A redundant degree of freedom robot arm multi-path point joint space path search method

Abstract

The application discloses a redundant degree of freedom mechanical arm multi-path point joint space path searching method, which comprises the following steps: step one, a redundant degree of freedom mechanical arm model is established, and a target end position matrix of the mechanical arm at each path point specified by task demand is obtained; step two, a limited group of alternative joint angle solutions corresponding to the end position matrix of each path point is solved by an inverse kinematics solving method, and the limited group of alternative joint angle solutions of all path points are combined to form an all-process alternative joint angle solution library; step three, an improved particle swarm optimization algorithm is designed, the fitness of each particle is calculated, and iterative updating is performed; step four, the particle with the optimal fitness is extracted, and the joint angle solution of each path point corresponding to the optimal particle is outputted, so that the mechanical arm reaches the target end position. The application solves the problem that a traditional algorithm is prone to falling into a local optimal solution, realizes efficient and accurate joint space path searching of the redundant mechanical arm, and has important research value.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of mechanical arm path search, and relates to a redundant degree of freedom mechanical arm multi-path point joint space path search method. BACKGROUND

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

[0003] Traditional mechanical arm path planning methods mostly rely on geometric models and heuristic algorithms, and are mostly planned in Cartesian coordinate space. Although these methods can solve the path planning problem to some extent, they often have difficulty in dealing with complex constraint conditions in high-dimensional space. In addition, for redundant degree of freedom mechanical arms, since they can reach the same end position in three-dimensional space in multiple ways, path planning in Cartesian coordinate space cannot meet the task requirements. Therefore, the characteristics of joint space need to be considered, and the advantages and disadvantages of multiple paths need to be comprehensively evaluated to optimize the motion trajectory and ensure efficient and smooth operation.

[0004] Particle swarm optimization (PSO) is an intelligent algorithm that simulates the hunting activities of bird flocks. As an optimization method based on swarm intelligence, PSO has been widely used in various optimization problems such as function optimization, machine learning, image processing, etc. Compared with other optimization algorithms such as genetic algorithm (GA) and ant colony algorithm (ACO), PSO has a simpler mathematical model and fewer parameter settings, is easier to implement, and has a short convergence time. However, traditional PSO is prone to fall into local optimal solution when dealing with joint space path search of redundant degree of freedom mechanical arms, resulting in unsatisfactory optimization effect. This is because the updating mechanism of PSO based on current particle position and velocity may not be able to fully explore all possible solutions in complex high-dimensional space, leading to the inability to find the global optimal path in some cases. SUMMARY

[0005] In order to solve the above technical problems existing in the prior art, the application proposes a redundant degree of freedom mechanical arm multi-path point joint space path search method, which aims to improve the path search efficiency and accuracy of redundant degree of freedom mechanical arms in the case of multiple path points. The specific technical scheme is as follows:

[0006] A redundant degree of freedom mechanical arm multi-path point joint space path search method comprises:

[0007] Step one, establish a redundant degree of freedom robot arm model, get the robot in its task demand specified at each path point of the target end pose matrix;

[0008] Step two, by inverse kinematics solving method, for each path point corresponding to the end pose matrix solving a finite group of alternative joint angle solution, and all path point of the finite group of alternative joint angle solution combination, form the whole process alternative joint angle solution library;

[0009] Step three, design improved particle swarm optimization algorithm, calculate the fitness of each particle and iterative update;

[0010] Step four, extract the optimal fitness of the particle, output the optimal particle corresponding to each path point of the joint angle solution, so that the robot arm reaches the target end position.

[0011] Further, the step one, specifically includes:

[0012] S1.1, establish a redundant degree of freedom robot arm model, determine the direction of each joint rotation axis and the distance between each joint;

[0013] S1.2, according to the robot arm model in each joint to establish joint coordinate system, thus establish the standard DH parameter table of robot arm, and establish the coordinate conversion 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 corresponding mechanical arm end effector rotation direction, thus get the target end pose matrix of the robot arm at each path point.

