Multi-path-point joint space path searching method for redundant-degree-of-freedom mechanical arm

Abstract

The invention discloses a redundant degree-of-freedom mechanical arm multi-path-point joint space path searching method which comprises the following steps: step 1, establishing a redundant degree-of-freedom mechanical arm model, and acquiring a target tail end pose matrix of the mechanical arm at each path point specified by a task demand of the mechanical arm; step 2, through an inverse kinematics solving method, solving a limited group of alternative joint angle solutions for the tail end pose matrix corresponding to each path point, and combining the limited group of alternative joint angle solutions of all path points to form a whole-process alternative joint angle solution library; 3, designing an improved particle swarm optimization algorithm, calculating the fitness of each particle, and carrying out iterative updating; and fourthly, the particles with the optimal fitness are extracted, the joint angle solutions of all the path points corresponding to the optimal particles are output, and the mechanical arm reaches the target tail end position. According to the method, the problem that a traditional algorithm is prone to falling into a local optimal solution is solved, efficient and accurate joint space path searching of the redundant mechanical arm is achieved, and the important research value is achieved.

Description

Technical Field

[0001] The present invention belongs to the field of robotic arm path search, and relates to a multi-path point joint space path search method for a redundant degree-of-freedom robotic arm. Background Art

[0002] With the rapid development of automation technology, redundant degree-of-freedom robotic arms have been widely used in various fields such as industrial production, medical treatment, service, and household due to their flexibility and adaptability. Compared with traditional 6-degree-of-freedom robotic arms, redundant degree-of-freedom robotic arms can execute diverse tasks more effectively in complex environments; however, the increase in redundant degrees of freedom also brings complexity to robotic arm path planning, especially in joint space path planning. How to effectively search for the optimal path is one of the current research focuses.

[0003] Most traditional robotic arm path planning methods rely on geometric models and heuristic algorithms, and mostly perform planning for the Cartesian coordinate space. Although they can solve path planning problems to a certain extent, they often struggle to handle complex constraint conditions in high-dimensional spaces; in addition, for redundant degree-of-freedom robotic arms, since they can reach the same end position in multiple ways in three-dimensional space, path planning for redundant degree-of-freedom robotic arms in the Cartesian coordinate space cannot meet the task requirements. It is necessary to consider the characteristics of the joint space, comprehensively evaluate the advantages and disadvantages of multiple paths, so as to optimize the motion trajectory and ensure efficient and stable operation.

[0004] The Particle Swarm Optimization (PSO) algorithm is an intelligent algorithm that simulates the foraging activities of bird flocks. As an optimization method based on swarm intelligence, it has been widely applied to various optimization problems, such as function optimization, machine learning, image processing, etc. Compared with other optimization algorithms such as the Genetic Algorithm (GA) and the Ant Colony Optimization (ACO), PSO has a simpler mathematical model and fewer parameter settings, is easier to implement, and is easy to control, with a short convergence time. However, when traditional PSO is used to handle the joint space path search of redundant degree-of-freedom robotic arms, it is prone to falling into local optimal solutions, resulting in unsatisfactory optimization effects. This is because the update mechanism of PSO based on the current particle position and velocity may not be able to fully explore all possible solutions in complex high-dimensional spaces, resulting in its inability to find the global optimal path in some cases. Summary of the Invention

[0005] In order to solve the above technical problems existing in the prior art, the present invention proposes a multi-path point joint space path search method for a redundant degree-of-freedom robotic arm, aiming to improve the path search efficiency and accuracy of a redundant degree-of-freedom robotic arm in the case of multiple path points. The specific technical solution is as follows:

[0006] A multi-path point joint space path search method for a redundant degree-of-freedom robotic arm, comprising:

[0007] Step 1: Establish a redundant degree-of-freedom robotic arm model and obtain the target end-effector pose matrix at each path point specified by the task requirements of the robotic arm;

[0008] Step 2: Through the inverse kinematics solution method, solve a finite set of alternative joint angle solutions for the end-effector pose matrix corresponding to each path point, and combine the finite sets of alternative joint angle solutions for all path points to form a full-process alternative joint angle solution library;

[0009] Step 3: Design an improved particle swarm optimization algorithm, calculate the fitness of each particle and perform iterative updates;

[0010] Step 4: Extract the particle with the optimal fitness and output the joint angle solutions of each path point corresponding to the optimal particle, so that the robotic arm reaches the target end position.

