Tree climbing robot joint trajectory optimization method

Abstract

The present application relates to a kind of tree climbing robot joint trajectory optimization method, to solve the initial population distribution uneven in the robot joint trajectory optimization of traditional algorithm, easily fall into local optimum and other problems. First, the robot movement trajectory is mapped to joint space, and the optimization of trajectory planning is established, and it is made to satisfy each physical constraint in movement process. Subsequently, by introducing improved Tent mixed queue mapping initial population strategy, the diversity and global search capability of population are enhanced;At the same time, combined with adaptive global guide strategy, excellent individual is dynamically selected, to avoid algorithm falling into local optimum;Finally, in the late stage of algorithm, refractive learning strategy is fused, the randomness of local search is increased, and the accuracy and stability of solution are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of robot intelligent control, and in particular to a joint trajectory optimization method for a tree-climbing robot. BACKGROUND

[0002] When performing tasks, a tree-climbing robot not only needs to stably adhere to the tree trunk against gravity, but also needs to flexibly cope with various complex environmental challenges, including but not limited to irregularities on the surface of the tree trunk (such as protrusions, depressions, cracks, etc.), the staggered distribution of branches, and the nonlinearity of the motion trajectory due to wind force and tree growth. These environmental factors greatly increase the difficulty of robot path planning and motion control, resulting in problems such as insufficient control accuracy and poor stability in practical applications for traditional control algorithms. In order to improve the flexibility and control effect of the tree-climbing robot in complex environments, researchers have been exploring and optimizing control algorithms. However, the commonly used optimization algorithms, such as genetic algorithms and particle swarm optimization algorithms, while improving control performance to some extent, still have some inherent limitations. For example, these algorithms are prone to fall into local optimal solutions, i.e., they may converge to a solution that is not globally optimal during the search process, thereby limiting the further improvement of robot performance. Therefore, there is an urgent need for an improved optimization method to solve the above problems. Such a method should have stronger global search ability to avoid falling into local optimal solutions, and at the same time, it should have faster convergence speed to meet the real-time requirements of the tree-climbing robot. Possible improvement directions include: SUMMARY

[0003] The purpose of the present application is to provide a joint trajectory optimization method for a tree-climbing robot to solve the problem that the current optimization algorithm has a low uniformity of initial population distribution when applied to robot joint trajectory optimization, and is prone to fall into local optimal solutions during the algorithm process. Specifically, the method includes the following steps:

[0004] Step S1. Establish a robot joint trajectory optimization model. Map the robot motion trajectory to the joint space, convert the robot trajectory planning problem to an optimization problem of joint motion, and establish its optimization model. Use Bernstein functions to construct the acceleration model of each joint motion of the robot, use the coefficients of Bernstein functions as the decision vector of the optimization problem, and minimize the maximum acceleration as the optimization objective to ensure the continuity and smoothness of the motion speed curve, and also consider the balance and stability of the actuator.

[0005] Step S2. Establishing the improved butterfly optimization algorithm. First, by introducing the improved Tent chaotic mapping initial population strategy, the diversity and global search ability of the population are enhanced; at the same time, combined with the adaptive global guidance strategy, the excellent individuals are dynamically selected to avoid the algorithm falling into local optimum; finally, the refraction learning strategy is fused in the later stage of the algorithm to increase the randomness of local search, improve the accuracy and stability of the solution.

[0006] Step S3. Application of the improved butterfly optimization algorithm in robot joint trajectory optimization. The decision vector β of the joint motion optimization problem is equivalent to the position vector Xi of the butterfly in the improved butterfly optimization algorithm. That is, Xi = β, that is, Xi = [xi1, xi2, …, xid] = β = [β0, β1, …, βn]. The number of variables in the decision vector is equal to the dimension of the position vector. N + 1 = d. The optimal decision vector corresponds to the optimal position vector Xbest in the algorithm. That is, Xbest = [xi1*, xi2*, …, xid*] = β* = [β0*, β1*, …, βn*]. The maximum acceleration αmax in the optimization problem corresponds to the fitness fi in the algorithm, that is, fi = αmax = max α(y), y ∈ [0, Time]. The minimum maximum acceleration minαmax corresponds to the optimal fitness fbest, that is, fbest = minαmax = min max{α(y), y ∈ [0, Time]}. The improved butterfly optimization algorithm is used to optimize the robot joint trajectory.

