motion and obstacle avoidance system 100 for a joint-constrained redundant robotic arm is provided, including an obstacle avoidance task setting module 101, a multi-task optimization scheme construction module 102, an equivalent transformation module 103, a quadratic programming problem solving module 104, and a robotic arm drive module 105.

[0078] The obstacle avoidance task setting module 101 is used to determine the safe distance d between the robotic arm and the obstacle;

[0079] The multi-task optimization scheme construction module 102 is used to construct a multi-task optimization scheme for the repetitive motion and obstacle avoidance at the position layer based on quadratic programming (QP) for a specific robotic arm. The designed minimization objective function is the repetitive motion performance index φ(θ) = ||θ - θ0|| / 2, which is constrained by the Jacobian equality constraint f(θ) = r E Considering the inequality constraints for obstacle avoidance ||p C -p O||≥d and considering the two-end constraint θ of the joint limit - ≤θ≤θ + Where θ represents the joint angle position, θ0 represents the initial joint angle position, f(θ) represents the three-dimensional coordinates of the robotic arm end effector at joint angle position θ, and r E p represents the motion trajectory of the end effector of the robotic arm. C and p O Let θ represent the coordinates of the criterion point C and the obstacle point O, respectively. + and θ - These represent the upper and lower limits of the joint angle position, respectively.

[0080] Through equivalent transformation, the above inequality constraints and double-ended constraints are rearranged into a single inequality constraint g(θ)≤r. I This is used to consider obstacle avoidance constraints and joint limit constraints, where g(θ)=[-||p C -p O || T ,θ T ,-θ T ] T r I =[-d,θ +T ,-θ -T ] T superscript T Represents the transpose of a matrix and a vector;

[0081] The equivalent transformation module 103 is used to convert the QP problem in the multi-task optimization scheme construction module into a nonlinear equation system h(t,y)=0 based on the nonlinear complementary problem NCP function and KKT conditions, whereby the specific expression of the NCP function is defined as follows: δ→0 + It is the perturbation term that makes the NCP function continuously differentiable, with the symbol... It is the Hadamard product, where λ and μ are the equality constraints f(θ) = r E and the inequality constraint g(θ)≤r I The corresponding Lagrange multipliers are:

[0082]

[0083] Among them, J E J represents the Jacobian matrix of the robotic arm's end effector. C Let J be the Jacobian matrix of the criterion point C. I This indicates the inequality constraint g(θ)≤r. I The Jacobian matrix is ​​defined as:

[0084]

[0085] Where I represents the identity matrix of appropriate dimensions;

[0086] The quadratic programming problem-solving module 104 is used to solve the optimal solution of the QP problem. First, an error monitoring function e(t) := h(t,y) is defined. The error monitoring function is a set of nonlinear equations obtained by the equivalent transformation module. Then, the evolution rule of the zero-form neural network ZNN is applied. A ZNN solver was designed, where γ > 0 is the convergence parameter. The optimal solution to the QP problem was finally obtained through the ZNN solver, and then the joint angle position θ of the robot arm was obtained.

[0087] The robotic arm drive module 105 is used to transmit the solution result θ in the quadratic programming problem solving module to the lower-level controller, driving the robotic arm to complete the specified end-effector task.

[0088] It should be noted that the position-layer repetitive motion and obstacle avoidance system of the joint-constrained redundant robotic arm of the present invention corresponds one-to-one with the position-layer repetitive motion and obstacle avoidance method of the joint-constrained redundant robotic arm of the present invention. The technical features and beneficial effects described in the embodiments of the position-layer repetitive motion and obstacle avoidance method of the joint-constrained redundant robotic arm are applicable to the embodiments of position-layer repetitive motion and obstacle avoidance of the joint-constrained redundant robotic arm. For details, please refer to the description in the embodiments of the method of the present invention, which will not be repeated here.

[0089] Furthermore, in the above embodiments of the position-layer repetitive motion and obstacle avoidance system of the joint-constrained redundant robotic arm, 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 software implementation convenience. That is, the internal structure of the position-layer repetitive motion and obstacle avoidance system of the joint-constrained redundant robotic arm can be divided into different program modules to complete all or part of the functions described above.

[0090] Referring to Figure 9, in one embodiment, an electronic device is provided for implementing a position-layer repetitive motion and obstacle avoidance method for a joint-constrained redundant robotic arm. The electronic device 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 position-layer repetitive motion and obstacle avoidance program 203 for a joint-constrained redundant robotic arm.