[0011] Further, Step 1 specifically includes:

[0012] S1.1: Establish a redundant degree-of-freedom robotic arm model, determine the rotational axis directions of each joint and the distances between each joint;

[0013] S1.2: Establish joint coordinate systems at each joint according to this robotic arm model, thereby establishing a standard DH parameter table for the robotic arm and establishing a coordinate transformation matrix between the world coordinate system and the first joint coordinate system;

[0014] S1.3: Specify the position coordinates of each path point in the world coordinate system and the rotational directions of the end-effector of the robotic arm corresponding to each path point, thereby obtaining the target end-effector pose matrix of the robotic arm at each path point.

[0015] Further, Step 2 specifically includes:

[0016] S2.1: Adopt an inverse kinematics solution method based on the arm angle, and solve a finite set of alternative joint angle solutions for the end-effector pose matrix corresponding to each path point;

[0017] S2.2: Combine the finite sets of alternative joint angle solutions for each path point to form a full-process alternative joint angle solution library.

[0018] Further, in S2.1, for each path point, calculate the effective arm angle range according to its end-effector pose matrix, traverse all effective arm angles with a granularity of 0.01, and calculate the joint angle solutions that meet the joint limits according to each arm angle.

[0019] Further, Step 3 specifically includes:

[0020] S3.1. Design an improved particle swarm optimization algorithm and set its various parameters, including the number of particles, the maximum number of iterations, the objective function, the initial position of each particle, the initial personal best value of each particle, the initial local best value of each particle, the initial global best value of the particle swarm, the inertia weight, the personal learning factor, the local learning factor, and the global learning factor. Each particle represents a set of joint angle solutions selected for each path point.

[0021] S3.2. For each particle, calculate the fitness based on its initial position and the objective function. If the fitness is better than the current personal best value of the particle, update the personal best value of the particle to this fitness. If the fitness is better than the current local best value of the particle, update the local best value of the particle to this fitness. If the fitness is better than the current global best value of the particle swarm, update the global best value of the particle swarm to this fitness.

[0022] S3.3. For each particle, calculate the flying speed of the particle according to the improved particle swarm optimization algorithm formula, and add the current position of each particle to the flying speed to obtain the new position of the particle.

[0023] S3.4. Substitute the new position of each particle into S3.2 to recalculate the new fitness, and repeat the subsequent process of S3.2 until the maximum number of iterations is reached.

[0024] Furthermore, in S3.1, the objective function is the cumulative rotation angle of all joints of the robotic arm throughout the process, that is where θ i,j represents the rotation angle of joint j at the i-th path point, n represents the number of path points, τ j represents the rotation angle threshold set for each joint, and λ represents the weight parameter; the initial position of each particle is randomly generated, and the initial personal best value, initial local best value, and initial global best value of each particle are all set to infinity.

[0025] Furthermore, in S3.1, an adaptive mechanism is introduced for setting the inertia weight. Considering the iteration number of the particle and the objective value of the particle comprehensively, at the beginning, the inertia weight is increased to enhance the global search ability of the particle. When a particle flies near the optimal point, the inertia weight is decreased to increase the local search ability of the particle. The specific expression is as follows:

[0026] ω = μtanhδ,

[0027] where,

[0028]

[0029] where, ω represents the inertia weight, ω max and ω minrepresents the maximum and minimum values of the set inertia weight, iteration represents the current iteration number of the particle, and max_iteration represents the set maximum number of loops; the ratio μ quantifies the relative distance between the individual best p i,d , the local best l i,d and the global best g d , which is used to adjust the influence of the exploration behavior related to the particle's self-experience; in the initial stage of the search, δ is close to ω max , resulting in an increase in the value of ω, expanding the particle search space. As the optimization progresses, ω gradually decreases, prompting the particle to concentrate in the local area near the current best position.