[0007] Further, the robot joint trajectory optimization model is established, including the following steps:

[0008] Step S11. Defining the initial state of the robot joint as {ps, vs, αs}, and after Time time, the final state of the robot joint as {pe, ve, αe}; wherein ps, vs, αs are the initial state of the robot joint position, velocity and acceleration, Time is the trajectory optimization time, pe, ve, αe are the final state of the robot joint position, velocity and acceleration.

[0009] Step S12. The robot joint motion displacement calculation formula is The robot joint motion velocity calculation formula is

[0010] Step S13. Establishing the optimization goal: taking the minimum value of the maximum acceleration of the robot joint during motion as the optimization goal, the specific expression is minαmax = min max{|α(y)|, y ∈ [0, Time]}.

[0011] .Step S14. Establish constraint condition 1: The speed of the joint during the robot movement is less than the maximum speed vmax, which can be expressed as v(y)≤vmax, y∈[0,Time].

[0012] .Step S15. Establish constraint condition 2: the absolute value of the joint acceleration is less than the maximum jerk γmax, which can be expressed as abs{(y1)-α(y2)] / [y1-y2]}≤γmax, y1, y2∈[0,Time].

[0013] Step S16. Establish constraint condition 3: The initial and final robot joint positions are ps and pe respectively, which can be expressed as The robot joint velocities at the initial and final states are vs and ve respectively, which can be expressed as The robot joint accelerations in the initial and final states are αs and αe respectively.

[0014] Step S17. Assuming that the acceleration of the robot joint motion is continuous within the time period Time, it can be described by the Bernstein function, specifically: Where τ = y / Time∈[0,1], τ is the normalized time variable, n is the highest degree of the polynomial, and βk is the corresponding coefficient. is the number of combinations. Therefore, the joint trajectory optimization problem is transformed into an optimization problem with constraints, using βk as the optimization variable.

[0015] Furthermore, establishing an improved butterfly optimization algorithm includes the following steps:

[0016] Step S21: Create algorithm initialization and initial population. Define the butterfly population size as N, the maximum number of iterations as Tm, and the dimension of the optimization problem as d.

[0017] Step S22: Generate the initial population using the improved Tent chaos mapping strategy to enhance the diversity of solutions and ensure that the population covers a wide range of search space. The improved Tent chaos mapping formula is as follows:

[0018] If xi(t)<0.7, then xi(t+1)=xi(t) / 0.7

[0019] If xi(t)≥0.7, then xi(t+1)=(1-xi(t)) / 0.3

[0020] .Where xi(t) is the position of the i-th butterfly individual.

[0021] According to the formula μ = cI ^ a, calculate the butterfly scent;

[0022] Step S23. An adaptive global guidance mechanism is used for the butterfly optimization algorithm, i.e., the search direction and speed of the butterfly individual are dynamically adjusted according to the position and fitness value of the butterfly individual, to improve the balance between global search and local development. The position of each individual in the butterfly optimization algorithm is updated, and the ith individual of the population is updated according to the following formula:

[0023] Xi(t+1) = Xi(t) + S * (Xbets(t) - Xi(t)) + γ * (rand - 0.5) * μ

[0024] S = Smin + (Smax - Smin) / {1 + exp^[δ * (fbest - fi)]}

[0025] . Where S is the adaptive step size, γ = 0.5 is the disturbance factor, rand is a random number between [0, 1], Xbets is the current global optimal solution. fbest is the global optimal fitness value, fi is the fitness value of the individual, δ = 0.25 is the adjustment coefficient, Smax and Smin are the upper and lower limits of the step size. In each iteration, the moving step size β of the butterfly is dynamically adjusted according to the fitness difference. If the fitness value of the current individual is poor, the step size is large, to strengthen the global search; and when the fitness value is close to the global optimum, the step size is reduced, to strengthen the local development.

