Tree-climbing robot joint trajectory optimization method

Abstract

The invention relates to a joint trajectory optimization method for a tree-climbing robot, and aims to solve the problems that initial population distribution is uneven and local optimum is likely to occur in robot joint trajectory optimization in a traditional algorithm. The method comprises the following steps: firstly, mapping a motion track of a robot to a joint space, establishing optimization of track planning, and enabling the track planning to meet various physical constraints in a motion process; then, by introducing an improved Tent mixed queue mapping initial population strategy, the diversity and global search ability of the population are enhanced; meanwhile, in combination with a self-adaptive global guidance strategy, excellent individuals are dynamically selected, and the algorithm is prevented from falling into local optimum; and finally, fusing a refraction learning strategy in the later stage of the algorithm, increasing the randomness of local search, and improving the precision and stability of the solution.

Description

Technical Field

[0001] The present invention relates to the field of robot intelligent control, and in particular to a method for optimizing the joint trajectories of a tree-climbing robot. Background Art

[0002] When performing tasks, tree-climbing robots not only need to overcome gravity and stably attach to tree trunks, but also need to flexibly respond to various complex environmental challenges, including but not limited to irregularities on the surface of tree trunks (such as bumps, depressions, cracks, etc.), staggered distribution of branches, and nonlinear motion trajectories caused by wind and tree growth. These environmental factors greatly increase the difficulty of robot path planning and motion control, resulting in traditional control algorithms often showing problems such as insufficient control accuracy and poor stability in practical applications. In order to improve the flexibility and control effect of tree-climbing robots in complex environments, researchers have been exploring and optimizing control algorithms. However, currently commonly used optimization algorithms, such as genetic algorithms and particle swarm optimization algorithms, can improve control performance to a certain extent, but still have some inherent limitations. For example, these algorithms are prone to fall into local optimal solutions, that is, they may converge to a solution that is not the global optimal solution too early 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. This method should have stronger global search capabilities to avoid falling into local optimal solutions; at the same time, it should also have a faster convergence speed to meet the real-time requirements of tree-climbing robots. Possible improvement directions include: Summary of the invention

[0003] The purpose of the present invention is to provide a method for optimizing the joint trajectory of a tree-climbing robot, so as to solve the problem that the initial population distribution is not uniform enough and the algorithm is prone to fall into a local optimal solution during the algorithm process when the current optimization algorithm is applied to the optimization of the joint trajectory of the robot. The method specifically includes the following steps:

[0004] Step S1. Establish a robot joint trajectory optimization model. Map the robot motion trajectory to the joint space, transform the robot trajectory planning problem into the joint motion optimization problem, and establish its optimization model. Use the Bernstein function to construct the robot joint motion acceleration model, use the coefficient of the Bernstein function as the decision vector of the optimization problem, and minimize the maximum acceleration as the optimization goal to ensure the continuity and stability of the motion speed curve, while taking into account the balance and stability of the actuator.

[0005] .Step S2. Establish an improved butterfly optimization algorithm. First, by introducing the improved tent mixed team 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, excellent individuals are dynamically selected to avoid the algorithm from falling into the local optimum; finally, the refraction learning strategy is integrated in the later stage of the algorithm to increase the randomness of the local search and 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=maxα(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 robot joint trajectory is optimized using the improved butterfly optimization algorithm.

[0007] Furthermore, establishing the robot joint trajectory optimization model includes the following steps:

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

[0009] Step S12. The calculation formula of robot joint motion displacement is: The calculation formula of robot joint motion speed is:

[0010] .Step S13. Establish an optimization target: The minimum maximum acceleration of the joint during the robot's motion is used as the optimization target. 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's motion 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 state 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] . Further, establishing the 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 the search space extensively. The improved Tent chaos mapping 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

[0018] .Where xi(t) is the position of the i-th butterfly individual.

[0019] . According to the formula μ = cI^a, calculate the butterfly scent;

[0020] Step S23. Use the adaptive global guidance mechanism for the butterfly optimization algorithm, that is, dynamically adjust the search direction and speed according to the position and fitness value of the butterfly individual, so as to improve the balance between global search and local development. Update the position of each individual in the butterfly optimization algorithm, and update the i-th individual of the population according to the following formula: Xi(t+1)=Xi(t)+S*(Xbets(t)-Xi(t))+γ*(rand-0.5)*μ S=Smin+(Smax-Smin) / {1+exp^[δ*(fbest-fi)]}

[0021] .Wherein, S is the adaptive step size, γ=0.5 is the disturbance 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 moving step size β is dynamically adjusted according to the fitness difference. If the current individual's fitness value is poor, the step size is larger to strengthen the global search; when the fitness value is close to the global optimum, the step size is reduced to strengthen local development.

