Mechanical arm time optimal trajectory planning method based on improved salat swarm optimization algorithm

Abstract

The invention relates to the technical field of multi-degree-of-freedom mechanical arm control, in particular to a mechanical arm time optimal trajectory planning method based on an improved salat swarm optimization algorithm, which aims at time optimization, optimizes the working time of a mechanical arm and ensures that the mechanical arm always moves under constraint conditions. Specifically, five improvement strategies including cubic chaos-refraction reverse learning initialization, self-adaptive auditory sensitivity, an elite pool weighted guide search behavior, a spiral Levy flight predation behavior and a salmons warning behavior are provided for an original salmons swarm optimization algorithm, the problem that the convergence efficiency of the salmons swarm optimization algorithm is low is solved, and the working efficiency of a mechanical arm is improved; and a motion track is constructed through a 5-7-5 polynomial interpolation function, so that stable transition of the whole track of the mechanical arm in the motion process is ensured, sudden speed change or jitter is avoided, abrasion and energy consumption of the mechanical arm are reduced, and good dynamic performance is achieved.

Description

Technical Field

[0001] The invention relates to the technical field of multi-degree-of-freedom robotic arm control, and in particular to a method for time-optimal trajectory planning of a robotic arm based on an improved sand cat swarm optimization algorithm. Background Art

[0002] With the rapid development of industrial automation and robotics, robotic arms, as their core executive components, play an irreplaceable role in many fields such as precision manufacturing, advanced medical care, smart agriculture and even deep space exploration. The trajectory planning of the robotic arm is a key link in its motion control, which directly affects the operation efficiency, accuracy and safety. Through effective trajectory planning, the robotic arm can move efficiently in the workspace and accurately complete various complex tasks.

[0003] In the context of pursuing efficient production, trajectory planning time has become a key indicator for measuring the performance of the robot arm. By optimizing the trajectory planning time indicator, not only can the robot arm's operation process be accelerated, but it can also better meet the actual application scenario's demand for efficient operation, promoting the dual improvement of production efficiency and quality.

[0004] Currently, traditional optimization algorithms, such as genetic algorithms and particle swarm optimization algorithms, are often faced with problems such as poor global search capabilities, slow convergence speed, and easy to fall into local optimal solutions in the application process of time-optimal trajectory planning. It is difficult to ensure that the trajectory is smooth, continuous and without mutations while ensuring the optimal planning time. Summary of the invention

[0005] The object of the present invention is to provide a method for time optimal trajectory planning of a robotic arm based on an improved sand cat swarm optimization algorithm, aiming to ensure the stable operation of the robotic arm while improving the working efficiency of the robotic arm.

[0006] To achieve the above object, the present invention provides a method for time optimal trajectory planning of a manipulator based on an improved sand cat swarm optimization algorithm, comprising the following steps:

[0007] Step 1: According to the established robot arm kinematic model, the mapping relationship between the joint space and the end effector Cartesian space is established;

[0008] Step 2: For a given path point in Cartesian space, the interpolation angles of each joint of the robot arm in the joint space are obtained through the mapping relationship constructed in step 1 and the inverse kinematics solution;

[0009] Step 3: Use the 5-7-5 mixed polynomial interpolation function to generate smooth and continuous position, velocity, acceleration, and jerk trajectories based on the interpolation angles in the joint space;

[0010] Step 4: Based on the kinematic constraints, optimize the motion trajectory with the goal of time optimization;

[0011] Step 5: Taking the motion time in each segment of trajectory planning as the optimization target, the improved sand cat swarm optimization algorithm is used to optimize the robot arm trajectory running time;

[0012] Step 6: According to the time optimization principle, output the optimal solution for the optimized robot arm trajectory planning.

[0013] Optionally, the transformation relationship of the connecting rod i-1 coordinate system relative to the i coordinate system in step 1 is expressed by a homogeneous transformation matrix:

[0014]

[0015] Among them, θ i is the angle of rotation around the z-axis of the i coordinate system, d i is the distance of translation along the z-axis of the i coordinate system, α i is the angle of rotation around the x-axis of the i coordinate system, a i is the distance translated along the x-axis of the i coordinate system.

