Robot autonomous learning and adaptive trajectory planning method oriented to man-machine cooperation

Abstract

The invention provides a robot autonomous learning and adaptive trajectory planning method oriented to man-machine cooperation aiming at a mechanical arm simulating a human teaching sample to obtain a motion skill and generalizing the motion skill to an adaptive obstacle avoidance behavior of a new situation, and specifically, a dynamic motion primitive algorithm is introduced to carry out learning and generalization of a motion trajectory of the mechanical arm. Based on the initial state and the search area of a generalized trajectory improved particle swarm algorithm, rapid search of a local obstacle avoidance trajectory is achieved, and mechanical arm motion trajectory planning with an autonomous obstacle avoidance function is comprehensively achieved. The method has the advantages that the method has high consistency with an original generalization track and wider adaptability, and the path searching efficiency is remarkably improved; a virtual simulation experiment and a physical experiment verify that the method has good stability and practicability.

Description

Technical Field

[0001] The present invention relates to the field of robot arm motion trajectory planning, and in particular to a robot autonomous learning and adaptive trajectory planning method for human-machine collaboration. Background Art

[0002] Robotic arm imitation learning, also known as teaching learning, mainly includes trajectory learning methods based on splines, statistical models, affine transformations, and dynamic motion primitives. Among them, the dynamic motion primitive proposed in 2002 is a strategy for encoding motion in a dynamic system in the form of nonlinear differential equations. It has high computational efficiency, continuous generated trajectories, and simple generalization. It is widely used in the movement and operation of robotic arms. This method has been proven to be effective in teaching robots how to perform some human tasks, such as swinging in table tennis, playing drums, writing, and performing human-computer interaction tasks, such as collaborative carrying of objects by humans and robotic arms, and collaborative polishing, assembly, and other manufacturing tasks.

[0003] However, in the adaptive behavior of the robot arm, autonomous obstacle avoidance is an unavoidable research issue. In recent years, robot obstacle avoidance based on DMPs has become a hot topic. The obstacle avoidance strategies derived from this algorithm can be roughly divided into two types. One is to add coupling terms to the dynamic model, such as: speed angle coupling terms, variable attractor obstacle avoidance system, geometric obstacle avoidance combined with artificial potential field, etc., but these methods are limited to conditions such as simple obstacle geometry and single environment. The other is to learn the coupling terms in combination with intelligent control algorithms, such as using the feedback information of the sensor to avoid complex obstacles; using neural networks to learn the mapping relationship between sensor feedback information and coupling terms. However, when faced with multiple obstacles, planning failures are prone to occur.

[0004] In recent years, robot path planning based on intelligent algorithms has also been a hot topic, including particle swarm algorithm, genetic algorithm, ant colony algorithm, artificial fish school algorithm, neural network algorithm, etc. Among them, particle swarm algorithm is widely used due to its advantages of simple parameters, fast convergence speed, and low computational complexity. However, the algorithm has limited improvement in running time and is difficult to meet the needs of online path planning.

[0005] In view of the above problems, the present invention proposes a robot autonomous learning and adaptive trajectory planning method for human-machine collaboration, introduces a dynamic motion primitive algorithm to learn and generalize the robot arm motion trajectory, improves the initial state and search area of ​​the particle swarm algorithm based on the generalized trajectory, realizes the rapid planning of local obstacle avoidance trajectory, and comprehensively realizes the robot arm motion trajectory planning with autonomous obstacle avoidance. Numerical simulation analysis, simulation experiments and physical experiments were carried out to verify the constructed algorithm. Summary of the invention

[0006] The purpose of the present invention is to solve the problems in the prior art and to propose a robot autonomous learning and adaptive trajectory planning method for human-machine collaboration.

[0007] A robot autonomous learning and adaptive trajectory planning method for human-machine collaboration is proposed. Based on the basic framework of the improved DMP algorithm, a particle swarm algorithm is integrated to propose a new obstacle avoidance algorithm, which is denoted as the DMP-PSO algorithm. The specific steps include:

[0008] S1: The DMP algorithm learns the characteristic parameters corresponding to the trajectory through a single teaching method;

[0009] S2: Change the environmental conditions to allow DMP to generate generalized trajectories that adapt to the new environment; use machine vision to identify obstacles in real time in the new environment and perform normalized descriptions;

[0010] S3: Real-time detection of collisions. For obstacles that cause trajectory interference, a particle swarm algorithm is used to search for the local optimal path.