[0022] Step S24: Apply the refraction learning strategy to the local development stage 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 of the population is updated according to the following formula: Xi(t+1)=Xi(t)+η*(Xr(t)-Xi(t)) η=ηmin+(ηmax-ηmin)*t / Tm

[0023] .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. t is the current iteration number. The refractive index is dynamically adjusted according to the progress of local development during the iteration process, ensuring that the algorithm can quickly explore the solution space in the early stage and more accurately optimize the local solution in the later stage.

[0024] Step S25. If the optimal fitness fi is less than the current optimal fitness fbest, update the current optimal fitness and the current optimal position;

[0025] Step S26. Update the sensory factor according to the following formula c(t+1)=c(t)+0.025 / (c(t)*Tm).

[0026] .Furthermore, the application of the improved butterfly optimization algorithm in robot joint trajectory optimization includes the following steps:

[0027] .Step S31. Give the initial parameters of the improved butterfly optimization algorithm, such as stimulation intensity I, sensation factor c, power exponent a and switching probability P.

[0028] Step S32: Create an initial population X by using the improved Tent chaotic mapping, as shown in the following formula: Specifically, it is the acceleration model coefficients of N rows and n columns. 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

[0029] .Calculate the maximum acceleration of each butterfly. And determine whether the constraints are met, including the initial and final positions, initial and final velocities, initial and final accelerations, and the limits of maximum velocity and maximum acceleration.

[0030] Step S33. According to the three constraints in steps S14-S16, determine whether the current population meets the constraints; if the constraints are not met, regenerate a set of butterfly position vectors, i.e., decision vectors;

[0031] Step S34. Calculate the fitness of each butterfly according to step S13, i.e., the minimum maximum joint acceleration;

[0032] .Step S35. Calculate the minimum value of the fitness of all butterflies in step S34, and use it as the current optimal fitness, and the corresponding butterfly position is the current optimal position.

[0033] Step S36: Initialize loop variables. Determine whether the maximum number of iterations has been reached. If so, stop the iteration and output the optimal fitness value of the butterfly individual and the optimal acceleration model coefficient. If not, continue to execute steps S37 to S312.

[0034] Step S37. Execute steps S38 to S312 for each butterfly;

[0035] Step S38. Generate a random number R. If the random number R is less than the switching probability P, then according to step S23, the butterfly position is updated by the adaptive global optimal guidance factor;

[0036] Step S39. If the random number R is greater than or equal to the switching probability P, then according to step S24, the butterfly position is updated by the refraction learning strategy;

[0037] Step S310: Determine the constraint conditions according to step S33. Calculate the fitness of all butterflies according to step S34;

[0038] Step S311. Update the current optimal fitness and the current optimal position according to the greedy strategy;

[0039] .Step S312. Update the feeling factor. BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 Schematic diagram of a joint trajectory optimization method for a tree-climbing robot S1-Establish a robot joint trajectory optimization model, S2-Establish an improved butterfly optimization algorithm, S3-Application of the improved butterfly optimization algorithm in robot joint trajectory optimization. DETAILED DESCRIPTION The implementation of the present invention will be described in detail below with reference to the accompanying drawings in the embodiments of the present invention.

[0040] . Referring to the figure, the present invention provides a method for optimizing the joint trajectory of a tree-climbing robot, comprising the following steps

[0041] Step S1. Establish a robot joint trajectory optimization model. Map the robot motion trajectory to the joint space, transform the robot trajectory planning problem into the joint motion optimization problem, and establish its optimization model. Use the Bernstein function to construct the robot joint motion acceleration model, use the coefficient of the Bernstein function as the decision vector of the optimization problem, and minimize the maximum acceleration as the optimization goal to ensure the continuity and stability of the motion speed curve, while taking into account the balance and stability of the actuator.

[0042] .Step S2. Establish an improved butterfly optimization algorithm. First, by introducing the improved tent mixed team 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, excellent individuals are dynamically selected to avoid the algorithm from falling into the local optimum; finally, the refraction learning strategy is integrated in the later stage of the algorithm to increase the randomness of the local search and improve the accuracy and stability of the solution.

[0043] .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=maxα(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 robot joint trajectory is optimized using the improved butterfly optimization algorithm.

[0044] Furthermore, establishing the robot joint trajectory optimization model includes the following steps:

[0045] .Step S11. Define the initial state of the robot joint as {ps, vs, αs}. After Time, the final state of the robot joint is {pe, ve, αe}; where ps, vs, αs are the initial state robot joint position, velocity and acceleration respectively, Time is the trajectory optimization time, pe, ve, αe are the terminal state robot joint position, velocity and acceleration respectively.

[0046] Step S12. The calculation formula of robot joint motion displacement is: The calculation formula of robot joint motion speed is:

[0047] .Step S13. Establish an optimization target: The minimum maximum acceleration of the joint during the robot's motion is used as the optimization target. The specific expression is minαmax=min max{|α(y)|,y∈[0,Time]}.