[0015] Further, the step two, specifically includes:

[0016] S2.1, using inverse kinematics solving method based on arm angle, for each path point corresponding to the end pose matrix, solving a finite group of alternative joint angle solution;

[0017] S2.2, the finite group of alternative joint angle solution of each path point combination, form the whole process alternative joint angle solution library.

[0018] Further, in S2.1, for each path point, according to its end pose matrix to calculate the effective arm angle range, to 0.01 as the granularity of all the effective arm angle, according to each arm angle calculated to meet the joint limit joint angle solution.

[0019] Further, the step three, specifically includes:

[0020] S3.1, design an improved particle swarm optimization algorithm, and set various parameters therein, the various parameters including particle quantity, maximum cycle number, objective function, initial position of each particle, initial individual optimal value of each particle, initial local optimal value of each particle, initial particle swarm optimal value, inertia weight, individual learning factor, local learning factor, global learning factor, each particle representing a set of joint angle solutions selected by each path point;

[0021] S3.2, for each particle, calculate the fitness based on the initial position and the objective function, if the fitness is better than the current individual optimal value of the particle, update the particle individual optimal value to the fitness; if the fitness is better than the current local optimal value of the particle, update the particle local optimal value to the fitness; if the fitness is better than the current particle swarm optimal value, update the particle swarm optimal value to the fitness;

[0022] S3.3, for each particle, calculate the flight speed of the particle according to the improved particle swarm optimization algorithm formula, add the current position of each particle to the flight 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 cycle number is reached.

[0024] Further, in S3.1, the objective function is the cumulative rotation angle of all joints of the robot arm 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, and λ represents the weight parameter; the initial position of each particle is randomly generated, and the initial individual optimal value, the initial local optimal value and the initial particle swarm optimal value of each particle are all set to infinity.

[0025] Further, in S3.1, the setting of the inertia weight introduces an adaptive mechanism, which comprehensively considers the iteration number of the particle and the target value of the particle. In the initial stage, the inertia weight is increased to enhance the global search ability of the particle. When the particle flies to the vicinity of the optimal point, the inertia weight is reduced to increase the local search ability of the particle. The specific expression is as follows:

[0026] ω = μ tanh δ,

[0027] wherein,

[0028]

[0029] wherein, ω represents the inertia weight, ω max and ω mindenotes the maximum and minimum inertia weight set, iteration denotes the current iteration number of the particle, and max iteration represents the maximum iteration number set; the ratio μ quantifies the relative distance between the individual best p i,d , local best l i,d , and global best g d , 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 an increase in the value of ω, so that the search space of the particle is enlarged, and as the optimization proceeds, ω gradually decreases, prompting the particle to concentrate in the local area around the current best position.

[0030] Further, in S3.1, a joint dynamic adjustment mechanism is introduced for the individual learning factor c1, the global learning factor c2, and the local learning factor c3, and the values of the learning factors are related to the current iteration number of the particle, and the periodicity of the trigonometric function is used, in the initial stage of the search, the cos 2 term in c1 starts from a high value, encouraging the particle to explore different areas of the search space; as the optimization proceeds, c1 decreases, and c2 and c3 increase, so that the focus of the algorithm shifts to finding potential solutions, and the specific expressions are as follows:

[0031]

[0032] Where iteration denotes the current iteration number of the particle, and max iteration represents the maximum iteration number set.

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

[0034] V new = ω * V old + c1 r1 (p best -p) + c2 r2 (g best -p) + c3 r3 (l best -p),

[0035] Where V new denotes the flight speed of the particle, V old denotes the flight speed of the particle in the last iteration, r1 and r2 are random numbers between 0 and 1, p denotes the current position of the particle, p best denotes the individual best value of the current particle, g best denotes the global best value of the current particle, and l best denotes the local best value of the current particle.

[0036] Further, the step four is specifically extracting a group of particle positions with optimal fitness in all cycles and optimal fitness corresponding to the group of particle positions, outputting joint angle solutions of each path point corresponding to the group of particle positions and target function values corresponding to the group of particle positions, so that the mechanical arm reaches the target end position.