[0030] Further, in S3.1, for the individual learning factor c1, the global learning factor c2, and the local learning factor c3, a joint dynamic adjustment mechanism for the learning factors is introduced. The values of the learning factors are associated with the current iteration number of the particle, and using the periodic characteristics of trigonometric functions, in the initial stage of the search, the cos 2 term in c1 starts from a high value, encouraging the particle to explore different regions of the search space; as the optimization progresses, c1 decreases while c2 and c3 increase, shifting the focus of the algorithm to finding potential solutions. The specific expressions are as follows:

[0031]

[0032] where iteration represents the current iteration number of the particle, and max_iteration represents the set maximum number of loops.

[0033] Further, in S3.3, the formula for calculating the flight speed of the particle is:

[0034] V new = ω * V old + c1r1(p best - p) + c2r2(g best - p) + c3r3(l best - p),

[0035] where V new represents the particle flight speed, V old represents the flight speed of the particle in the previous iteration, r1 and r2 are random numbers between 0 and 1, p represents the current position of the particle, p best represents the individual optimal value of the current particle, g best represents the population optimal value of the current particle, and l best represents the local optimal value of the current particle.

[0036] Further, step four is specifically as follows: extract a set of particle positions with the optimal fitness in all loops, as well as the optimal fitness corresponding to this set of particle positions, and output the joint angle solutions of each path point corresponding to this set of particle positions and the corresponding objective function values, so that the robotic arm reaches the target end position.

[0037] Beneficial effects: By introducing an improved particle swarm optimization algorithm, the method of the present invention solves the limitations existing in the multi-path point path planning method for robotic arms with redundant degrees of freedom in the prior art, especially the problem that traditional algorithms are prone to fall into local optimal solutions during the joint space path search process. Moreover, this method realizes efficient and accurate joint space path search for redundant robotic arms, and has important research value. Description of the Drawings

[0038] Figure 1 is a schematic diagram of the 7-DOF S-R-S configuration robotic arm model of this embodiment;

[0039] Figure 2 is a schematic diagram of the concept of the arm angle parameter introduced in this embodiment;

[0040] Figures 3 to 8 is a curve graph of the joint angle changing with the arm angle in one case of the robotic arm of this embodiment. Detailed Embodiment

[0041] In order to make the objectives, technical solutions, and technical effects of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the drawings in the specification and embodiments.

[0042] This embodiment discloses a multi-path point joint space path search method for a robotic arm with redundant degrees of freedom based on an improved particle swarm optimization algorithm, including the following steps:

[0043] Step one: Establish a robotic arm model with redundant degrees of freedom, and obtain the target end pose matrix of the robotic arm at each path point according to the specified positions of each path point. Specifically, it includes:

[0044] S1.1: Establish a robotic arm model with redundant degrees of freedom, including the rotation axis directions of each joint and the distances between each joint.

[0045] As Figure 1 shown, this embodiment establishes a model for a 7-DOF S-R-S configuration robotic arm.

[0046] S1.2: Establish joint coordinate systems at each joint according to this robotic arm model, thereby establishing a standard DH parameter table for the robotic arm. At the same time, establish a coordinate transformation matrix between the world coordinate system and the first joint coordinate system.

[0047] The standard DH parameter table is shown in Table 1 below.

[0048] Table 1:

[0049]

[0050] Among them, d BS represents the distance between the base of the robotic arm and the second joint, d SE represents the distance between the second joint and the fourth joint of the robotic arm, d EW represents the distance between the fourth joint and the sixth joint of the robotic arm, d WT represents the distance between the sixth joint and the seventh joint of the robotic arm, i.e., the end effector.

[0051] S1.3. Specify the position coordinates of each path point in the world coordinate system and the rotation direction of the end effector of the robotic arm corresponding to each path point, so as to obtain the target end pose matrix of the robotic arm at each path point.