[0048] .Step S14. Establish constraint condition 1: The speed of the joint during the robot's motion is less than the maximum speed vmax, which can be expressed as v(y)≤vmax, y∈[0,Time].

[0049] .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].

[0050] Step S16. Establish constraint condition 3: The initial and final state 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.

[0051] 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.

[0052] . Further, establishing the improved butterfly optimization algorithm includes the following steps:

[0053] 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.

[0054] 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 the search space extensively. The improved Tent chaos mapping 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

[0055] .Wherein, xi(t) is the position of the i-th butterfly individual.

[0056] . According to the formula μ = cI^a, calculate the butterfly scent;

[0057] Step S23. Use the adaptive global guidance mechanism for the butterfly optimization algorithm, that is, dynamically adjust the search direction and speed according to the position and fitness value of the butterfly individual, so as to improve the balance between global search and local development. Update the position of each individual in the butterfly optimization algorithm, and update the i-th individual of the population according to the following formula: Xi(t+1)=Xi(t)+S*(Xbets(t)-Xi(t))+γ*(rand-0.5)*μ S=Smin+(Smax-Smin) / {1+exp^[δ*(fbest-fi)]}

[0058] .Wherein, S is the adaptive step size, γ=0.5 is the disturbance 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 moving step size β is dynamically adjusted according to the fitness difference. If the current individual's fitness value is poor, the step size is larger to strengthen the global search; when the fitness value is close to the global optimum, the step size is reduced to strengthen local development.

[0059] Step S24: Apply the refraction learning strategy to the local development stage 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 of the population is updated according to the following formula: Xi(t+1)=Xi(t)+η*(Xr(t)-Xi(t)) η=ηmin+(ηmax-ηmin)*t / Tm

[0060] .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. t is the current iteration number. The refractive index is dynamically adjusted according to the progress of local development during the iteration process, ensuring that the algorithm can quickly explore the solution space in the early stage and more accurately optimize the local solution in the later stage.

[0061] Step S25. If the optimal fitness fi is less than the current optimal fitness fbest, update the current optimal fitness and the current optimal position;

[0062] Step S26. Update the sensory factor according to the following formula c(t+1)=c(t)+0.025 / (c(t)*Tm).

[0063] .Furthermore, the application of the improved butterfly optimization algorithm in robot joint trajectory optimization includes the following steps:

[0064] .Step S31. Give the initial parameters of the improved butterfly optimization algorithm, such as stimulation intensity I, sensation factor c, power exponent a and switching probability P.

[0065] Step S32: Create an initial population X by using the improved Tent chaotic mapping, as shown in the following formula: Specifically, it is the acceleration model coefficients of N rows and n columns. 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

[0066] .Calculate the maximum acceleration of each butterfly. And determine whether the constraints are met, including the initial and final positions, initial and final velocities, initial and final accelerations, and the limits of maximum velocity and maximum acceleration.

[0067] Step S33. According to the three constraints in steps S14-S16, determine whether the current population meets the constraints; if the constraints are not met, regenerate a set of butterfly position vectors, i.e., decision vectors;

[0068] Step S34. Calculate the fitness of each butterfly according to step S13, i.e., the minimum maximum joint acceleration;

[0069] .Step S35. Calculate the minimum value of the fitness of all butterflies in step S34, and use it as the current optimal fitness, and the corresponding butterfly position is the current optimal position.

[0070] Step S36: Initialize loop variables. Determine whether the maximum number of iterations has been reached. If so, stop the iteration and output the optimal fitness value of the butterfly individual and the optimal acceleration model coefficient. If not, continue to execute steps S37 to S312.

[0071] Step S37. Execute steps S38 to S312 for each butterfly;

[0072] Step S38. Generate a random number R. If the random number R is less than the switching probability P, then according to step S23, the butterfly position is updated by the adaptive global optimal guidance factor;

[0073] Step S39. If the random number R is greater than or equal to the switching probability P, then according to step S24, the butterfly position is updated by the refraction learning strategy;

[0074] Step S310: Determine the constraint conditions according to step S33. Calculate the fitness of all butterflies according to step S34;

[0075] .Step S311. Update the current optimal fitness and current optimal position according to the greedy strategy.

[0076] .Step S312. Update the feeling factor.