[0037] Beneficial effects: the method introduces an improved particle swarm optimization algorithm, solves the limitations of the existing redundant degree mechanical arm multi-path point path planning method, especially in the joint space path search process, the traditional algorithm is easy to fall into local optimal solution, and the method realizes efficient and accurate joint space path search of the redundant mechanical arm, and has important research value. BRIEF DESCRIPTION OF DRAWINGS

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

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

[0040] Figures 3 to 8 is a curve graph of the joint angle change with the arm angle in one case of the mechanical arm of the embodiment. DETAILED DESCRIPTION

[0041] In order to make the purpose, technical scheme and technical effect of the present application clearer, the present application is further described in detail below in combination with the drawings and examples of the specification.

[0042] The embodiment discloses a redundant degree mechanical arm multi-path point joint space path search method based on an improved particle swarm optimization algorithm, comprising the following steps:

[0043] Step one, establish a redundant degree mechanical arm model, and obtain the target end pose matrix of the mechanical arm at each path point according to the specified position of each path point. Specifically, it includes:

[0044] S1.1, establish a redundant degree mechanical arm model, including the rotation axis direction of each joint and the distance between each joint.

[0045] As shown in the table, Figure 1 The embodiment establishes a model for a 7-DOF S-R-S configuration mechanical arm.

[0046] S1.2, establish a joint coordinate system at each joint according to the mechanical arm model, thereby establishing a standard DH parameter table of the mechanical arm, and at the same time, establishing 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.

[0048] Table 1:

[0049]

[0050] wherein, d BS represents the distance between the base of the robot arm and the 2nd joint, d SE represents the distance between the 2nd joint and the 4th joint of the robot arm, d EW represents the distance between the 4th joint and the 6th joint of the robot arm, d WT represents the distance between the 6th joint and the 7th joint, i.e. the end effector of the robot arm.

[0051] S1.3, specifying the position coordinates of each path point in the world coordinate system and the corresponding rotation direction of the end effector of the robot arm at each path point, thereby obtaining the target end pose matrix of the robot arm at each path point.

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

[0053]

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

[0055] Step two, using an inverse kinematics solving method based on arm angle, solving a finite set of alternative joint angle solutions for the end pose matrix corresponding to each path point, and combining all the finite sets of alternative joint angle solutions for all path points to form a library of alternative joint angle solutions for the whole process. Specifically includes:

[0056] S2.1, since the robot arm studied has redundant degrees of freedom, for each target end pose matrix, there are no joint angles that satisfy the end pose matrix. This embodiment uses an inverse kinematics solving method based on arm angle to solve a finite set of alternative joint angle solutions for the end pose matrix corresponding to each path point.

[0057] This embodiment introduces the concept of arm angle ψ, as shown in Figure 2 .

[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] Rodrigues' formula is introduced, which is expressed as follows:

[0064] Rot(k, θ) = I + sin θ * [k x] + (1 - cos θ) * [k x] 2 , k = [k1 k2 k3] T ,

[0065] where I is a unit matrix, [k x] is the skew-symmetric matrix of k, and the formula represents the rotation matrix corresponding to the pose obtained by rotating an arbitrary vector k in three-dimensional space by an angle θ. θ1, θ2 and θ3 are solved by the following trigonometric functions.

[0066]

[0067] cos θ2 = -A s (3,2) sin ψ - B s (3,2) cos ψ - 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 x y3,

[0075] where, z0=

[001] T ,

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

[0077]

[0078] cos θ2= A w (3,3) sin ψ + B w (3,3) cos ψ + C w (3,3),

[0079]

[0080] where,

[0081] where, Next, the feasible interval of arm angle ψ is determined:

[0082] First, the mechanical limits of each joint of the robot arm are determined as shown in Table 2.

[0083] Table 2:

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

[0085] θ4 is independent of arm angle ψ, and for the other six joints, their joint angle expressions can be arranged as follows:

[0086] cos θ i = a sin ψ + b cos ψ + c, i = 2, 6 (1)

[0087]

[0088] where, 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 j = 1, 3, 5, 7, which is also arranged by referring to the formula in the previous formula.