[0016] Optionally, in step 3, according to the interpolation angle of the joint space, the movement of each joint is regarded as consisting of multiple continuous segments, and the interpolation function corresponding to each joint is generated using the 5-7-5 mixed polynomial method; the equation of the segmented trajectory is expressed as follows:

[0017]

[0018] Among them, l ik (t) represents the polynomial trajectory at the kth part of the ith joint, a i1k Represents the kth coefficient of the first-stage interpolation function of the i-th joint trajectory.

[0019] Optionally, the optimization objective function expression in step 4 is as follows:

[0020]

[0021] Where T is the total running time of the robot. j is the time of the jth point, n is the number of path points;

[0022] The kinematic constraints are defined as:

[0023]

[0024] Among them, Q imax ,V imax ,A imax ,J imaxare the maximum angular displacement, maximum angular velocity, maximum angular acceleration and maximum angular jerk of the i-th joint, q i (t),v i (t),a i (t),j i (t) are the angle, angular velocity, angular acceleration and angular jerk of the i-th joint respectively.

[0025] Optionally, the execution process of step 5 includes the following steps:

[0026] Step 5.1: Generate the initial population through cubic chaos-refraction reverse learning;

[0027] Step 5.2: Calculate the fitness function value of the sand cat individuals, that is, the total running time of each joint of the robot arm represented by each individual, compare the fitness function value of each initial individual, and take the individual with the smallest function value as the global and local optimal solution;

[0028] Step 5.3: According to the balance factor R, the algorithm is selected to execute the exploration or development behavior strategy, and the position of the individual population is updated according to the corresponding action strategy. If |R|>1, the sand cat exploration behavior is executed, otherwise the sand cat predation behavior is executed;

[0029] Step 5.4: Execute the sand cat vigilance behavior strategy and update the current position of the sand cat individual in space;

[0030] Step 5.5: Determine whether the updated individual position, i.e., the running time of each stage, meets the constraint conditions of the robot trajectory operation in step 4. If so, recalculate the fitness value corresponding to the individual according to the updated individual position information. Otherwise, jump to steps 5.3 and 5.4 to re-update the qualified individuals.

[0031] Step 5.6: Based on the updated fitness value, update the global optimal solution and the local optimal solution;

[0032] Step 5.7: According to the time optimization principle, output the optimal solution for the optimized robot arm trajectory planning.

[0033] The present invention provides a method for time optimal trajectory planning of a manipulator based on an improved sand cat swarm optimization algorithm. With time optimization as the goal, the working time of the manipulator is optimized, and it is ensured that the manipulator always moves under constraints. Specifically, five improvement strategies are proposed for the original sand cat swarm optimization algorithm: cubic chaos-refractive reverse learning initialization, adaptive auditory sensitivity, elite pool weighted guided search behavior, spiral Levy flight predation behavior, and sand cat vigilance behavior. The problem of slow convergence efficiency of the sand cat swarm algorithm is improved, and the working efficiency of the manipulator is improved. In addition, a motion trajectory is constructed through a 5-7-5 polynomial interpolation function to ensure a smooth transition of the overall trajectory of the manipulator during the motion process, avoid sudden speed changes or jitters, reduce the wear and energy consumption of the manipulator, and achieve good dynamic performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0035] Figure 1 The present invention is a schematic flow chart of the steps of a method for time optimal trajectory planning of a manipulator based on an improved sand cat swarm optimization algorithm.

[0036] Figure 2 It is a schematic diagram of the convergence of the fitness value of joint 1 over time of the improved sand cat swarm optimization algorithm and the comparison algorithm according to a specific embodiment of the present invention.

[0037] Figure 3 It is a schematic diagram of the convergence of the fitness value of the improved sand cat swarm optimization algorithm and the comparison algorithm at joint 2 over time according to a specific embodiment of the present invention.

[0038] Figure 4 It is a schematic diagram of the convergence of the fitness value of the improved sand cat swarm optimization algorithm and the comparison algorithm at joint 3 over time according to a specific embodiment of the present invention.

[0039] Figure 5 It is a schematic diagram of the convergence of the fitness value of the improved sand cat swarm optimization algorithm and the comparison algorithm at joint 4 over time according to a specific embodiment of the present invention.