[0091] 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 electronic device 200, such as the portable hard drive of the electronic device 200. In other embodiments, the first memory 202 can also be an external storage device of the electronic device 200, such as a plug-in portable hard drive, smart media card (SMC), secure digital card (SD), flash card, etc., equipped on the electronic device 200. Furthermore, the first memory 202 can include both internal and external storage units of the electronic device 200. The first memory 202 can be used not only to store application software and various types of data installed on the electronic device 200, such as the code for the position layer repetitive motion and obstacle avoidance program 203 of the joint-constrained redundant robotic arm, but also to temporarily store data that has been output or will be output.

[0092] In some embodiments, the first processor 201 may be composed of integrated circuits, such as a single packaged integrated circuit or multiple integrated circuits 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 electronic device 200 and process data.

[0093] Figure 9 only shows an electronic device with components. Those skilled in the art will understand that the structure shown in Figure 9 does not constitute a limitation on the electronic device 200, and may include fewer or more components than shown, or combine certain components, or have different component arrangements.

[0094] The position-layer repetitive motion and obstacle avoidance program 203 of the joint-constrained redundant robotic arm stored in the first memory 202 of the electronic device 200 is a combination of multiple instructions. When run in the first processor 201, it can achieve the following:

[0095] Step 1: Determine the safe distance d between the robotic arm and the obstacle;

[0096] Step 2: Based on the specific robotic arm, construct a multi-task optimization scheme for repetitive motion and obstacle avoidance at the position layer using quadratic programming (QP). The designed minimization objective function is the repetitive motion performance index φ(θ) = ||θ - θ0|| / 2, constrained by the Jacobian equality constraint f(θ) = r E Considering the inequality constraints for obstacle avoidance ||p C -p O ||≥d and considering the two-end constraint θ of the joint limit - ≤θ≤θ + Where θ represents the joint angle position, θ0 represents the initial joint angle position, f(θ) represents the three-dimensional coordinates of the robotic arm end effector at joint angle position θ, and r E p represents the motion trajectory of the end effector of the robotic arm. C and p O Let θ represent the coordinates of the criterion point C and the obstacle point O, respectively. + and θ - These represent the upper and lower limits of the joint angle position, respectively.

[0097] Through equivalent transformation, the above inequality constraints and double-ended constraints are rearranged into a single inequality constraint g(θ)≤r. I This is used to consider obstacle avoidance constraints and joint limit constraints, where g(θ)=[-||p C -p O || T ,θ T ,-θ T ] T r I =[-d,θ +T ,-θ -T ] T superscript T Represents the transpose of a matrix and a vector;

[0098] Step 3: Based on the nonlinear complementarity problem NCP function and KKT conditions, the QP problem in Step 2 is equivalently transformed into a nonlinear equation system h(t,y)=0, where the specific expression of the NCP function is defined as follows: δ→0 + It is the perturbation term that makes the NCP function continuously differentiable, with the symbol... It is the Hadamard product, where λ and μ are the equality constraints f(θ) = r E and the inequality constraint g(θ)≤r I The corresponding Lagrange multipliers are:

[0099]

[0100] Among them, J EJ represents the Jacobian matrix of the robotic arm's end effector. C Let J be the Jacobian matrix of the criterion point C. I This indicates the inequality constraint g(θ)≤r. I The Jacobian matrix is ​​defined as:

[0101]

[0102] Where I represents the identity matrix of appropriate dimensions;

[0103] Step 4: Define the error monitoring function e(t):=h(t,y). The error monitoring function is the nonlinear equation system obtained in Step 3, and is defined according to the evolution rule of the ZNN (Zero Neural Network). A ZNN solver was designed, where γ > 0 is the convergence parameter. The optimal solution to the QP problem was obtained through the ZNN solver, and then the joint angle position θ of the robot arm was obtained.

[0104] 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.

[0105] Furthermore, if the modules / units integrated in the electronic device 200 are implemented as software functional units and sold or used as independent products, they can be stored in a non-volatile computer-readable storage medium. The computer-readable medium may include: any entity or device capable of carrying the computer program code, a recording medium, a USB flash drive, a portable hard drive, a magnetic disk, an optical disk, a computer memory, or a read-only memory (ROM).