[0089] For joint 2 and joint 6, the sum-difference product operation of the trigonometric function is performed on equation (1) to convert it to:

[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 joint 1, joint 3, joint 5, joint 7, the arm angle can be solved from the above formula (2):

[0107]

[0108] wherein,

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

[0110] b = -2a n + 2a d * tan θ,

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

[0112] Differentiating both sides of equation (2) with respect to the arm angle ψ, we get:

[0113]

[0114] in,

[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] Setting the derivative of equation (4) to 0, we can find the corresponding arm angle, i.e., the stationary point of the joint angle:

[0119]

[0120] when a t 2 +b t 2 -c t 2 <0 and c t When >0, θ generally changes with ψ as follows: Figure 3 As shown, however, due to the special properties of the tangent function, if the joint angle θ reaches ±180° within the arm angle range [-π, π], a 360° jump will occur. In this case, the change of θ with ψ is as follows: Figure 4 As shown in the figure, the feasible arm angle range can be calculated based on this figure and the joint limit.

[0121] when a t 2 +b t 2 -c t 2 <0 and c t When <0, θ generally changes with ψ as follows: Figure 5As shown, however, due to the particularity of the tangent function, if the joint angle θ reaches

[0122] ±180° within the arm angle range [-π, π], a 360° jump will occur, at which time θ changes with ψ as shown in Figure 6 Based on this figure, the feasible arm angle range can be calculated in combination with the joint limits.

[0123] When a t 2 +b t 2 -c t 2 >0, it can be seen from the analysis formula (4) that there are two stationary points of the joint angle θ at this time, let the minimum value of the joint angle be θ min , and the corresponding arm angle be ψ min ; let the maximum value of the joint angle be θ max , and the 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, θ changes with ψ as shown in Figure 7 When a t 2 +b t 2 -c t 2 >0 and c t <0, θ changes with ψ as shown in Figure 8 Take the maximum value of θ min and the lower joint limit as the actual lower joint limit, and take the minimum value of θ max and the upper joint limit as the actual upper joint limit, and based on this figure, the feasible arm angle range can be calculated in combination with the actual joint limits.

[0126] The effective arm angle range of each joint angle of the robot arm is obtained according to the above classification, and the intersection of the seven effective arm angle ranges is the effective arm angle range of the robot arm under the given end pose, and the arm angle value within the range can ensure that the corresponding joint angle does not exceed the joint limit.

[0127] S2.2, combine the finite group of alternative joint angle solutions of each path point to form a full-process alternative joint angle solution library.

[0128] In this embodiment, for each path point, the step calculates the effective arm angle range according to the end pose matrix, traverses all the effective arm angles with a granularity of 0.01, calculates the joint angle solutions that meet the joint limit according to each arm angle, and combines them together as the candidate joint angle solution library of the path point.

[0129] Step three, design an improved particle swarm optimization algorithm, calculate the fitness of each particle and update iteratively. Specifically, it includes:

[0130] S3.1, define various parameters in the improved particle swarm optimization algorithm, including 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, and each particle represents a set of joint angle solutions selected by 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, and 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 particle swarm optimal value of each particle are set to infinity; at the same time, the number of particles and the maximum number of loops are set to appropriate values.

[0132] Based on the traditional PSO, the concept of local optimal particle is introduced, which is defined as the particle with the highest 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 areas in complex optimization problems.

[0133] An adaptive mechanism is introduced for the setting of the inertia weight, which takes into account the iteration number of the particle and the target value of the particle. A larger inertia weight is used in the early stage to enhance the global search ability of the particle, and when the particle flies near the optimal point, the inertia weight is reduced to increase the local search ability of the particle. The specific expression is as follows:

[0134] ω = μtanhδ,

[0135] Where,

[0136]

[0137] Where, ω represents the inertia weight, ωmax and ω min denote the maximum and minimum values of the inertia weight set, iteration denotes the current iteration number of the particle, and max iteration represents the maximum number of iterations set. The ratio μ quantifies the relative distance between the individual best, local best, and global best of a particle, and is used to adjust the influence of the exploration behavior related to the particle's own 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 focus more on the local area around the current best position.