[0026] Step S24. A refraction learning strategy is applied to the local development stage of the butterfly optimization algorithm, and the refraction learning strategy is used to finely adjust the individual. The position of each individual in the butterfly optimization algorithm is updated, and the ith individual of the population is updated according to the following formula:

[0027] Xi(t+1) = Xi(t) + η * (Xr(t) - Xi(t))

[0028] η = ηmin + (ηmax - ηmin) * t / Tm

[0029] . Where η is the refraction coefficient, ηmax and ηmin are the maximum and minimum refraction coefficients respectively; xr is the position of the randomly selected reference individual. t is the current iteration number. The refraction coefficient is dynamically adjusted according to the progress of the local development in the iteration process, to ensure that the algorithm can quickly explore the solution space in the early stage, and can more accurately optimize the local solution in the later stage.

[0030] Step S25. If the fitness fi is less than the current optimal fitness fbest, update the current optimal fitness and the current optimal position;

[0031] Step S26. Update the sensory factor according to the following formula

[0032] c(t+1) = c(t) + 0.025 / (c(t) * Tm).

[0033] Further, the application of the improved butterfly optimization algorithm in robot joint trajectory optimization includes the following steps:

[0034] Step S31. The initial parameters of the improved butterfly optimization algorithm are given, such as the stimulation intensity I, the sensory factor c, the power index a, and the switching probability P.

[0035] Step S32. An initial population X is created by the improved Tent chaotic mapping, see the following formula. Specifically, it is an acceleration model coefficient of N rows and n columns.

[0036]

[0037] If xi(t) < 0.7, then xi(t+1) = xi(t) / 0.7

[0038] If xi(t) ≥ 0.7, then xi(t+1) = (1-xi(t)) / 0.3

[0039] The maximum acceleration of each butterfly is calculated. Whether the constraint conditions are met is judged, including the start and end positions, the start and end speeds, the start and end accelerations, and the limits of the maximum speed and the maximum acceleration.

[0040] Step S33. According to the three constraint conditions in steps S14-S16, it is judged whether the current population meets the constraint conditions; if the constraint conditions are not met, a set of position vectors of butterflies, i.e., decision vectors, are regenerated;

[0041] Step S34. The fitness of each butterfly, i.e., the minimum maximum joint acceleration, is calculated according to step S13.

[0042] Step S35. The minimum value of the fitness of all butterflies in step S34 is found, and it is taken as the current optimal fitness. The corresponding butterfly position is the current optimal position.

[0043] Step S36. The loop variable is initialized. It is judged whether the maximum number of iterations is reached. If it is met, the iteration is stopped, and the optimal fitness value of the butterfly individual and the optimal acceleration model coefficient are output. If it is not met, steps S37-S312 are continued to be executed.

[0044] Step S37. Steps S38-S312 are executed for each butterfly.

[0045] Step S38. A random number R is generated. If the random number R is less than the switching probability P, the butterfly position is updated according to step S23 by the adaptive global optimal guiding factor.

[0046] . Step S39. If the random number R is greater than or equal to the switching probability P, the butterfly position is updated according to the refraction learning strategy according to step S24;

[0047] . Step S310. The constraint condition is judged according to step S33. The fitness of all butterflies is calculated according to step S34;

[0048] . Step S311. The current optimal fitness and the current optimal position are updated according to the greedy strategy;

[0049] . Step S312. The sensory factor is updated. BRIEF DESCRIPTION OF DRAWINGS

[0050] Figure 1 A principle diagram of a tree climbing robot joint trajectory optimization method

[0051] S1-establishes a robot joint trajectory optimization model, S2-establishes an improved butterfly optimization algorithm, and S3-applies the improved butterfly optimization algorithm in robot joint trajectory optimization. DETAILED DESCRIPTION

[0052] The embodiments of the present application will be described in detail below with reference to the accompanying drawings.