[0011] In the above-mentioned robot autonomous learning and adaptive trajectory planning method for human-machine collaboration, the improved DMP algorithm can be specifically expressed as:

[0012]

[0013] Where: x, v∈R are the position and velocity of the specified point of the system, x0∈R is the initial position, g∈R is the target position, K, D∈R are the elastic constant and damping constant, τ∈R is the scaling factor that characterizes the duration of the motion, and s∈(0,1) is the reparameterization of time t∈[0,T], which is determined by the canonical system:

[0014]

[0015] a>0 is a predefined constant that determines the exponential decay of the regular system. f(s) is the nonlinear forcing term, which is the product of the comprehensive center point obtained by the linear combination of N force fields and the phase variable, and can be represented by a nonlinear Gaussian weighting function:

[0016]

[0017] Where: ω is the weight, N is the number of basis functions; φ i (s) is the Gaussian basis function. c is the center of the Gaussian basis function and is evenly distributed over time [0, T]. h is the width of the Gaussian basis function.

[0018]

[0019]

[0020] In the learning and generalization of dynamic motion primitives, formula (1) can be regarded as the basic formula of the DMP algorithm, and is also the basis for encoding and learning the teaching trajectory. The core is to obtain the characteristic parameters of the forcing term corresponding to the teaching trajectory, that is, the weight value ω corresponding to different basis functions. The primary task of the encoding procedure is to obtain the teaching information based on the teaching trajectory. Movement time t∈{Δt,2Δt,…,nΔt} (Δt is the set step length), the initial position of the trajectory x0=x demo (0), and the target position g = x demo (nΔt), the specific steps of learning the characteristic parameters corresponding to the trajectory are as follows:

[0021] Step 1: Substitute the above coded information into formula (1) to obtain:

[0022]

[0023] Step 2: Construct the loss function:

[0024]

[0025] ε(t)=x(t)(g-x0) (10)

[0026] Step 3: Solve the loss function:

[0027] The local weighted regression method is used to solve equation (9) and obtain the weight ω i .

[0028] Step 4: Develop a discrete sequence of velocity, displacement, and acceleration measurements of the motion, and then complete the learning process.

[0029] By changing the initial position x0 and the target position g of the motion, a new trajectory with similar trajectory features to the taught trajectory is obtained, which is called trajectory generalization.

[0030] In the above-mentioned robot autonomous learning and adaptive trajectory planning method for human-machine collaboration, in the process of searching the local optimal path by the particle swarm algorithm, it is assumed that the population size of the particle swarm is n, the dimension of the search area is j, and X ij =(X i1 ,X i2 ,…,X ij ) is the current position of particle i, V ij =(V i1 ,V i2 ,…,V ij ) is the current velocity of particle i; P ij =(P i1 ,P i2 ,…,P ij ) is the optimal position searched by particle i, P gj=(P g1 ,P g2 ,…,P gj ) is the optimal position searched by the entire particle swarm, and the speed and position update formulas are as follows:

[0031] V ij (k+1)=ωV ij (k)+c1r1(P ij (k)-X ij (k))+c2r2(P gj (k)-X ij (k)) (11)

[0032] X ij (k+1)=X ij (k)+V ij (k+1) (12)

[0033] Where: V ij (k)+1) and X ij (k+1) are the j-th component of the velocity and position of particle i at the (k+1)th iteration, P ij (k) is the j-th dimension component of the optimal position solution of particle i after the k-th iteration, and P gj (k) The j-th dimension component of the optimal position solution after the k-th iteration of the particle swarm; ω is the inertia weight; c1 is the cognitive factor; c2 is the social factor; r1 and r2 are random numbers in the interval [0, 1]. The detailed steps of the algorithm are as follows:

[0034] Step 1: Initialize the particle swarm. Randomly initialize the position x of the i-th particle (a total of n particles) i and speed v i ;

[0035] Step 2: Evaluate the fitness value of each particle and obtain the global optimum. Calculate the objective function value of each particle respectively. The particle with the smallest objective function value is taken as the global optimal particle.