[0138] For the individual learning factor c1, the global learning factor c2, and the local learning factor c3, a joint dynamic adjustment mechanism of learning factors is introduced, which links the value of the learning factor to the current iteration number of the particle. By utilizing the periodicity of the trigonometric function, 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 particles to explore different regions of the search space. As the optimization progresses, c1 decreases, while c2 and c3 increase, causing the algorithm to shift its focus to finding potential solutions. This dynamic adjustment ensures that the algorithm maintains robust exploration in the early stages and smoothly transitions to fine exploitation in the later stages, thereby improving its navigation ability in the complex optimization landscape typical of robot trajectory planning. The specific expressions are as follows:

[0139]

[0140] where iteration denotes the current iteration number of the particle, and max iteration represents the maximum number of iterations set.

[0141] This step further improves the performance of the traditional PSO in the joint search of a redundant manipulator with multiple path points by introducing the concept of local optimal particles, an adaptive inertia weight mechanism, and a joint dynamic adjustment mechanism of learning factors, effectively solving the challenges faced by redundant degree of freedom manipulators in practical applications.

[0142] S3.2, for each particle, based on their initial position and the objective function, calculate the fitness, if the fitness is better than the current individual optimal value of the particle, update the individual optimal value of the particle to the fitness; if the fitness is better than the current local optimal value of the particle, update the local optimal value of the particle to the fitness; if the fitness is better than the current particle swarm optimal value, update the particle swarm optimal value to the fitness.

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

[0144] The particle flight speed calculation formula is:

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

[0146] Wherein V new represents the flight speed of the particle, V old represents the flight speed of the particle at the last iteration, r1 and r2 are random numbers between 0 and 1, p represents the current position of the particle, p best represents the current particle individual optimal value, g best represents the current particle group optimal value, l best represents the current particle local optimal value.

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

[0148] Step four, extract the particle with the optimal global fitness, output the joint angle solution of each path point corresponding to the optimal particle, so that the robot arm reaches the target end position.

[0149] Specifically, extract a group of particle positions with the optimal fitness in all cycles, and the optimal fitness corresponding to the group of particle positions, output the joint angle solution of each path point corresponding to the group of particle positions and the target function value corresponding to the group of particle positions, so that the robot arm reaches the target end position.

[0150] The above is only the preferred embodiment of the present application, and does not limit the present application in any form. Although the implementation process of the present application has been described in detail in the foregoing, those skilled in the art can still modify the technical solutions recorded in the foregoing examples, or replace some of the technical features. Any modification, equivalent replacement, etc. within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A redundant degree of freedom robotic arm multi-path point joint space path search method, characterized by, Comprise: Step one, the establishment of redundant degree of freedom robot model, get the robot in its designated at each path point of the target end pose matrix; Step two, by inverse kinematics solving method, for each path point corresponding to the end pose matrix is solved out of a finite group of candidate joint angle solution, and all path points of the finite group of candidate joint angle solution combination, form the whole process of candidate joint angle solution library; Step three, design improved particle swarm optimization algorithm, calculate the fitness of each particle and iterative update, including: S3.1, design improved particle swarm optimization algorithm, and set the various parameters, the parameters include particle number, maximum number of cycles, 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, inertia weight, individual learning factor, local learning factor, global learning factor, each particle represents a group of each path point selected joint angle solution; The setting of the inertia weight introduces the adaptive mechanism, comprehensive consideration of the iteration number of particles and the target value of the particle, the initial by increasing the inertia weight to enhance the global search ability of the particle, when the particle flight to the optimal point near, then reduce the inertia weight increases the local search ability of the particle, the specific expression as follows: ， Wherein, ， ， wherein, represents the inertia weight, and represents the set maximum and minimum values of the inertia weight, represents the current iteration number of the particle, represents the set maximum number of iterations; the ratio quantifies the relative distance between the individual best , local best and global best of the particle, and is used to adjust the influence of the exploration behavior related to the particle's self-experience; at the initial stage of the search, is close to , resulting in an increase of the value of , so that the search space of the particle is enlarged, and as the optimization proceeds, is gradually decreased, prompting the particle to concentrate in the local region around the current best position. S3.2, for each particle, based on its initial position and objective function to calculate the fitness, if the fitness is better than the current individual optimal value of the particle, the particle individual optimal value is updated to the fitness; If the fitness is better than the current local optimal value of the particle, the particle local optimal value is updated to the fitness; If the fitness is better than the current particle swarm optimal value, the particle swarm optimal value is updated to the fitness; S3.3, for each particle, according to the improved particle swarm optimization algorithm formula to calculate the flight speed of the particle, the current position of each particle and flight speed are added, the new position of the particle is obtained; S3.4, the new position of each particle is substituted into S3.2 to recalculate the new fitness, and repeat S3.2 subsequent process, until the maximum number of cycles is reached; Step four, extract the optimal fitness of the particle, output the joint angle solution of each path point corresponding to the optimal particle, so that the robot reaches the target end position.