[0053] . Referring to Figure 1 The present application provides a tree climbing robot joint trajectory optimization method, comprising the following steps

[0054] . Step S1. A robot joint trajectory optimization model is established. The robot motion trajectory is mapped to the joint space, the robot trajectory planning problem is converted into an optimization problem of joint motion, and the optimization model is established. Bernstein function is used to construct the acceleration model of each joint motion of the robot, the coefficients of the Bernstein function are used as the decision vector of the optimization problem, the optimization target is to minimize the maximum acceleration, the continuity and smoothness of the motion speed curve are ensured, and the balance and stability of the actuator are considered.

[0055] . Step S2. An improved butterfly optimization algorithm is established. First, the improved Tent mixed queue mapping initial population strategy is introduced to enhance the diversity and global search ability of the population. At the same time, combined with the adaptive global guidance strategy, excellent individuals are dynamically selected to avoid the algorithm falling into local optimum. Finally, the refraction learning strategy is fused in the later stage of the algorithm to increase the randomness of local search and improve the precision and stability of the solution.

[0056] Step S3. Application of improved butterfly optimization algorithm in robot joint trajectory optimization. The decision vector β of joint motion optimization problem is equivalent to the position vector Xi of butterfly in improved butterfly optimization algorithm. That is, Xi = β, that is, Xi = [xi1, xi2, …, xid] = β = [β0, β1, …, βn]. The number of variables in the decision vector is equal to the dimension of the position vector. N + 1 = d. The optimal decision vector corresponds to the optimal position vector Xbest in the algorithm. That is, Xbest = [xi1*, xi2*, …, xid*] = β* = [β0*, β1*, …, βn*]. The maximum acceleration a max in the optimization problem corresponds to the fitness fi in the algorithm, that is, fi = a max = max a (y), y ∈ [0, Time]. The minimum maximum acceleration min a max corresponds to the optimal fitness fbest, that is, fbest = min a max = min max {a (y), y ∈ [0, Time]}. The improved butterfly optimization algorithm is used to optimize the robot joint trajectory.

[0057] . Further, the robot joint trajectory optimization model is established, including the following steps:

[0058] . Step S11. Define the initial state of the robot joint as {ps, vs, a s}, and after Time time, the final state of the robot joint as {pe, ve, a e}; wherein ps, vs, a s are the initial state of the robot joint position, velocity and acceleration, Time is the trajectory optimization time, pe, ve, a e are the final state of the robot joint position, velocity and acceleration.

[0059] . Step S12. The robot joint motion displacement calculation formula is The robot joint motion velocity calculation formula is

[0060] . Step S13. Establish the optimization goal: the minimum value of the maximum acceleration of the joint during the robot motion as the optimization goal, the specific expression is min a max = min max {a (y) |, y ∈ [0, Time]}.

[0061] . Step S14. Establish constraint condition 1: the velocity of the robot joint during the motion is less than the maximum velocity vmax, which is written as v (y) ≤ vmax, y ∈ [0, Time].

[0062] . Step S15. Establish constraint condition 2: the absolute value of the jerk of the joint is less than the maximum jerk γmax, which is written as abs {a (y1) - a (y2)} / [y1 - y2] ≤ γmax, y1, y2 ∈ [0, Time].

[0063] Step S16. Establish constraint condition 3: initial and final state robot joint positions are ps and pe, respectively, which can be written in the form of expression Initial and final state robot joint velocities are vs and ve, respectively, which can be written in the form of expression Initial and final state robot joint accelerations are as and ae, respectively.

[0064] Step S17. Assuming that the acceleration of robot joint motion is continuous within Time, it can be described by Bernstein function, specifically where τ = y / Time ∈ [0, 1], τ is the normalized time variable; n is the highest degree of polynomial. βk is the corresponding coefficient. is the combination number. Therefore, the joint trajectory optimization problem is converted into an optimization problem with βk as the optimization variable and constraints.