[0040] Figure 6 It is a schematic diagram of the convergence of the fitness value of the improved sand cat swarm optimization algorithm and the comparison algorithm at joint 5 over time according to a specific embodiment of the present invention.

[0041] Figure 7 It is a schematic diagram of the convergence of the fitness value of the improved sand cat swarm optimization algorithm and the comparison algorithm at joint 6 over time according to a specific embodiment of the present invention.

[0042] Figure 8 It is a curve diagram of the front angular displacement optimized by the improved sand cat swarm algorithm in a specific embodiment of the present invention.

[0043] Fig. 9 It is a graph of angular velocity before optimization by the improved sand cat swarm algorithm in a specific embodiment of the present invention.

[0044] Fig.10 It is a graph of the front angular acceleration optimized by the improved sand cat swarm algorithm in a specific embodiment of the present invention.

[0045] Fig.11 It is a graph of the front angular acceleration optimized by the improved sand cat swarm algorithm in a specific embodiment of the present invention.

[0046] Fig.12 It is a graph of angular displacement after optimization by the improved sand cat swarm algorithm in a specific embodiment of the present invention.

[0047] Fig.13 It is a graph of angular velocity after optimization of the improved sand cat swarm algorithm in a specific embodiment of the present invention.

[0048] Fig.14 It is a graph of angular acceleration after optimization of the improved sand cat swarm algorithm in a specific embodiment of the present invention.

[0049] Fig.15 It is a graph of angular acceleration after optimization of the improved sand cat swarm algorithm in a specific embodiment of the present invention. DETAILED DESCRIPTION

[0050] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limiting the present invention.

[0051] The present invention provides a method for time optimal trajectory planning of a manipulator based on an improved sand cat swarm optimization algorithm, comprising the following steps:

[0052] Step 1: According to the established robot arm kinematic model, the mapping relationship between the joint space and the end effector Cartesian space is established;

[0053] Step 2: For a given path point in Cartesian space, the interpolation angles of each joint of the robot arm in the joint space are obtained through the mapping relationship constructed in step 1 and the inverse kinematics solution;

[0054] Step 3: Use the 5-7-5 mixed polynomial interpolation function to generate smooth and continuous position, velocity, acceleration, and jerk trajectories based on the interpolation angles in the joint space;

[0055] Step 4: Based on the kinematic constraints, optimize the motion trajectory with the goal of time optimization;

[0056] Step 5: Taking the motion time in each segment of trajectory planning as the optimization target, the improved sand cat swarm optimization algorithm is used to optimize the robot arm trajectory running time;

[0057] Step 6: According to the time optimization principle, output the optimal solution for the optimized robot arm trajectory planning.

[0058] The specific robot arm space trajectory planning method process is as follows Figure 1 As shown, the following is further described in conjunction with specific embodiments and execution steps:

[0059] Step 1: According to the established robot kinematic model, the mapping relationship between the robot joint space and the end Cartesian space is obtained:

[0060] Knowing the angles of each link of the robot and the coordinate system parameters of the other links, the position and posture of the end effector can be solved to achieve position control and trajectory planning of the robot. In the DH coordinate system of the robot, the transformation relationship of the link i-1 coordinate system relative to the i coordinate system can be expressed by the homogeneous transformation matrix as follows:

[0061]

[0062] Taking a six-degree-of-freedom robotic arm as an example, its DH parameters are shown in the following table:

[0063]

[0064] Among them, θ i is the angle of rotation around the z-axis of the i coordinate system, d i is the distance of translation along the z-axis of the i coordinate system, α i is the angle of rotation around the x-axis of the i coordinate system, a i is the distance translated along the x-axis of the i coordinate system.

[0065] According to the above table and combined with the transformation matrix between the links, the pose transformation matrix of the robot link end coordinate system relative to the base coordinate system is obtained as follows:

[0066]

[0067] Step 2: Based on the path points of the robot in Cartesian space, the interpolation angles of each joint of the robot in the joint space are obtained by inverting the mapping relationship in step 1:

[0068] The path points that the robot arm needs to traverse in Cartesian space include the initial point, two path points and the end point. Through inverse kinematics solution, each path point in Cartesian space is mapped back to the joint space to obtain the corresponding joint angle.