Claims

1. A method for optimizing joint trajectories of a tree-climbing robot, characterized in that: The following steps are involved: 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 the joint motion optimization problem to establish its optimization model; using the Bernstein function to construct the robot joint motion acceleration model, using the Bernstein function coefficient as the decision vector of the optimization problem, and taking minimizing the maximum acceleration as the optimization goal; Step S2. Establish an improved butterfly optimization algorithm; based on the traditional butterfly optimization algorithm, introduce an improved tent mixed team mapping strategy to initialize the population; at the same time, combine the adaptive global guidance strategy to update the butterfly position; finally, integrate the refraction learning strategy in the later stage of the algorithm to update the population strategy; Step S3. Application of the improved butterfly optimization algorithm in the optimization of robot joint trajectories; the decision vector of the joint motion optimization problem is equivalent to the position vector of the butterfly in the improved butterfly optimization algorithm; the number of variables in the decision vector is equal to the dimension of the position vector; the optimal decision vector corresponds to the optimal position vector in the algorithm; the maximum acceleration in the optimization problem corresponds to the fitness in the algorithm; the minimum maximum acceleration corresponds to the optimal fitness; the robot joint trajectories are optimized using the improved butterfly optimization algorithm.

2. According to claim 1, a tree climbing robot joint trajectory optimization method is characterized in that: Step S1 establishes the robot joint trajectory optimization model as: Step S11. Define the initial state of the robot joint as {ps, vs, αs}, and after Time, the final state of the robot joint is {pe, ve, αe}; where ps, vs, αs are the initial state robot joint position, velocity and acceleration, respectively, Time is the trajectory optimization time, pe, ve, αe are the final state robot joint position, velocity and acceleration, respectively; Step S12. The calculation formula of robot joint motion displacement is: The calculation formula of robot joint motion speed is: Step S13. Establishing an optimization target: Taking the minimum value of the maximum acceleration of the joint during the robot's motion as the optimization target, the specific expression is minαmax=min max{|α(y)|,y∈[0,Time]}; 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]; Step S15. Establish constraint condition 2: the absolute value of the joint jerk is less than the maximum jerk γmax, which can be expressed as abs{(y1)-α(y2)] / [y1-y2]}≤γmax, y1,y2∈[0,Time]; Step S16. Establish constraint condition 3: The initial and final state 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; Step S17. Use the Bernstein function to describe the acceleration of the robot joint motion, 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 number of combinations.

3. According to claim 1, a tree climbing robot joint trajectory optimization method is characterized in that: Step S2 establishes the improved butterfly optimization algorithm as: Step S21. Define algorithm parameters: define the butterfly population size as N, the maximum number of iterations as Tm, and the dimension of the optimization problem as d; stimulus intensity I, sensory factor c, power exponent a, and switching probability P; Step S22. Initialize the population: Generate the initial population using the improved Tent chaotic mapping strategy, 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 Where Xi(t) is the position of the i-th butterfly at time t, i = 1, 2, 3, ... N; According to the formula μ = cI^a, calculate the butterfly scent; Step S23. In the global exploration phase of the butterfly algorithm, an adaptive global guidance mechanism is used to adjust the position of each butterfly. 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)]} 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, Smin are the upper and lower limits of the step size, and the ^ symbol represents 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. The update formula is as follows: Xi(t+1)=Xi(t)+η*(Xr(t)-Xi(t)) η=ηmin+(ηmax-ηmin)*t / Tm 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; t is the current iteration number, and Tm is the maximum iteration number; Step S25. If the best fitness fi is less than the current best fitness fbest, then update the current best fitness and the current best position; Step S26. Update the perception factor according to the following formula: c(t+1)=c(t)+0.025 / (c(t)*Tm).

4. According to claim 1, a tree climbing robot joint trajectory optimization method is characterized in that: The application of the improved butterfly optimization algorithm in step S3 in the robot joint trajectory optimization is: Step S31. According to step S21, initial parameters of the improved butterfly optimization algorithm are given; Step S32. According to step S22, an initial population X is created by using an improved Tent chaotic mapping; Step S33. According to the three constraints in steps S14-S16, determine whether the current population meets the constraints; if the constraints are not met, regenerate a set of butterfly position vectors, i.e., decision vectors; Step S34. Calculate the fitness of each butterfly according to step S13, i.e., the minimum maximum joint acceleration; Step S35. Find the minimum value of the fitness of all butterflies in step S34, and use it as the current optimal fitness, and the corresponding butterfly position is the current optimal position; Step S36. Initialize the loop variable and determine whether it has reached the maximum number of iterations. If it has, stop the iteration and output the optimal fitness value and optimal position of the butterfly individual; if it has not, continue to execute steps S37 to S12; Step S37. Execute steps S38 to S312 for each butterfly; Step S38. Generate a random number R. If the random number R is less than the switching probability P, then according to step S23, update the butterfly position by the adaptive global optimal guidance factor; Step S39. If the random number R is greater than or equal to the switching probability P, then according to step S24, the butterfly position is updated by the refraction learning strategy; Step S310. Determine the constraint conditions according to step S33; calculate the fitness of all butterflies according to step S34; Step S311. Update the current optimal fitness and the current optimal position according to the greedy strategy; Step S312: Update the perception factor.

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