[0065] Further, the improved butterfly optimization algorithm includes the following steps:

[0066] Step S21. Create algorithm initialization and initial population. Define the butterfly population size as N, the maximum number of iterations as Tm, and the dimension of the optimization problem as d.

[0067] Step S22. Use the improved Tent chaotic mapping strategy to generate the initial population to enhance the diversity of solutions and ensure that the population widely covers the search space. The improved Tent chaotic mapping formula is as follows:

[0068] If xi(t) < 0.7, then xi(t+1) = xi(t) / 0.7

[0069] If xi(t) ≥ 0.7, then xi(t+1) = (1-xi(t)) / 0.3

[0070] where xi(t) is the position of the i-th butterfly individual.

[0071] According to the formula μ = cI^a, the butterfly fragrance is calculated;

[0072] Step S23. Use the adaptive global guidance mechanism for the butterfly optimization algorithm, that is, dynamically adjust the search direction and speed of the butterfly individual according to its position and fitness value to improve the balance between global search and local development. The position of each individual in the butterfly optimization algorithm is updated, and the i-th individual of the population is updated according to the following formula:

[0073] Xi(t+1) = Xi(t) + S*(Xbets(t)-Xi(t)) + γ*(rand-0.5)*μ

[0074] S=Smin+(Smax-Smin) / {1+exp^[δ*(fbest-fi)]}

[0075] Where S is the adaptive step size, γ = 0.5 is the perturbation factor, rand is a random number between [0, 1], and Xbets is the current global optimal solution. fbest is the global optimal fitness value, fi is the individual fitness value, δ = 0.25 is the adjustment coefficient, and Smax and Smin are the upper and lower limits of the step size. In each iteration, the butterfly's movement step size β is dynamically adjusted based on the fitness difference. If the current individual fitness value is poor, the step size is increased to strengthen the global search; when the fitness value approaches the global optimum, the step size is reduced to strengthen local exploration.

[0076] Step S24: Apply the refraction learning strategy to the local development phase of the butterfly optimization algorithm, and use the refraction learning strategy to fine-tune the individuals. The position of each individual in the butterfly optimization algorithm is updated, and the i-th individual in the population is updated according to the following formula:

[0077] Xi(t+1)=Xi(t)+η*(Xr(t)-Xi(t))

[0078] η=ηmin+(ηmax-ηmin)*t / Tm

[0079] Where η is the refractive index, ηmax and ηmin are the maximum and minimum refractive indexes, respectively; xr is the randomly selected reference individual position; and t is the current iteration number. The refractive index is dynamically adjusted during the iteration process based on the progress of local development, ensuring that the algorithm can quickly explore the solution space in the early stages and more accurately optimize local solutions in the later stages.

[0080] Step S25. If the optimal fitness fi is less than the current optimal fitness fbest, then update the current optimal fitness and the current optimal position;

[0081] Step S26. Update the sensory factor according to the following formula

[0082] c(t+1)=c(t)+0.025 / (c(t)*Tm).

[0083] Furthermore, the application of the improved butterfly optimization algorithm in robot joint trajectory optimization includes the following steps:

[0084] .Step S31. Give the initial parameters of the improved butterfly optimization algorithm, such as stimulation intensity I, sensation factor c, power index a and switching probability P.

[0085] Step S32: Create an initial population X by using the improved Tent chaotic map, as shown in the following formula: Specifically, it is an acceleration model coefficient with N rows and n columns.

[0086]

[0087] If xi(t) < 0.7, then xi(t+1) = xi(t) / 0.7

[0088] If xi(t) ≥ 0.7, then xi(t+1) = (1-xi(t)) / 0.3

[0089] Calculate the maximum acceleration of each butterfly, and determine whether the constraint conditions are met, including the start and end positions, start and end speeds, start and end accelerations, and the limits of maximum speed and maximum acceleration.