[0036] Step 3: Speed ​​and position update: In each iteration, the particle updates itself by tracking its individual best historical position and the global best position.

[0037] Step 4: Optimal value update, calculate the objective function value of each particle separately, and compare it with the objective function value corresponding to the individual historical optimal position. If the current objective function value is smaller, use the current position to update the historical optimal position. At the same time, compare the objective function value corresponding to the current particle historical optimal position with the global optimal position, and the one with the smaller objective function value is updated to the global optimal position;

[0038] Step 5: Termination condition. The iteration termination condition usually selects the objective function value of the current global optimal position to be less than the set value or the number of iterations reaches the maximum number of iterations, and records and outputs the optimal solution.

[0039] In the above-mentioned robot autonomous learning and adaptive trajectory planning method for human-robot collaboration, numerical simulation and virtual simulation experiments are used to verify the DMP-PSO algorithm.

[0040] Compared with the prior art, the present invention has the following advantages:

[0041] 1. Compared with the speed angle method and artificial potential field method based on DMP, the DMP-PSO algorithm constructed in the present invention has higher consistency with the original generalized trajectory and wider adaptability; compared with the path planning of the PSO algorithm, in addition to having the path learning and generalization capabilities, it also significantly improves the path search efficiency.

[0042] 2. The DMP-PSO algorithm constructed by the present invention has the ability to learn and generalize paths in three-dimensional space, and has a good obstacle avoidance effect for obstacles of different shapes, and retains the characteristics of the original generalized trajectory to the greatest extent.

[0043] 3. The DMP-PSO algorithm designed in this paper can control the robot arm to find an effective path from the starting point to the end point according to the generalized trajectory, and perceive obstacles, terrain and other information in the environment, and respond accordingly based on this information. The movement is relatively smooth, without sliding or loss of control. Therefore, this method has good stability and practicality. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 This is a schematic diagram of the framework for integrating DMP and PSO obstacle avoidance in a robot autonomous learning and adaptive trajectory planning method for human-machine collaboration proposed by the present invention.

[0045] Figure 2 This is a DMP learning and generalization trajectory diagram in a robot autonomous learning and adaptive trajectory planning method for human-machine collaboration proposed by the present invention.

[0046] Figure 3 This is a path planning diagram under different methods in a robot autonomous learning and adaptive trajectory planning method for human-machine collaboration proposed by the present invention.

[0047] Figure 4 Path graph generated for the speed-angle method.

[0048] Figure 5 Path diagram generated for the artificial potential field method.

[0049] Figure 6This is a path diagram generated by MDP-PSO in the robot autonomous learning and adaptive trajectory planning method for human-machine collaboration proposed by the present invention.

[0050] Figure 7 This is a path map generated by a basic particle swarm algorithm in a robot autonomous learning and adaptive trajectory planning method for human-machine collaboration proposed by the present invention.

[0051] Figure 8 This is the obstacle avoidance trajectory diagram in three-dimensional space of the DMP-PSO algorithm in the robot autonomous learning and adaptive trajectory planning method for human-machine collaboration proposed by the present invention.

[0052] Fig. 9 This is a trajectory planning diagram in the CoppeliaSim environment in a robot autonomous learning and adaptive trajectory planning method for human-machine collaboration proposed in the present invention.

[0053] Fig.10 This is a diagram of the material transfer process in a physical verification experiment of a robot autonomous learning and adaptive trajectory planning method for human-machine collaboration proposed in the present invention.

[0054] Fig.11 This is a diagram of the robot arm regression process in the physical verification experiment of the robot autonomous learning and adaptive trajectory planning method for human-machine collaboration proposed by the present invention. DETAILED DESCRIPTION

[0055] Reference Figure 1-11 The present invention provides a robot autonomous learning and adaptive trajectory planning method for human-machine collaboration, which integrates the particle swarm algorithm under the basic framework of the improved DMP algorithm and proposes a new obstacle avoidance algorithm, which is recorded as the DMP-PSO algorithm: specifically, it includes the following steps:

[0056] S1: The DMP algorithm learns the characteristic parameters corresponding to the trajectory through a single teaching method, including encoding and learning the teaching trajectory;

[0057] S2: Change the environmental conditions to allow DMP to generate generalized trajectories that adapt to the new environment; use machine vision to identify obstacles in real time in the new environment and perform normalized descriptions;

[0058] S3: Real-time detection of collisions. For obstacles that cause trajectory interference, a particle swarm algorithm is used to search for the local optimal path.