2. The redundant degree-of-freedom robotic arm multi-path point-joint space path search method of claim 1, wherein, The step one, specifically includes: S1.1, the establishment of redundant degree of freedom robot model, determine the direction of rotation of each joint and the distance between each joint; S1.2, according to the robot model at each joint to establish joint coordinate system, thus the establishment of robot standard DH parameter table, and the establishment of the coordinate conversion 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 corresponding mechanical arm end effector rotation direction of each path point, thus get the target end pose matrix of the robot at each path point.

3. The redundant degree-of-freedom robotic arm multi-path point-joint space path search method of claim 2, wherein, The step two, specifically includes: S2.1, using the inverse kinematics solving method based on arm angle, for each path point corresponding to the end pose matrix, solve out of a finite group of candidate joint angle solution; S2.2, combining the finite set of candidate joint angle solutions of each path point to form a library of candidate joint angle solutions of the whole process.

4. The redundant degree-of-freedom robotic arm multi-path point-joint space path search method of claim 3, wherein, In S2.1, for each path point, the effective arm angle range is calculated according to the end pose matrix, all effective arm angles are traversed with a granularity of 0.01, and the joint angle solution that meets the joint limit is calculated according to each arm angle.

5. The redundant degree-of-freedom robotic arm multi-path point-joint space path search method of claim 1, wherein, In S3.1, the objective function is the cumulative rotation angle of all joints of the robotic arm throughout the entire process, i.e. ,in Indicates the first Path point joints rotation angle, Represents the number of path points. This represents the rotation angle threshold set for each joint. This represents the weighting parameter; the initial position of each particle is randomly generated, and the initial individual optimal value, initial local optimal value, and initial swarm optimal value of each particle are all set to infinity.

6. The redundant degree-of-freedom robotic arm multi-path point-joint space path search method of claim 1, wherein, In S3.1, for individual learning factor , global learning factor and local learning factor , a joint dynamic adjustment mechanism is introduced, which links the value of learning factor with the current iteration number of particle, and utilizes the periodicity of trigonometric function, in the initial stage of search, , the term starts from a high value, encouraging particles to explore different regions of search space; as the optimization proceeds, decreases, while and increase, making the algorithm focus on finding potential solutions, the specific expressions are as follows: ， ， 。 7. The redundant degree-of-freedom robotic arm multi-path point-joint-space path search method of claim 6, wherein, In S3.3, the flight speed calculation formula of the particle is: ， wherein denotes the particle flight velocity, denotes the particle flight velocity at the last iteration, and is a random number between 0 and 1, denotes the current position of the particle, denotes the current particle individual best value, denotes the current particle swarm best value, denotes the current particle local best value.

8. The redundant degree-of-freedom robotic arm multi-path point-joint space path search method of claim 1, wherein, The fourth step is specifically: extracting a set of particle positions with the optimal fitness in all cycles, and the optimal fitness corresponding to the set of particle positions, outputting the joint angle solution of each path point corresponding to the set of particle positions and the target function value corresponding to the set of particle positions, so that the mechanical arm reaches the target end position.

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