[0069] Step 3: Based on the interpolation angles of each joint of the robot in the joint space in step 2, use the 5-7-5 mixed polynomial interpolation function to generate the continuous trajectory equations of the position, velocity and acceleration of the robot:

[0070] According to the joint space interpolation points obtained in step 2, the movement of each joint is regarded as consisting of multiple continuous segments, and the interpolation function corresponding to each joint is generated using the 5-7-5 mixed polynomial method. The equations of each segment trajectory are as follows:

[0071]

[0072] Among them, l ik (t) represents the polynomial trajectory at the kth part of the ith joint, a i1k Represents the kth coefficient of the first-stage interpolation function of the i-th joint trajectory. According to the constraints of the multi-time polynomial, the displacement of each joint's initial point, two path points and end point is known, the position, velocity, acceleration and jerk between the path points, that is, the third-order derivative of the trajectory are continuous at the two middle path points, and the velocity, acceleration and jerk between the starting point and the end point are 0. Solve the polynomial to obtain the relationship matrix A between the joint interpolation points and the coefficients. The solution is as follows:

[0073]

[0074] θ=[x i0 0 0 0 x i3 0 0 0 x i1 x i1 x i2 x i2 0 0 0 0 0 0 0 0] T

[0075] a=A -1 θ

[0076] Among them, θ represents the displacement matrix of the joint angle, a represents the coefficient matrix of the trajectory curve, and x ij represents the displacement of the j-th segment interpolation of the ith joint.

[0077] Step 4: Based on the kinematic constraints, the motion trajectory is optimized with the time optimal as the goal, that is, the fitness function is obtained based on the optimization target requirements and constraints, and the optimization target function is defined as:

[0078]

[0079] Where T is the total running time of the robot. j is the time of the jth point, and n is the number of path points.

[0080] The kinematic constraints are defined as:

[0081]

[0082] Among them, Q imax ,V imax ,A imax ,J imax are the maximum angular displacement, maximum angular velocity, maximum angular acceleration and maximum angular jerk of the i-th joint, q i (t),v i (t),a i (t),j i (t) are the angle, angular velocity, angular acceleration and angular jerk of the i-th joint respectively.

[0083] Step 5: Taking the motion time in each segment of trajectory planning as the optimization target, the improved sand cat swarm optimization algorithm is used to optimize the robot arm trajectory running time, which specifically includes the following steps:

[0084] S1: Generate the initial population through cubic chaos-refraction reverse learning. The cubic chaos operator formula is as follows:

[0085]

[0086] y i+1 =4y i 3 -3y i

[0087] -1 <y i <1,y i ≠0; i=0,1,2,…n

[0088] Among them, X(i) is the population position after the cubic chaos map is initialized, and n represents the population size. First, a randomly generated d-dimensional vector y is used on n d-dimensional populations. 1 As the first operator, each dimension value is between [-1,1], and then each dimension of the first operator is traversed to generate the remaining (n-1) operators. Finally, the data obtained by the cubic chaos operator is mapped to the population to obtain the initial solution.

[0089] After using cubic chaos mapping to generate the initial solution, the refraction reverse learning strategy is introduced to expand the search range by generating reverse positions. In two-dimensional coordinates, the x-axis represents the search range and the y-axis represents the convex lens. Through lens imaging, the projection of object X on the x-axis is X * , the projection of height h is h * , the functional relationship is specifically expressed as follows:

[0090]

[0091] Among them, l b with u b Represents the upper and lower bounds of the position, transforms the above formula, and obtains the reverse solution X * The expression is:

[0092]

[0093] Among them, X * is the reverse solution of the initial solution obtained by the current search agent after refraction reverse learning. Using greedy selection, a better population is selected as the initial population between the initial solution of the chaotic mapping and the refraction reverse solution, which is expressed as follows:

[0094]

[0095] Where Pos(i) represents the position of the i-th sand cat individual, f(X(i)) and f(X * (i)) are search agents X(i) and X * (i) The fitness value of

[0096] S2: Calculate the fitness function value of the sand cat individuals, that is, the running time of each joint of the robot arm represented by each individual at each stage, compare the fitness function value of each initial individual, and take the individual with the smallest function value as the global and local optimal solution;