[0090] Step S33. Determine whether the current population meets the constraint conditions according to the three constraint conditions in steps S14-S16; if the constraint conditions are not met, then a set of butterfly position vectors, i.e., decision vectors, are re-generated;

[0091] Step S34. Calculate the fitness of each butterfly, i.e., the minimum maximum joint acceleration, according to step S13;

[0092] Step S35. Find the minimum value of the fitness of all butterflies in step S34, and take it as the current optimal fitness, and the corresponding butterfly position as the current optimal position.

[0093] Step S36. Initialize the loop variable. Determine whether the maximum number of iterations is reached; if it is met, stop the iteration and output the optimal fitness value of the butterfly individual and the optimal acceleration model coefficient; if it is not met, continue to execute steps S37-S312;

[0094] Step S37. Execute steps S38-S312 for each butterfly;

[0095] Step S38. Generate a random number R, and if the random number R is less than the switching probability P, then update the butterfly position according to step S23 by the adaptive global optimal guiding factor;

[0096] Step S39. If the random number R is greater than or equal to the switching probability P, then update the butterfly position according to step S24 by the refraction learning strategy;

[0097] Step S310. Determine the constraint condition according to step S33. Calculate the fitness of all butterflies according to step S34;

[0098] Step S311. Update the current optimal fitness and the current optimal position according to the greedy strategy.

[0099] Step S312. Update the sensory factor.

Claims

1. A method for optimizing joint trajectories of a tree-climbing robot, characterized in that: The method comprises the following steps: Step S1. Establishing a robot joint trajectory optimization model; mapping the robot motion trajectory to the joint space, converting the robot trajectory planning problem into an optimization problem of joint motion, and establishing an optimization model thereof; using Bernstein function to constitute an acceleration model of each joint motion of the robot, taking the coefficients of the Bernstein function as the decision vectors of the optimization problem, and taking minimizing the maximum acceleration as the optimization objective; Step S2. Establishing an improved butterfly optimization algorithm; on the basis of the traditional butterfly optimization algorithm, an improved Tent chaotic mapping strategy is introduced to initialize the population; at the same time, a self-adaptive global guidance strategy is combined to update the butterfly position; finally, a refraction learning strategy is fused to update the population strategy in the later stage of the algorithm; the specific step S2 is as follows: Step S21. Defining algorithm parameters: defining the size of the butterfly population as N, the maximum number of iterations as Tm, and the dimension of the optimization problem as d; the stimulus intensity I, the sensory factor c, the power index a and the switching probability P; Step S22. Initializing the population: using the improved Tent chaotic mapping strategy to generate the initial population, and the formula is as follows: If Xi(t) < 0.7, then Xi(t+1) = Xi(t) / 0.7; If Xi(t) ≥ 0.7, then Xi(t+1) = (1-Xi(t)) / 0.3 Wherein, Xi(t) is the position of the i-th butterfly individual at t time, i = 1, 2, 3, … N; According to the formula μ = cI^a, the butterfly fragrance is calculated; Step S23. In the global exploration stage of the butterfly algorithm, the position of each butterfly is updated by using the self-adaptive global guidance mechanism, and the formula is as follows: Xi(t+1) = Xi(t) + S*(Xbets(t)-Xi(t))+ γ*(rand-0.5)*μ S = Smin + (Smax-Smin) / {1+exp^[-δ*(fbest-fi)]} Wherein, S is the adaptive step, γ = 0.5 is the disturbance factor, rand is a random number between 0 and 1, Xbets is the current global optimal solution; fbest is the global optimal fitness value, fi is the fitness value of the individual, δ = 0.25 is the adjustment coefficient, Smax and Smin are the upper and lower limits of the step, and the ^ symbol represents the power; Step S24. In the local development stage of the butterfly optimization algorithm, the refraction learning strategy is used to update the position of each butterfly, and the update formula is as follows: Xi(t+1) = Xi(t) + η*(Xr(t)-Xi(t)) η = ηmin + (ηmax-ηmin)*t / Tm Wherein, η is the refraction coefficient, ηmax and ηmin are the maximum refraction coefficient and the minimum refraction coefficient respectively; Xr is the position of the randomly selected reference individual; t is the current iteration number, and Tm is the maximum iteration number; Step S25. If the fitness fi is less than the current optimal fitness fbest, the current optimal fitness and the current optimal position are updated; Step S26. The sensory factor c is updated according to the following formula: c(t+1) = c(t) + 0.025 / (c(t)*Tm). Step S3. Application of improved butterfly optimization algorithm in robot joint trajectory optimization; the decision vector of joint motion optimization problem is equivalent to the position vector of butterfly in improved butterfly optimization algorithm; the number of variables in decision vector is equal to the dimension of position vector; the optimal decision vector corresponds to the optimal position vector in algorithm; the maximum acceleration in optimization problem corresponds to the fitness in algorithm; the minimum maximum acceleration corresponds to the optimal fitness; the improved butterfly optimization algorithm is used to optimize robot joint trajectory.