[0106] 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 described above. 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 RAMbus dynamic RAM (RDRAM), etc.

[0107] 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.

[0108] 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 repetitive position-layer motion and obstacle avoidance in a joint-constrained redundant robotic arm, characterized in that, The process includes the following steps: Step 1, determining the safe distance d between the robotic arm and the obstacle; Step 2, constructing a multi-task optimization scheme for the robotic arm based on quadratic programming (QP) for repetitive motion at the position layer and obstacle avoidance, with the designed minimization objective function being the repetitive motion performance index φ(θ)=||θ-θ0|| / 2, constrained by the Jacobian equality constraint f(θ=r E Considering the inequality constraints for obstacle avoidance ||p C -p O ||≥d and considering the two-end constraint θ of the joint limit - ≤θ≤θ + Where θ represents the joint angle position, θ0 represents the initial joint angle position, f(θ) represents the three-dimensional coordinates of the robotic arm end effector at joint angle position θ, and r E p represents the motion trajectory of the end effector of the robotic arm. C and p O Let θ represent the coordinates of the criterion point C and the obstacle point O, respectively. + and θ - These represent the upper and lower limits of the joint angle position, respectively. Through equivalent transformation, the above inequality constraints and double-ended constraints are rearranged into a single inequality constraint g(θ)≤r. I This is used to consider obstacle avoidance constraints and joint limit constraints, where g(θ)=[-||p C -p O || T ,θ T ,-θ T ] T r I =[-d,θ +T ,-θ -T ] T superscript T Representing the transpose of matrices and vectors; Step 3: Based on the nonlinear complementarity problem NCP function and KKT conditions, the QP problem in Step 2 is equivalently transformed into the nonlinear equation system h(t,y)=0, where the specific expression of the NCP function is defined as δ→0 + It is the perturbation term that makes the NCP function continuously differentiable, with the symbol... It is the Hadamard product, where λ and μ are the equality constraints f(θ) = r E and the inequality constraint g(θ)≤r I The corresponding Lagrange multipliers are: Among them, J E J represents the Jacobian matrix of the robotic arm's end effector. C Let J be the Jacobian matrix of the criterion point C. I This indicates the inequality constraint g(θ)≤r. I The Jacobian matrix is ​​defined as: Where I represents an identity matrix of appropriate dimension; Step 4: Define the error monitoring function e(t):=h(t,y), the error monitoring function is the nonlinear equation system obtained in Step 3, according to the evolution rule of the zero-dimensional neural network ZNN. A ZNN solver is designed, where γ > 0 is the convergence parameter. The optimal solution to the QP problem is obtained through the ZNN solver, and then the joint angle position θ of the robotic arm is obtained. Step 5: The solution result θ in step 4 is passed to the lower computer controller to drive the robotic arm to complete the specified end-effector task.

2. The method for repetitive position-layer motion and obstacle avoidance of a joint-constrained redundant robotic arm according to claim 1, characterized in that, The criterion point C is on a link of a robotic arm and is closest to the obstacle point O.

3. The method for repetitive motion and obstacle avoidance at the position layer of a joint-constrained redundant robotic arm 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(θ)=r E The inequality constraint equation is g(θ)≤r I , where θ = [θ1, θ2,…, θ7] T ∈R 7 f(θ) represents the three-dimensional coordinates of the robotic arm's end effector at the joint angle θ, and r E Describes the motion trajectory of the end effector of the robotic arm, g(θ)≤r I Used to consider obstacle avoidance constraints and joint limit constraints.

4. The method for repetitive position-layer motion and obstacle avoidance of a joint-constrained redundant robotic arm according to claim 3, characterized in that, In the position layer kinematic equations of the robotic arm, the performance index ||θ-θ0|| / 2 is designed to be minimized, and obstacle avoidance constraints and joint limit constraints are considered to establish a position layer repetitive motion and obstacle avoidance scheme for the joint-constrained redundant robotic arm. After equivalent transformation, the position-level repetitive motion and obstacle avoidance scheme of the aforementioned joint-constrained redundant robotic arm can be uniformly represented as a general QP problem, where the objective function is to minimize the repetitive motion performance index ||θ-θ0|| / 2, constrained by the equality constraint f(θ)=r E and the inequality constraint g(θ)≤r I Based on the NCP function and KKT conditions, the QP problem is equivalently transformed into a nonlinear system of equations h(t,y)=0.