[0052] The expression of the target end pose matrix of the robotic arm at each path point is as follows:

[0053]

[0054] Among them, [nx, ny, nz] respectively represent the projection components of the unit vector in the positive X-axis direction of the end coordinate system of the robotic arm on the X, Y, and Z axes in the world coordinate system. [ox, oy, oz] respectively represent the projection components of the unit vector in the positive Y-axis direction of the end coordinate system of the robotic arm on the X, Y, and Z axes in the world coordinate system. [ax, ay, az] respectively represent the projection components of the unit vector in the positive Z-axis direction of the end coordinate system of the robotic arm on the X, Y, and Z axes in the world coordinate system. [px, py, pz] respectively represent the components of the position of the end effector of the robotic arm on the X, Y, and Z axes in the world coordinate system.

[0055] Step 2. Adopt an inverse kinematics solution method based on the arm angle to solve a finite set of alternative joint angle solutions for the end pose matrix corresponding to each path point, and combine the finite sets of alternative joint angle solutions of all path points to form a whole-process alternative joint angle solution library. Specifically, it includes:

[0056] S2.1. Since the robotic arm under study has redundant degrees of freedom, for each target end pose matrix, there are countless sets of joint angles that satisfy this end pose matrix. In this embodiment, an inverse kinematics solution method based on the arm angle is adopted to solve a finite set of alternative joint angle solutions for the end pose matrix corresponding to each path point.

[0057] In this embodiment, the concept of arm angle ψ is introduced, as Figure 2 shown.

[0058] For θ4:

[0059] p SW = [-d WT *ax + px - d WT *ay + py - d WT *az + pz] T ,

[0060]

[0061] θ4 = π - ∠SEW,

[0062] For θ1, θ2, and θ3:

[0063] Introduce the Rodriguez formula, the expression is as follows:

[0064] Rot(k,θ) = I + sinθ * [k×] + (1 - cosθ)[k×] 2 , k = [k1 k2 k3] T ,

[0065] where, I is the identity matrix, [k×] is the skew-symmetric matrix of k, and this formula represents the rotation matrix corresponding to the attitude obtained by rotating the angle θ around any vector k in three-dimensional space. Solve θ1, θ2, θ3 by the following trigonometric functions.

[0066]

[0067] cosθ2 = -A s (3,2)sinψ - B s (3,2)cosψ - C s (3,2),

[0068]

[0069] where,

[0070] where, u SW is the unit vector corresponding to p SW .

[0071] where,

[0072] y3 = -Rot(k,∠ESW),

[0073] x3 = (p SW + y3 * d SE + cos(θ4) * d EW ) / (sin(θ4) * d EW ),

[0074] z3 = x3 × y3,

[0075] Among them, z0 =

[001] T ,

[0076] For θ5, θ6, and θ7, they are solved by the following trigonometric functions:

[0077]

[0078] cosθ2 = A w (3,3)sinψ + B w (3,3)cosψ + C w (3,3),

[0079]

[0080] Among them,

[0081] Among them, Next, determine the feasible range of the arm angle ψ:

[0082] First, determine the mechanical limits of each joint of the robotic arm as shown in Table 2 below.

[0083] Table 2:

[0084] Joint i Lower limit of joint Upper limit of joint 1 -170° 170° 2 -120° 120° 3 -170° 170° 4 -120° 120° 5 -170° 170° 6 -120° 120° 7 -170° 170°

[0085] θ4 has nothing to do with the arm angle ψ. For the other 6 joints, their joint angle expressions can be sorted out as follows:

[0086] cosθ i = asinψ + bcosψ + c, i = 2, 6 (1)

[0087]

[0088] Among them, i = 2, 6. For θ2, a = -A s (3,2), b = -B s (3,2), c = -C s (3,2); for θ6, a = A w (3,3), b = B w (3,3), c = C w (3,3); the same is true for the cases of j = 1, 3, 5, 7, which are all sorted out and expressed according to the formulas in the previous text.