[0097] S3: Select an algorithm to execute exploration or development behavior strategy according to the balance factor R, and update the position of the individual population according to the corresponding action strategy, including:

[0098] r represents the sensitivity of the sand cat to low-frequency noise:

[0099] r=r G ×rand(0,1)

[0100] As the number of iterations increases, r G Represents a linearly decreasing sensitivity range from 2 to 0, expressed as:

[0101]

[0102] Among them, the sensitivity range of the sand cat is 2~0kHz, so S M The value of is 2; further, the present invention proposes an adaptive hearing sensitivity range r G Substituting the above formula, it can be expressed as:

[0103]

[0104] Among them, max_t is the maximum number of iterations, t is the current number of iterations, and the disturbance factor k∈(1,3) controls the decreasing amplitude of the auditory sensitivity range. The larger k is, the smaller the decreasing amplitude of the auditory sensitivity range is, and vice versa. rand(0,1) represents a random number from 0 to 1.

[0105] The balance factor R of the sand cat population behavior strategy is expressed as:

[0106] R = 2 × r G ×rand(0,1)-r G

[0107] Action strategies include:

[0108] If |R|>1, the sand cat exploration behavior is performed, and the position update equation is described as:

[0109] Pos(t+1)=r×(Pos bc (t)-rand(0,1)×Pos c (t))

[0110] In the formula, Pos(t+1) represents the updated position, t represents the current number of iterations, and Pos bc (t) represents the optimal candidate position, Pos c (t) represents the current position of the sand cat.

[0111] Furthermore, the present invention proposes an elite pool weighted guided exploration behavior strategy to replace the exploration behavior position update formula of the above-mentioned original sand cat group optimization algorithm, and updates the current position of the sand cat individual in space. The elite pool set is obtained by the formula:

[0112] Pos s (i) = {Pos(k):f(Pos(k)) <f(Pos(t))and i≠k},where i=1,2,…,N and k

[0113] ∈{1,2,......,N}

[0114] In the formula, Pos s(i) is the elite pool individual position set of the i-th sand cat, Pos(k) is the population member with a better objective function value than the i-th sand cat, and f(Pos(k)) is its objective function value. Weighted summation of each dimension of the elite pool individual position information is performed:

[0115]

[0116] Among them, q represents the number of individuals in the elite pool of the i-th sand cat in the current iteration, D q represents the weighted average of the individual positions in the elite pool of sand cats. rand{-1,1} represents the random increase or decrease of the position solution to provide opportunities to change the direction of the agent, so as to make a good scan of the given search space in all possible directions. Is a vector of the dimensions of the target optimization problem, and the components of each dimension are random numbers generated from the interval (1,2). The operation "*" represents the Hadamard product of two vectors (that is, all components of the result vector are formed by multiplying the corresponding components of the two given vectors). Generate a randomly sorted sequence P∈(1,q), introduce a probabilistic selection mechanism, and select an individual from the elite pool as a reference individual:

[0117]

[0118] Therefore, the position update formula of the elite pool weighted guided search strategy is:

[0119]

[0120] Among them, Pos b (t) is the position information of the current individual after the last iteration.

[0121] If |R|≤1, the sand cat predation behavior is executed, and the position update equation is described as:

[0122] Pos rnd =|rand(0,1)×Pos best (t)-pos c (t)|

[0123] Pos(t+1)=Pos best (t)-r×Pos rnd ×cos(θ)

[0124] Among them, Pos best (t) represents the global optimal position of the population, and θ is an arbitrary angle between 0 and 360 randomly generated based on the roulette wheel. rnd Represents a random position generated between the best position and the current position.

[0125] Furthermore, the present invention proposes a spiral Levy flight predation strategy to replace the predation behavior position update formula of the above-mentioned original sand cat group optimization algorithm to update the current position of the sand cat individual in space. The position update formula is expressed as follows:

[0126] Pos(t+1)=Pos best (t)-e zl ×cos(2πl)×r×Pos rnd ×Levy(D)

[0127] Where Levy(D) is the step size, which follows a Levy random distribution, D represents the dimension of the position vector, r is a constant used to define the shape of the logarithmic spiral, and l represents a random number in the range [-1,1].