[0059] Among them, the improvement can be specifically expressed as:

[0060]

[0061] Where: x, v∈R are the position and velocity of the specified point of the system, x0∈R is the initial position, g∈R is the target position, K, D∈R are the elastic constant and damping constant, τ∈R is the scaling factor that characterizes the duration of the motion, and s∈(0,1) is the reparameterization of time t∈[0,T], which is determined by the canonical system:

[0062]

[0063] a>0 is a predefined constant that determines the exponential decay of the regular system. f(s) is the nonlinear forcing term, which is the product of the comprehensive center point obtained by the linear combination of N force fields and the phase variable, and can be represented by a nonlinear Gaussian weighting function:

[0064]

[0065] Where: ω is the weight, N is the number of basis functions; φ i (s) is the Gaussian basis function. c is the center of the Gaussian basis function and is evenly distributed over time [0, T]. h is the width of the Gaussian basis function.

[0066]

[0067] 2.2 Learning and generalization of dynamic motion primitives

[0068] Formula (1) can be regarded as the basic formula of the DMP algorithm, and is also the basis for encoding and learning the teaching trajectory. Its core is to obtain the characteristic parameters of the forced term corresponding to the teaching trajectory, that is, the weight value ω corresponding to different basis functions. The primary task of the encoding procedure is to obtain the teaching information based on the teaching trajectory. Movement time t∈{Δt,2Δt,…,nΔt} (Δt is the set step length), the initial position of the trajectory x0=x demo (0), and the target position g = x demo (nΔt). The specific steps of learning are as follows:

[0069] Step 1: Substitute the above coded information into formula (1) to obtain:

[0070]

[0071] Step 2: Construct the loss function:

[0072]

[0073] ε(t)=x(t)(g-x0) (10)

[0074] Step 3: Solve the loss function:

[0075] The local weighted regression method is used to solve equation (9) and obtain the weight ωi .

[0076] Step 4: Develop a discrete sequence of velocity, displacement, and acceleration measurements of the motion, and then complete the learning process.

[0077] By changing the initial position x0 and the target position g of the motion, a new trajectory with similar trajectory features to the taught trajectory is obtained, which is called trajectory generalization. Figure 1 The results of teaching the DMP algorithm with a known trajectory and then changing the target position, the initial position, and the target position and the initial position simultaneously to generalize the trajectory are described.

[0078] In the particle swarm algorithm, assuming that the population size of the particle swarm is n, the dimension of the search area is j, and X ij =(X i1 ,X i2 ,…,X ij ) is the current position of particle i, V ij =(V i1 ,V i2 ,…,V ij ) is the current velocity of particle i; P ij =(P i1 ,P i2 ,…,P ij ) is the optimal position searched by particle i, P gj =(P g1 ,P g2 ,…,P gj ) is the optimal position searched by the entire particle swarm. The speed and position update formulas are as follows:

[0079] V ij (k+1)=ωV ij (k)+c1r1(P ij (k)-X ij (k))+c2r2(P gj (k)-X ij (k)) (10)

[0080] X ij (k+1)=X ij (k)+V ij (k+1) (11)

[0081] Where: V ij (k+1) and X ij (k+1) are the j-th component of the velocity and position of particle i at the (k+1)th iteration, P ij (k) is the j-th dimension component of the optimal position solution of particle i after the k-th iteration, and P gj(k) The j-th dimension component of the optimal position solution after the k-th iteration of the particle swarm; ω is the inertia weight; c1 is the cognitive factor; c2 is the social factor; r1 and r2 are random numbers in the interval [0, 1]. The detailed steps of the algorithm are as follows:

[0082] Step 1: Initialize the particle swarm. Randomly initialize the position x of the i-th particle (a total of n particles) i and speed v i .