[0089] For Joint 2 and Joint 6, perform the sum-to-product operation of trigonometric functions on Equation (1) and transform it into:

[0090]

[0091] is one of the conversion parameters.

[0092] Definition:

[0093]

[0094] When Z min > 1 or Z max < -1,

[0095]

[0096] When Z min < -1 and -1 ≤ Z max ≤ 1,

[0097]

[0098] When Z min < -1 and Z max > 1,

[0099] ψ ∈ [-π, π];

[0100] When -1 ≤ Z min < 1 and -1 ≤ Z max ≤ 1,

[0101]

[0102] When 1 ≤ Z min < 1 and Z max > 1,

[0103]

[0104] When a = b = 0,

[0105] ψ ∈ [-π, π];

[0106] For joints 1, 3, 5, 7, the arm angles can be solved from the above formula (2) as follows:

[0107]

[0108] Where,

[0109] a = tanθ * c d - b d * tanθ - c n + b n ,

[0110] b = -2a n + 2a d * tanθ,

[0111] c = tanθ * cd +b d *tanθ - c n -b n ,

[0112] Taking the derivative of both sides of Equation (2) with respect to the arm angle ψ gives:

[0113]

[0114] where,

[0115] a t = b d c n -b n c d ,

[0116] b t = a n c d -a d c n ,

[0117] c t = a n b d -a d b n ,

[0118] Letting the derivative in Equation (4) be 0, the corresponding arm angle can be obtained, that is, the stationary points of the joint angle are:

[0119]

[0120] When a t 2 +b t 2 -c t 2 < 0 and c t > 0, generally, the variation of θ with ψ is as shown in Figure 3 . However, due to the particularity of the tangent function, if within the arm angle range [-π, π], the joint angle θ reaches ±180°, then a 360° jump will occur. At this time, the variation of θ with ψ is as shown in Figure 4 . Based on this figure and combined with the joint limit, the feasible arm angle interval can be calculated.

[0121] When a t 2 +b t 2 -c t 2 < 0 and c t < 0, generally, the variation of θ with ψ is as shown in Figure 5As shown, however, due to the particularity of the tangent function, if within the arm angle range [-π, π], the joint angle θ reaches

[0122] ±180°, a 360° jump will occur. At this time, the variation of θ with ψ is as Figure 6 shown. Based on this figure and combined with joint limits, the feasible arm angle interval can be calculated.

[0123] When a t 2 +b t 2 -c t 2 >0, analyzing Equation (4) shows that there are two stationary points for the joint angle θ at this time. Let the minimum value of the joint angle be θ min , and its corresponding arm angle be ψ min ; let the maximum value of the joint angle be θ max , and its corresponding arm angle be ψ max , that is:

[0124]

[0125] When a t 2 +b t 2 -c t 2 >0 and c t >0, the variation of θ with ψ is as Figure 7 shown. When a t 2 +b t 2 -c t 2 >0 and c t <0, the variation of θ with ψ is as Figure 8 shown. Take the larger value of θ min and the lower joint limit as the actual lower joint limit, and take the smaller value of θ max and the upper joint limit as the actual upper joint limit. Based on this figure and combined with the actual joint limits, the feasible arm angle interval can be calculated.

[0126] For each joint of the robotic arm, find the corresponding effective arm angle interval according to the above classification. Taking the intersection of the 7 effective arm angle intervals can obtain the effective arm angle range of the robotic arm under the given end pose. The arm angle values within this range can ensure that the corresponding joint angles do not exceed the joint limits.

[0127] S2.2. Combine the finite sets of alternative joint angle solutions for each path point to form a library of alternative joint angle solutions for the whole process.

[0128] In this embodiment, for each path point, the effective arm angle range is calculated according to its end pose matrix. All effective arm angles are traversed at a granularity of 0.01, and the joint angle solutions that meet the joint limits are calculated for each arm angle and combined together as the alternative joint angle solution library for this path point.