[0128]

[0129] The adaptive spiral factor z is expressed as follows:

[0130]

[0131] Among them, μ represents a constant, the parameter z changes with the number of iterations, and the shape of the helix is ​​dynamically adjusted according to the value of the cosine function. The parameter l update formula is as follows:

[0132]

[0133] When the coefficient l is initially in the range of [-1, 1], it eventually evolves to the new domain [-2, 0] as the iteration proceeds. The algorithm improves the development accuracy of later iterations by lowering the final distance lower limit of the parameter l value range.

[0134] S4: Furthermore, the present invention adds the alert behavior of sand cats on the basis of the original sand cat group optimization algorithm behavior, and updates the current position of the sand cat individual in space. When the sand cat is at the edge of the group and its fitness is higher than the global optimal value, it needs to quickly escape to the vicinity of the global optimal position:

[0135] Pos(b(i+1))=Pos best (t)+β|Pos b (b(i))-Pos best (t)|

[0136] Among them, b(i) represents the i-th individual in the randomly selected vigilant sand cat set, and the vigilant sand cats account for 30% of the sand cat population. b(b(i)) and Pos(b(i+1)) represent the positions of the alert sand cat before and after the update, respectively, and β is a random number that conforms to the standard normal distribution. When the sand cat is in the middle of the group, that is, the fitness value is equal to the current global optimal solution, it realizes that there may be danger and needs to change its position to get closer to other sand cats to avoid being preyed on. An adaptive Gauss-Cauchy mutation perturbation is proposed, and the formula is expressed as follows:

[0137] X(b(i+1))=Pos best (t)×(1+μ 1 ×Gauss(σ)+μ 2 ×cauchy(σ)

[0138] Among them, Pos(b(i+1)) is the optimal position Pos of the group in the tth iteration best (t) is the position after the Gauss-Cauchy mutation perturbation, Gauss(σ) is the Gauss mutation operator, Gauss(σ) is the Cauchy mutation operator, μ 1 =1-(t / T) 2 , μ 2 =(t / T) 2 , the weight coefficient of the mutation operator changes gradually in a nonlinear way to ensure that each iterative disturbance is uniform and smooth. At the same time, through the horizontal crossover operation, two different individuals are cross-operated on the same dimension, so that different individuals can learn from each other, split the solution space of the multidimensional problem into a semi-group hypercube, and search the edge of the space, while reducing blind spots and improving the global optimization ability of the algorithm, so as to jump out of the local optimal solution. The specific expression is as follows:

[0139]

[0140] Among them, r 1 and r 2 are all random numbers in [0,1], c 1 and c 2 are all random numbers within [-1,1]. After performing the adaptive Gaussian-Cauchy mutation perturbation and lateral crossover operations, the greedy strategy is used to determine the position update to select a better position to jump out of the local optimum, which is specifically expressed as follows:

[0141]

[0142] S5: Determine whether the updated individual position, i.e., the running time of each stage, meets the constraint conditions of the robot trajectory operation in step 4. If so, recalculate the fitness value corresponding to the individual according to the updated individual position information. Otherwise, jump to S3 and S4 to re-update the qualified individuals.

[0143] S6: Based on the updated fitness value, update the global optimal solution and the local optimal solution;

[0144] S7: Determine whether the algorithm has reached the maximum number of iterations. If so, terminate and output the current global optimal solution. Otherwise, jump to S3 and continue iterating.

[0145] Step 6: According to the time optimization principle, output the optimal solution for the optimized robot arm trajectory planning.

[0146] The following is a comparison between the improved sand cat colony optimization algorithm and other algorithms in conjunction with the embodiments:

[0147] The DH parameter table of the six-degree-of-freedom robotic arm in the embodiment is as follows:

[0148]

[0149] Given 4 path points in Cartesian space as interpolation points of the motion trajectory, as shown in the following table,

[0150]

[0151] The joint angles of each joint in the joint space at each interpolation point are solved through the inverse kinematics of the robot, and the velocity constraints of each joint of the robot are given, as shown in the following table:

[0152]

[0153] Initialize the movement time interval between each joint interpolation point, set the initial interpolation time between each path point to 1s, construct a 5-7-5 polynomial trajectory, and obtain the front angular displacement, velocity, acceleration, and jerk curves optimized by the improved sand cat swarm algorithm.