[0083] Step 2: Evaluate the fitness value of each particle and obtain the global optimum. Calculate the objective function value of each particle separately, and the particle with the smallest objective function value is regarded as the global optimal particle.

[0084] Step 3: Speed ​​and position update. In each iteration, the particle updates itself by tracking its individual best historical position and the global best position.

[0085] Step 4: Optimal value update. Calculate the objective function value of each particle separately and compare it with the objective function value corresponding to the individual historical optimal position. If the current objective function value is smaller, use the current position to update the historical optimal position. At the same time, compare the objective function value corresponding to the current particle historical optimal position with the global optimal position, and the one with the smaller objective function value is updated to the global optimal position.

[0086] Step 5: Termination condition. The iteration termination condition usually selects the objective function value of the current global optimal position to be less than the set value or the number of iterations reaches the maximum number of iterations, and records and outputs the optimal solution.

[0087] In order to verify the obstacle avoidance performance of MDP-PSO, the present invention compares MDP-PSO, velocity angle method, artificial potential field method and basic particle swarm algorithm by means of numerical simulation, including trajectory planning and analysis in two-dimensional space and trajectory planning and analysis in three-dimensional space;

[0088] Among them, the trajectory planning and analysis DMP algorithm generalized trajectory in two-dimensional space is Figure 1 The trajectory of the initial position (0, 0) and the target position (30, 20) shown in ; the normalized obstacle is a circular quadratic curve with a center of (9, 7) and a radius of 4 mm. The paths generated by the four algorithms in the above environment are as follows Figure 3 As shown, Figure 4 , Figure 5 , Figure 6 , Figure 7 They are the path generation of velocity angle method, artificial potential field method, MDP-PSO, and basic particle swarm algorithm (PSO);

[0089] Depend on Figure 3It can be clearly seen from the results shown that the path generated by DMP-PSO not only completes the obstacle avoidance task, but also retains the shape characteristics of the original trajectory as much as possible.

[0090] In order to further analyze the characteristics of each algorithm, multiple groups of normalized obstacle combinations with different relative position relationships are set up, each group contains two circular obstacles, specifically: the two obstacles in combination one are a circle with a center of (9, 7) and a radius of 4 mm, and a circle with a center of (21, 13) and a radius of 3 mm; the two obstacles in combination two are a circle with a center of (9, 7) and a radius of 4 mm, and a circle with a center of (18, 16.2) and a radius of 3 mm; the two obstacles in combination three are a circle with a center of (9, 7) and a radius of 4 mm, and a circle with a center of (18, 10.8) and a radius of 3 mm. Figures 4 to 7 The paths of velocity angle method, artificial potential field method, MDP-PSO and PSO algorithm in three combination environments are given in turn;

[0091] Figure 4 The working principle of the velocity angle method shown is that the particle is affected by the obstacle and produces a velocity angle component that deviates from the obstacle, causing the direction of the motion velocity to deviate, thereby driving the motion trajectory to bypass the obstacle. When the particle moves away from the current obstacle, the velocity direction gradually recovers. Figure 4 (b) shows that when the generalized motion trajectory is affected by the previous obstacle, the motion velocity direction is deflected and bypasses the obstacle, but the new velocity deflection angle generated by the obstacle in front of the motion direction is not enough to make the particle motion trajectory bypass the obstacle, resulting in a collision. The results show that this method is limited to multiple consecutive obstacles.

[0092] Figure 5 The working principle of the artificial potential field method shown in the figure is that there is a potential field force distributed around the obstacle, the direction is perpendicular to the quadratic curve (surface), and the closer to the obstacle, the greater the potential field force. The particle is affected by the field force and produces an acceleration component perpendicular to the quadratic curve (surface), thereby driving the motion trajectory to bypass the obstacle. However, when the distance between two obstacles is close, the potential fields generated by the two obstacles overlap, and the mutual influence leads to a certain uncertainty in the size and direction of the potential field in the overlapping area, causing the particle to produce random jumps in the trajectory when passing through the area, as shown in Figure 5 (c) The results show that this method is limited by the positions between multiple obstacles.