[0129] Step 3: Design an improved particle swarm optimization algorithm, calculate the fitness of each particle and perform iterative updates. Specifically, it includes:

[0130] S3.1: Define each parameter in the improved particle swarm optimization algorithm. Each parameter includes the number of particles, the maximum number of iterations, the objective function, the initial position of each particle, the initial individual optimal value of each particle, the initial local optimal value of each particle, the initial global optimal value of the particle swarm, the inertia weight, the individual learning factor, the local learning factor, and the global learning factor. Each particle represents a set of joint angle solutions selected for each path point.

[0131] The objective function is the cumulative rotation angle of all joints in the whole process, that is where θ i,j represents the rotation angle of joint j at the i-th path point, n represents the number of path points, τ j represents the rotation angle threshold set for each joint, λ represents the weight parameter; and the initial position of each particle is randomly generated. Since the goal is to make the objective function as small as possible, the initial individual optimal value, the initial local optimal value, and the initial global optimal value of each particle are all set to infinity; at the same time, the number of particles and the maximum number of iterations are set to appropriate values.

[0132] Based on the traditional PSO, the concept of local optimal particles is introduced. The local optimal particles are defined as the particles with the best fitness among the current particle and its two adjacent particles in the search space. By integrating this local neighborhood information, the algorithm can more accurately understand its local search environment, which significantly improves the algorithm's ability to explore key regions in complex optimization problems.

[0133] For the setting of the inertia weight, an adaptive mechanism is introduced, which comprehensively considers the iteration number of the particles and the objective value of the particles. A larger inertia weight is used in the initial stage to enhance the global search ability of the particles. When a particle flies near the optimal point, the inertia weight is reduced to increase the local search ability of the particles. The specific expression is as follows:

[0134] ω = μtanhδ,

[0135] where,

[0136]

[0137] where, ω represents the inertia weight, ωmax and ω min represent the maximum and minimum values of the set inertial weight, iteration represents the current iteration number of the particle, and max_iteration represents the set maximum number of loops. The ratio μ quantifies the relative distances among the particle's individual best, local best, and global best, and is used to adjust the influence of the exploration behavior related to the particle's self-experience. In the initial stage of the search, δ is close to ω max , resulting in a relatively large value of ω, which enables the particles to explore a wider search space and enhances their global detection ability. As the optimization progresses, ω gradually decreases, prompting the particles to concentrate more on the local area near the current best position.

[0138] For the individual learning factor c1, global learning factor c2, and local learning factor c3, a learning factor joint dynamic adjustment mechanism is introduced, which associates the values of the learning factors with the current iteration number of the particle. Utilizing the periodic characteristics of trigonometric functions, exploration and exploitation are adaptively balanced throughout the optimization process. In the initial stage of the search (t = 0), the cos 2 term in c1 starts from a very high value, encouraging the particles to explore different regions of the search space. As the optimization progresses, c1 decreases while c2 and c3 increase, shifting the focus of the algorithm towards finding potential solutions. This dynamic adjustment ensures that the algorithm maintains robust exploration in the early stage and smoothly transitions to fine exploitation in the later stage, thereby improving its navigation ability in the typical complex optimization landscape of robot trajectory planning. The specific expressions are as follows:

[0139]

[0140] where iteration represents the current iteration number of the particle, and max_iteration represents the set maximum number of loops.

[0141] This step further improves the traditional PSO by introducing the concepts of local optimal particles, an adaptive mechanism for inertial weight, and a learning factor joint dynamic adjustment mechanism, which can further enhance its performance in the multi-path point joint search of redundant manipulators, thus effectively solving the challenges faced by redundant degree-of-freedom manipulators in practical applications.

[0142] S3.2. For each particle, calculate the fitness based on their initial positions and the objective function. If the fitness is better than the current individual best value of the particle, update the particle's individual best value to this fitness; if the fitness is better than the current local best value of the particle, update the particle's local best value to this fitness; if the fitness is better than the current global best value of the particle swarm, update the global best value of the particle swarm to this fitness.

[0143] S3.3. For each particle, calculate the flight speed of the particle according to the improved particle swarm optimization algorithm formula, and add the current position of each particle to the flight speed to obtain the new position of the particle.