[0154] Furthermore, in order to verify the feasibility and superiority of the improved sand cat swarm optimization algorithm (YSCSO) in the trajectory planning of the robot arm with time as the optimization target, it is compared with the sand cat swarm optimization algorithm (SCSO), the whale optimization algorithm (WOA), the dung beetle optimization algorithm (DBO), the sparrow search algorithm (SSA), and the gray wolf optimization algorithm (GWO). Under the condition that the maximum number of iterations is 100, the time optimal trajectory planning in the joint space is performed according to the given joint angle. 10 experiments were carried out, the optimal value of each algorithm was recorded, the average value and standard deviation were solved, and the experimental results are shown in the following table. Comparing the experimental results of the five algorithms, the YSCSO algorithm proposed in the present invention shows the best running time and the best stability in the time optimal trajectory planning of the robot arm.

[0155]

[0156] The fitness values ​​of the improved sand cat swarm optimization algorithm and the comparison algorithm at each joint converge over time as shown in the figure Figures 2 to 7 shown.

[0157] The results show that after 100 iterations, the convergence curve of each algorithm for the running time of each joint of the robot arm has become stable. The WOA algorithm and the DBO algorithm performed poorly in terms of convergence speed and accuracy. Relatively speaking, the YSCSO algorithm performed better in these two aspects. It can not only find a better solution in the early stage of iteration, but also has more stable algorithm performance. Compared with the SCSO algorithm, the YSCSO algorithm not only retains the advantages of the original algorithm, but also significantly improves the convergence speed in the early stage, enhances the optimization ability of the algorithm, and is easier to jump out of the local optimal solution in the later stage and find the global optimal solution, which improves the stability of the solution result and makes the algorithm have higher solution quality and efficiency.

[0158] One of the experimental results is randomly selected. After optimization by the YSCSO algorithm, the time period of the 5-7-5 polynomial interpolation motion trajectory of each joint of the robotic arm is shown in the following table.

[0159]

[0160] See also Figures 8 to 15 , while ensuring that all joints meet the constraints of position, velocity, acceleration and jerk, select the maximum time of the six joints in each trajectory segment, which are t 1 =0.7066s,t 2 =0.5009s,t 3 =0.6569s, the total time is 1.8644 seconds, and the running time is shortened from 3 seconds to 1.8644 seconds, meeting the goal of time optimization.

[0161] The optimized result is constructed into a trajectory through the 5-7-5 polynomial. Compared with the motion trajectory before optimization, the obtained trajectory not only meets the requirements of passing through each path point, but also maintains continuity in position, velocity and acceleration. The trajectory curve of acceleration has no protrusions and fluctuations during the entire operation process, which meets the kinematic constraints.

[0162] In summary, the present invention optimizes the working time of the robotic arm and ensures that the robotic arm always moves under constraints, thereby ensuring the stable operation of the robotic arm and improving the working efficiency of the robotic arm.

[0163] Compared with the prior art, the advantages of the present invention are:

[0164] (1) The improved sand cat swarm optimization algorithm used in the present invention can more quickly search for the optimal running time of each joint and segment of the robot arm. Compared with the traditional swarm intelligence algorithm, the iteration speed is faster and the optimal time is shorter.

[0165] (2) The present invention proposes and solves a 5-7-5 polynomial trajectory, which can better fit complex motion trajectories while ensuring the smoothness of trajectory planning position, velocity, and acceleration, thereby reducing the impact during the movement of the robotic arm.

[0166] (3) The present invention is based on the sand cat swarm optimization algorithm SCSO, introduces cubic chaos-refraction reverse learning to initialize the population, uses adaptive auditory sensitivity to balance the relationship between the elite pool weighted guided search behavior and the spiral Levy flight predation behavior, increases the sand cat's vigilance behavior, and improves the overall optimization performance of the algorithm.