[0093] Depend on Figure 6 It can be clearly seen from the results that the path generated by DMP-PSO not only completes the obstacle avoidance task, but also retains the shape characteristics of the original trajectory as much as possible, while avoiding the limitations of the speed angle obstacle avoidance method and the artificial potential field obstacle avoidance method, indicating that the algorithm has strong adaptability.

[0094] Figure 7 The basic particle swarm algorithm shown in the figure achieves obstacle avoidance for all three scenes, but the shape characteristics of the generated path are quite different from the original trajectory. In addition, in the basic particle swarm algorithm, the particle swarm dimension is 10, and it takes 8.6 seconds to generate an obstacle avoidance trajectory after 1000 iterations; in the DMP-PSO algorithm, the particle swarm dimension is 5, and it takes 3.12 seconds to generate an obstacle avoidance trajectory after 100 iterations, which significantly improves the obstacle avoidance efficiency.

[0095] In summary, through the numerical simulation results and analysis in two-dimensional space, it can be seen that the DMP-PSO algorithm constructed in this paper has a higher consistency with the original generalized trajectory and a wider adaptability than the velocity angle method and artificial potential field method based on DMP; compared with the path planning of the PSO algorithm, in addition to the path learning and generalization capabilities, it also significantly improves the path search efficiency.

[0096] For obstacles with irregular geometric shapes and arbitrary positions in three-dimensional space, the smallest sphere (ellipsoid) is used to represent them. By the same token, the geometric obstacle avoidance method of the two-dimensional plane can be extended to three-dimensional space. First, the starting point and the end point where the original generalized trajectory of DMPs intersects with the spherical area of ​​the obstacle are taken as the starting position and the end position of the path search of the PSO algorithm; secondly, the generalized trajectory in the spherical obstacle space is sampled sparsely and set as the initial position of the particle in the PSO algorithm; then, a new obstacle avoidance path is searched in the vicinity of the spherical obstacle space; finally, the generalized trajectory outside the spherical obstacle space is merged with the obstacle avoidance path and the curve is smoothed to generate the final trajectory.

Claims

1. A robot autonomous learning and adaptive trajectory planning method for human-machine collaboration, characterized in that: A new obstacle avoidance algorithm is proposed by integrating the particle swarm algorithm under the basic framework of the improved DMP algorithm, which is recorded as the DMP-PSO algorithm. It specifically includes the following steps: S1: The DMP algorithm learns the characteristic parameters corresponding to the trajectory through a single teaching method, including encoding and learning the teaching trajectory; S2: Change the environmental conditions to allow DMP to generate generalized trajectories that adapt to the new environment; use machine vision to identify obstacles in real time in the new environment and perform normalized descriptions; S3: Real-time detection of collisions. For obstacles that cause trajectory interference, a particle swarm algorithm is used to search for the local optimal path.

2. The method for autonomous learning and adaptive trajectory planning of a robot for human-machine collaboration according to claim 1, characterized in that: The improved DMP algorithm can be specifically expressed as: Where: x, v∈R are the position and velocity of the specified point of the system, x0∈R is the initial position, g∈R is the target position, K, D∈R are the elastic constant and damping constant, τ∈R is the scaling factor that characterizes the duration of the motion, and s∈(0,1) is the reparameterization of time t∈[0,T], which is determined by the canonical system: a>0 is a predefined constant that determines the exponential decay of the regular system. f(s) is the nonlinear forcing term, which is the product of the comprehensive center point obtained by the linear combination of N force fields and the phase variable, and can be represented by a nonlinear Gaussian weighting function: φ i (s)=exp(-h i (sc i ) 2 ) (5) Where: ω is the weight, N is the number of basis functions; φ i (s) is the Gaussian basis function. c is the center of the Gaussian basis function and is evenly distributed over time [0, T]. h is the width of the Gaussian basis function. In the learning and generalization of dynamic motion primitives, formula (1) can be regarded as the basic formula of the DMP algorithm, and is also the basis for encoding and learning the teaching trajectory. The core is to obtain the characteristic parameters of the forcing term corresponding to the teaching trajectory, that is, the weight value ω corresponding to different basis functions. The primary task of the encoding procedure is to obtain the teaching information based on the teaching trajectory. Movement time t∈{Δt,2Δt,…,nΔt} (Δt is the set step length), the initial position of the trajectory x0=x demo (0), and the target position g = x demo (nΔt), the specific steps of learning the characteristic parameters corresponding to the trajectory are as follows: Step 1: Substitute the above coded information into formula (1) to obtain: Step 2: Construct the loss function: ε(t)=x(t)(g-x0) (10) Step 3: Solve the loss function: The local weighted regression method is used to solve equation (9) and obtain the weight ω i . Step 4: Develop a discrete sequence of velocity, displacement, and acceleration measurements of the motion, and then complete the learning process. By changing the initial position x0 and the target position g of the motion, a new trajectory with similar trajectory features to the taught trajectory is obtained, which is called trajectory generalization.