[0144] The formula for calculating the flight speed of the particle is as follows:

[0145] V new = ωV old + c1r1(p best - p) + c2r2(g best - p) + c3r3(l best - p),

[0146] where V new represents the flight speed of the particle, V old represents the flight speed of the particle in the previous iteration, r1 and r2 are random numbers between 0 and 1, p represents the current position of the particle, p best represents the individual optimal value of the current particle, g best represents the global optimal value of the current particle swarm, and l best represents the local optimal value of the current particle.

[0147] S3.4. Substitute the new position of each particle into S3.2 to recalculate the new fitness, and repeat the subsequent process of S3.2 until the maximum number of iterations is reached.

[0148] Step Four: Extract the particle with the optimal global fitness, and output the joint angle solutions of each path point corresponding to the optimal particle, so that the robotic arm reaches the target end position.

[0149] Specifically, extract a set of particle positions with the optimal fitness in all loops, as well as the optimal fitness corresponding to this set of particle positions, and output the joint angle solutions of each path point corresponding to this set of particle positions and their corresponding objective function values, so that the robotic arm reaches the target end position.

[0150] As described above, the above is only the preferred embodiment of the present invention, and does not impose any form of limitation on the present invention. Although the implementation process of the present invention has been described in detail above, for those familiar with the field, they can still modify the technical solutions recorded in the foregoing examples, or make equivalent replacements for some of the technical features. Any modifications, equivalent replacements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A multi-path point joint space path search method for a redundant degree-of-freedom robotic arm, characterized in that, Including: Step 1: Establish a redundant degree-of-freedom robotic arm model, and obtain the target end pose matrix of the robotic arm at each specified path point; Step 2: Through the inverse kinematics solution method, solve a finite set of alternative joint angle solutions for the end pose matrix corresponding to each path point, and combine the finite sets of alternative joint angle solutions of all path points to form a whole-process alternative joint angle solution library; Step 3: Design an improved particle swarm optimization algorithm, calculate the fitness of each particle and perform iterative updates; Step 4: Extract the particle with the optimal fitness, and output the joint angle solutions of each path point corresponding to the optimal particle, so that the robotic arm reaches the target end position.

2. The redundant degree-of-freedom robotic arm multi-path point joint space path search method according to claim 1, wherein The specific content of Step 1 includes: S1.1: Establish a redundant degree-of-freedom robotic arm model, determine the rotation axis directions of each joint and the distances between each joint; S1.2: Establish joint coordinate systems at each joint according to this robotic arm model, thereby establish a standard DH parameter table of the robotic arm, and establish a coordinate transformation matrix between the world coordinate system and the first joint coordinate system; S1.3: Specify the position coordinates of each path point in the world coordinate system and the rotation direction of the end effector of the robotic arm corresponding to each path point, thereby obtain the target end pose matrix of the robotic arm at each path point.

3. The multi-path point joint space path search method for a redundant degree-of-freedom robotic arm according to claim 2, characterized in that, The specific content of Step 2 includes: S2.1: Adopt an inverse kinematics solution method based on the arm angle, and solve a finite set of alternative joint angle solutions for the end pose matrix corresponding to each path point; S2.2: Combine the finite sets of alternative joint angle solutions of each path point to form a whole-process alternative joint angle solution library.

4. The redundant degree-of-freedom robotic arm multi-path point joint space path search method according to claim 3, wherein In S2.1, for each path point, calculate the effective arm angle range according to its end pose matrix, traverse all effective arm angles with a granularity of 0.01, and calculate the joint angle solutions that meet the joint limits according to each arm angle.