2. The joint trajectory optimization method for a tree climbing robot according to claim 1, wherein, Step S1. Establishing robot joint trajectory optimization model as: Step S11. Defining initial state of robot joint as {ps, vs, αs}, after Time time, final state of robot joint as {pe, ve, αe}; wherein, ps, vs, αs are initial state of robot joint position, velocity and acceleration respectively, Time is trajectory optimization time, pe, ve, αe are final state of robot joint position, velocity and acceleration respectively; Step S12. The robot joint motion displacement calculation formula is The robot joint motion velocity calculation formula is Step S13. Establishing optimization goal: taking the minimum value of the maximum acceleration of the joint in the process of robot motion as the optimization goal, and the specific expression is minα max = min max{|α(y)|, y ∈ [0, Time]}; Step S14. Establishing constraint condition 1: velocity of joint during robot motion is less than maximum velocity vmax, written as expression v(y)≤vmax, y∈[0, Time]; Step S15. Establishing constraint condition 2: absolute value of joint jerk is less than maximum jerk γmax, written as expression abs{[α(y1)-α(y2)] / [y1-y2]}≤γmax, y1, y2∈[0, Time]; Step S16. Establish constraint condition 3: initial and final state robot joint positions are ps and pe, respectively, which can be written in the form of an expression Initial and final state robot joint velocities are vs and ve, respectively, which can be written in the form of an expression Initial and final state robot joint accelerations are αs and αe, respectively Step S17. The Bernstein function is used to describe the acceleration of the joint movement of the robot, specifically: where τ = y / Time ∈ [0, 1], τ is the normalized time variable; n is the highest degree of the polynomial; βk is the corresponding coefficient; is the combination number.

3. The method of claim 1, wherein, Step S3. Application of improved butterfly optimization algorithm in robot joint trajectory optimization as: Step S31. According to step S21, initial parameters of improved butterfly optimization algorithm are given; Step S32. According to step S22, initial population X is created by improved Tent chaotic mapping; Step S33. According to three constraint conditions in steps S14-S16, whether current population satisfies constraint condition is judged; if constraint condition is not satisfied, a set of position vectors of butterfly, i.e. decision vector, is generated again; Step S34. According to step S13, fitness of each butterfly, i.e. minimum maximum joint acceleration, is calculated; Step S35. Minimum value of fitness of all butterflies in step S34 is calculated, and it is taken as current optimal fitness, corresponding butterfly position is current optimal position; Step S36. Loop variable is initialized, whether it reaches maximum iteration number is judged, if it is satisfied, iteration is stopped, and optimal fitness value of butterfly individual and optimal position are output; if it is not satisfied, steps S37-S312 are continuously executed; Step S37. Steps S38-S312 are executed for each butterfly; Step S38. Random number R is generated, if random number R is less than switching probability P, butterfly position is updated according to step S23 by self-adaptive global optimal guiding factor; Step S39. If random number R is greater than or equal to switching probability P, butterfly position is updated according to step S24 by refraction learning strategy; Step S310. Constraint condition is judged according to step S33; fitness of all butterflies is calculated according to step S34; Step S311. Current optimal fitness and current optimal position are updated according to greedy strategy; Step S312. Updating the sensory factor.

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