3. The method for autonomous learning and adaptive trajectory planning of a robot for human-machine collaboration according to claim 1, characterized in that: In the process of searching for the local optimal path by the particle swarm algorithm, assuming that the population size of the particle swarm is n, the dimension of the search area is j, and X ij =(X i1 ,X i2 ,…,X ij ) is the current position of particle i, V ij =(V i1 ,V i2 ,…,V ij ) is the current velocity of particle i; P ij =(P i1 ,P i2 ,…,P ij ) is the optimal position searched by particle i, P gj =(P g1 ,P g2 ,…,P gj ) is the optimal position searched by the entire particle swarm, and the speed and position update formulas are as follows: V ij (k+1)=ωV ij (k)+c1r1(P ij (k)-X ij (k))+c2r2(P gj (k)-X ij (k)) (11) X ij (k+1)=X ij (k0+V ij (k+1) (12) Where: V ij (k+1) and X ij (k+1) are the j-th component of the velocity and position of particle i at the (k+1)th iteration, P ij (k) is the j-th dimension component of the optimal position solution of particle i after the k-th iteration, and P gj (k) The j-th dimension component of the optimal position solution after the k-th iteration of the particle swarm; ω is the inertia weight; c1 is the cognitive factor; c2 is the social factor; r1 and r2 are random numbers in the interval [0, 1]. The detailed steps of the algorithm are as follows: Step 1: Initialize the particle swarm. Randomly initialize the position x of the i-th particle (a total of n particles) i and speed v i ; Step 2: Evaluate the fitness value of each particle and obtain the global optimum. Calculate the objective function value of each particle respectively. The particle with the smallest objective function value is taken as the global optimal particle. Step 3: Speed ​​and position update: In each iteration, the particle updates itself by tracking its individual best historical position and the global best position. Step 4: Optimal value update, calculate the objective function value of each particle separately, and compare it with the objective function value corresponding to the individual historical optimal position. If the current objective function value is smaller, use the current position to update the historical optimal position. At the same time, compare the objective function value corresponding to the current particle historical optimal position with the global optimal position, and the one with the smaller objective function value is updated to the global optimal position; Step 5: Termination condition. The iteration termination condition usually selects the objective function value of the current global optimal position to be less than the set value or the number of iterations reaches the maximum number of iterations, and records and outputs the optimal solution.

4. The method for autonomous learning and adaptive trajectory planning of a robot for human-machine collaboration according to claim 1, characterized in that: In the process of S2, sparse sampling is performed based on the generalized trajectory; The distance d between the sample point position and the center is determined according to the two-point distance formula, and the safety distance (safety line) is set according to the normalized obstacle geometry. When d is greater than the safety distance (S), it indicates that the generalized trajectory generated by DMPs is outside the range of obstacle interference, and the path is retained. When d is less than or equal to the safety distance, it indicates that the generalized trajectory generated by DMP is already within the range of obstacle interference. This sample point is recorded and set as the initial position of the particle swarm. At the same time, the two points closest to the safety line are used as the starting position and end position of the PSO algorithm search. Finally, the local search path and the generalized trajectory are fitted into the obstacle avoidance motion trajectory.

5. The method for autonomous learning and adaptive trajectory planning of a robot for human-machine collaboration according to claim 1, characterized in that: Numerical simulation, virtual simulation experiment and physical verification experiment are used to verify the DMP-PSO algorithm.

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