5. The method for repetitive position-layer motion and obstacle avoidance of a joint-constrained redundant robotic arm according to claim 4, characterized in that, The NCP function is continuously differentiable.

6. The method for repetitive position-layer motion and obstacle avoidance of a joint-constrained redundant robotic arm according to claim 1, characterized in that, By using the NCP function And define the error monitoring function e(t):=h(t,y), based on the evolutionary law. A ZNN solver was designed. Among them are: And there are M, N, D1 and Both represent matrices. Both D1 and D2 represent vectors, K1 = diag{(r I -g(θ))⊙S}, K2=diag{μ⊙S} are both diagonal matrices. The symbol ⊙ represents Hadamard division, and the element μ1 in the M matrix is ​​the first row element of the μ vector. elements in a vector These are the time derivatives of θ, λ, and μ, respectively, and the elements of the N matrix. J E r E The derivative with respect to time, the D2 vector and Elements in the matrix It is the trajectory of the obstacle's movement speed, the stated In the matrix It is J C The derivative with respect to time.

7. A position-layer repetitive motion and obstacle avoidance system for a joint-constrained redundant robotic arm, characterized in that, The method for position-level repetitive motion and obstacle avoidance of a joint-constrained redundant robotic arm according to any one of claims 1-6 includes an obstacle avoidance task setting module, a multi-task optimization scheme construction module, an equivalent transformation module, a quadratic programming problem solving module, and a robotic arm driving module. The obstacle avoidance task setting module is used to determine the safe distance d between the robotic arm and the obstacle. The multi-task optimization scheme construction module is used to construct a multi-task optimization scheme for position-level repetitive motion and obstacle avoidance based on quadratic programming (QP) for a specific robotic arm. The designed minimum objective function is the repetitive motion performance index φ(θ) = ||θ - θ0|| / 2, constrained by the Jacobian equality constraint f(θ) = r E Considering the inequality constraints for obstacle avoidance ||p C -p O ||≥d and considering the two-end constraint θ of the joint limit - ≤θ≤θ + Where θ represents the joint angle position, θ0 represents the initial joint angle position, f(θ) represents the three-dimensional coordinates of the robotic arm end effector at joint angle position θ, and r E p represents the motion trajectory of the end effector of the robotic arm. C and p O Let θ represent the coordinates of the criterion point C and the obstacle point O, respectively. + and θ - These represent the upper and lower limits of the joint angle position, respectively. Through equivalent transformation, the above inequality constraints and double-ended constraints are rearranged into a single inequality constraint g(θ)≤r. I This is used to consider obstacle avoidance constraints and joint limit constraints, where g(θ)=[-||p C -p O || T ,θ T ,-θ T ] T r I =[-d,θ +T ,-θ -T ] T superscript T Represents the transpose of a matrix and a vector; The equivalent transformation module is used to convert the QP problem in the multi-task optimization scheme construction module into a nonlinear equation system h(t,y)=0 based on the nonlinear complementarity problem NCP function and KKT conditions, where the specific expression of the NCP function is defined as follows: δ→0 + It is the perturbation term that makes the NCP function continuously differentiable, with the symbol... It is the Hadamard product, where λ and μ are the equality constraints f(θ) = r E and the inequality constraint g(θ)≤r I The corresponding Lagrange multipliers are: Among them, J E J represents the Jacobian matrix of the robotic arm's end effector. C Let J be the Jacobian matrix of the criterion point C. I This indicates the inequality constraint g(θ)≤r. I The Jacobian matrix is ​​defined as: Where I represents an identity matrix of appropriate dimension; the quadratic programming problem-solving module is used to solve the optimal solution to the QP problem. First, an error monitoring function e(t):=h(t,y) is defined. The error monitoring function is a set of nonlinear equations obtained by the equivalent transformation module, and then the evolution rule of the zero-form neural network ZNN is applied. A ZNN solver was designed, where γ > 0 is the convergence parameter. The optimal solution to the QP problem is obtained through the 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 in the quadratic programming problem solving module to the lower-level controller to drive the robotic arm to complete the specified end-effector task.

8. 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 executable by the at least one processor, the computer program instructions being executed by the at least one processor to enable the at least one processor to perform the position-layer repetitive motion and obstacle avoidance method of the joint-constrained redundant robotic arm as described in any one of claims 1-6.

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