5. The redundant degree-of-freedom robotic arm multi-path point joint space path search method according to claim 3, characterized in that, The specific content of Step 3 includes: S3.1: Design an improved particle swarm optimization algorithm and set each parameter therein. Each parameter includes the number of particles, the maximum number of loops, the objective function, the initial position of each particle, the initial individual optimal value of each particle, the initial local optimal value of each particle, the initial particle swarm optimal value, the inertia weight, the individual learning factor, the local learning factor, the global learning factor. Each particle represents a set of joint angle solutions selected for each path point; S3.2: For each particle, calculate the fitness based on its initial position and the objective function. If the fitness is better than the current individual optimal value of this particle, update the individual optimal value of this particle to this fitness; if the fitness is better than the current local optimal value of this particle, update the local optimal value of this particle to this fitness; if the fitness is better than the current particle swarm optimal value, update the particle swarm optimal value to this fitness; S3.3: For each particle, calculate the flight speed of this particle according to the improved particle swarm optimization algorithm formula, and add the current position of each particle to the flight speed to obtain the new position of the particle; S3.4: Substitute the new position of each particle into S3.2 to recalculate the new fitness, and repeat the subsequent process of S3.2 until the maximum number of loops is reached.

6. The redundant degree-of-freedom robotic arm multi-path point joint space path search method according to claim 5, wherein, In S3.1, the objective function is the cumulative rotation angle of all joints of the robotic arm throughout the process, that is where θ i,j represents the rotation angle of joint j at the i-th path point, n represents the number of path points, and τ j represents the rotation angle threshold set for each joint, λ represents the weight parameter; the initial position of each particle is randomly generated, and the initial individual optimum value, the initial local optimum value, and the initial particle swarm optimum value of each particle are all set to infinity.

7. The multi-path point joint space path search method for a redundant degree-of-freedom robotic arm according to claim 5, characterized in that, In S3.1, the setting of the inertia weight introduces an adaptive mechanism, comprehensively considering the iteration times of the particles and the objective values of the particles. In the initial stage, the global search ability of the particles is enhanced by increasing the inertia weight. When a particle flies near the optimal point, the inertia weight is reduced to increase the local search ability of the particles. The specific expression is as follows: ω = μtanhδ, where, where ω represents the inertia weight, ω max and ω min represent the maximum and minimum values of the set inertia weight, iteration represents the current iteration number of the particle, and max_iteration represents the set maximum number of loops; the ratio μ quantifies the relative distance between the individual best p i,d of the particle, the local best l i,d and the global best g d to adjust the influence of the exploration behavior related to the particle's self-experience; in the initial stage of the search, δ is close to ω max , resulting in an increase in the value of ω, expanding the particle search space. As the optimization progresses, ω gradually decreases, prompting the particle to concentrate in the local area near the current best position.

8. The multi-path point joint space path search method for a redundant degree-of-freedom robotic arm according to claim 5, wherein, In S3.1, for the individual learning factor c1, the global learning factor c2, and the local learning factor c3, a joint dynamic adjustment mechanism for the learning factors is introduced. The values of the learning factors are associated with the current iteration number of the particle, and using the periodic characteristics of trigonometric functions, at the initial stage of the search, the cos 2 term in c1 starts from a high value, encouraging the particle to explore different regions of the search space; as the optimization progresses, c1 decreases while c2 and c3 increase, shifting the focus of the algorithm towards finding potential solutions. The specific expressions are as follows: where iteration represents the current iteration times of the particle, and max_iteration represents the set maximum number of loops.

9. The redundant degree-of-freedom robotic arm multi-path point joint space path search method according to claim 5, wherein In S3.3, the calculation formula for the flying speed of the particle is: V new = ω * V old + c1r1(p best - p) + c2r2(g best - p) + c3r3(l best - p), Among which V new represents the particle flight speed, V old represents the particle flight speed in the previous iteration, r1 and r2 are random numbers between 0 and 1, p represents the current position of the particle, p best represents the current individual optimal value of the particle, g best represents the current global optimal value of the particle swarm, l best represents the current local optimal value of the particle.

10. The multi-path point joint space path search method for a redundant degree-of-freedom robotic arm according to claim 5, characterized in that The specific content of the fourth step is as follows: Extract a set of particle positions with the optimal fitness in all loops, as well as the optimal fitness corresponding to this set of particle positions, and output the joint angle solutions of each path point corresponding to this set of particle positions and their corresponding objective function values, so that the robotic arm reaches the target end position.

Images