[0167] What is disclosed above is only a preferred embodiment of the present invention, and it certainly cannot be used to limit the scope of rights of the present invention. Ordinary technicians in this field can understand that all or part of the processes of the above embodiment and equivalent changes made according to the claims of the present invention still fall within the scope of the invention.

Claims

1. A method for time optimal trajectory planning of a robotic arm based on an improved sand cat swarm optimization algorithm, characterized in that: The following steps are involved: Step 1: According to the established robot arm kinematic model, the mapping relationship between the joint space and the end effector Cartesian space is established; Step 2: For a given path point in Cartesian space, the interpolation angles of each joint of the robot arm in the joint space are obtained through the mapping relationship constructed in step 1 and the inverse kinematics solution; Step 3: Use the 5-7-5 mixed polynomial interpolation function to generate smooth and continuous position, velocity, acceleration, and jerk trajectories based on the interpolation angles in the joint space; Step 4: Based on the kinematic constraints, optimize the motion trajectory with the goal of time optimization; Step 5: Taking the motion time in each segment of trajectory planning as the optimization target, the improved sand cat swarm optimization algorithm is used to optimize the robot arm trajectory running time; Step 6: According to the time optimization principle, output the optimal solution for the optimized robot arm trajectory planning.

2. The method for time optimal trajectory planning of a manipulator based on an improved sand cat swarm optimization algorithm as claimed in claim 1, characterized in that: In step 1, the transformation relationship between the connecting rod i-1 coordinate system and the i coordinate system is expressed by the homogeneous transformation matrix: Among them, θ i is the angle of rotation around the z-axis of the i coordinate system, d i is the distance of translation along the z-axis of the i coordinate system, α i is the angle of rotation around the x-axis of the i coordinate system, a i is the distance translated along the x-axis of the i coordinate system.

3. The method for time optimal trajectory planning of a manipulator based on an improved sand cat swarm optimization algorithm as claimed in claim 2, characterized in that: In step 3, according to the interpolation angle of the joint space, the movement of each joint is regarded as consisting of multiple continuous segments, and the interpolation function corresponding to each joint is generated using the 5-7-5 mixed polynomial method; the equation of the segmented trajectory is expressed as follows: Among them, l ik (t) represents the polynomial trajectory at the kth part of the ith joint, a i1k Represents the kth coefficient of the first-stage interpolation function of the i-th joint trajectory.

4. The method for time optimal trajectory planning of a manipulator based on an improved sand cat swarm optimization algorithm as claimed in claim 3, characterized in that: The optimization objective function expression in step 4 is as follows: Where T is the total operation time of the robot; t j is the time of the jth point, n is the number of path points; The kinematic constraints are defined as: Among them, Q imax ,V imax ,A imax ,J imax are the maximum angular displacement, maximum angular velocity, maximum angular acceleration and maximum angular jerk of the i-th joint, q i (t),v i (t),a i (t),j i (t) are the angle, angular velocity, angular acceleration and angular jerk of the i-th joint respectively.

5. The method for time optimal trajectory planning of a manipulator based on an improved sand cat swarm optimization algorithm as claimed in claim 4, characterized in that: The execution process of step 5 includes the following steps: Step 5.1: Generate the initial population through cubic chaos-refraction reverse learning; Step 5.2: Calculate the fitness function value of the sand cat individuals, that is, the total running time of each joint of the robot arm represented by each individual, compare the fitness function value of each initial individual, and take the individual with the smallest function value as the global and local optimal solution; Step 5.3: According to the balance factor R, the algorithm is selected to execute the exploration or development behavior strategy, and the position of the individual population is updated according to the corresponding action strategy. If |R|>1, the sand cat exploration behavior is executed, otherwise the sand cat predation behavior is executed; Step 5.4: Execute the sand cat vigilance behavior strategy and update the current position of the sand cat individual in space; Step 5.5: Determine whether the updated individual position, i.e., the running time of each stage, meets the constraint conditions of the robot trajectory operation in step 4. If so, recalculate the fitness value corresponding to the individual according to the updated individual position information. Otherwise, jump to steps 5.3 and 5.4 to re-update the qualified individuals. Step 5.6: Based on the updated fitness value, update the global optimal solution and the local optimal solution; Step 5.7: According to the time optimality principle, output the optimized robot arm trajectory planning best solution.

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