Improved NSGA-III-based mobile manipulator space-time trajectory comprehensive performance optimization method

Abstract

The invention belongs to the field of robot motion planning and trajectory optimization, and discloses an improved NSGA-III (Non-dominated Sorting Genetic Algorithm-III)-based comprehensive performance optimization method for a space-time trajectory of a mobile mechanical arm. Comprising the steps of 1, generating an initial path of the mobile mechanical arm; 2, trajectory space-time parameterization representation is carried out; 3, a multi-objective function is established, specific task constraints are added, and a smooth and safe track meeting dynamic constraints is generated so that the mobile mechanical arm can complete a specific task; and step 4, improving an NSGA-II algorithm to realize trajectory optimization. According to the method, aiming at a plurality of targets such as obstacle avoidance, path smoothness, dynamic constraint and time optimization of the high-degree-of-freedom mobile mechanical arm, a spatial-temporal trajectory representation method is adopted to directly control waypoints and time, so that the calculation cost in the optimization process is reduced, efficient optimization is realized, and the optimization efficiency is improved. And an intelligent optimization algorithm is adopted to overcome the problem that an optimal solution is difficult to seek due to nonlinearity.

Description

Technical Field

[0001] The invention belongs to the field of robot motion planning and trajectory optimization, and in particular relates to a method for optimizing the spatiotemporal trajectory comprehensive performance of a mobile robot arm based on an improved NSGA-III. Background Art

[0002] With the development of automation and intelligent manufacturing, it has become a key requirement for mobile manipulators to achieve efficient operation in complex and changing working environments. When performing tasks, these manipulators not only have to face single goals such as the shortest path and the fastest arrival time, but also need to comprehensively consider multiple goals such as obstacle avoidance, path smoothness, vibration reduction, and energy consumption minimization to ensure comprehensive optimization of operations. However, traditional path planning and trajectory optimization methods often only focus on one or several goals, ignoring the balance and improvement of overall performance. Due to the many uncertainties and constraints in the actual environment, traditional optimization algorithms are prone to fall into local optimal solutions and cannot solve the problem globally. Local optimal solutions may lead to inefficient paths, increased operating costs, and even fail to meet safety and operational requirements in some cases. In addition, due to the high coupling relationship between time and space caused by traditional trajectory representation methods in the process of path planning, it is impossible to achieve joint optimization of time and space, resulting in the optimization results not being able to achieve both optimal time and space.

[0003] At present, the methods of robot motion planning are basically divided into three categories: search-based, sampling-based and optimization-based. The search-based methods mainly include Dijkstra algorithm, A* algorithm, D Lite algorithm, depth-first algorithm (dfs), etc. These algorithms can ensure the shortest path and adapt to dynamic complex non-convex environments. However, as the dimension increases, the search space will explode, and the dimension of the joint configuration space will increase exponentially with the number of robots. The sampling-based methods mainly include RRT*, bidirectional RRT, RRT-Conect, Dynamic-RRT, etc. These algorithms can effectively generate trajectories in solving high-dimensional and complex environments, but cannot guarantee the completeness and optimality of the solution within a limited time. The optimization-based methods mainly include methods based on traditional numerical optimization (such as chomp, stomp, AGD, Adam, etc.) and methods based on intelligent optimization (such as genetic algorithm, particle swarm algorithm, ant colony algorithm, etc.), which can obtain feasible trajectories under high-dimensional dynamic constraints, but are often trapped in local optimal solutions, especially in low-dimensional environments and complex obstacle shapes. It is difficult to find the optimal solution. For multi-objective optimization, due to its high problem and computational complexity, existing optimization algorithms often solve efficiently and often fall into local minima, which means that superior performance in one type of performance does not guarantee superior performance in other types of performance. The commonly used continuous-time trajectory representation methods currently include polynomial spline method, B-spline method, Bezier curve, etc. However, these methods have a high degree of coupling between time domain optimization and some require the combination of control points and cannot directly optimize the trajectory by controlling the path points. Summary of the invention

[0004] The purpose of the present invention is to provide a method for optimizing the comprehensive performance of spatiotemporal trajectory of a mobile manipulator based on an improved NSGA-III, so as to solve the technical problem that the complexity and nonlinearity of multi-objective functions are prone to fall into the local minimum during the optimization process.

[0005] In order to solve the above technical problems, the specific technical solution of the mobile manipulator spatiotemporal trajectory comprehensive performance optimization method based on improved NSGA-III of the present invention is as follows:

[0006] A method for optimizing the comprehensive performance of spatiotemporal trajectory of a mobile manipulator based on an improved NSGA-III comprises the following steps:

[0007] Step 1: Generate the initial path of the mobile robot: Use the A* algorithm to search for a given obstacle avoidance path from the starting point to the end point in a given obstacle environment as the initial trajectory for the subsequent trajectory optimization. This trajectory only generates multiple nodes, including spatial information but not time information;

[0008] Step 2: Temporal and spatial parameterization of trajectory: Simplify the initial path points generated by the A* algorithm, classify them according to the distance to the obstacle and the number of the closest obstacle, and use the MINCO parameter method to represent the trajectory of these simplified trajectory points;

[0009] Step 3: Establish a multi-objective function and add specific task constraints to generate a smooth, safe trajectory that satisfies dynamic constraints for the mobile robot to complete a specific task;

[0010] Step 4: Improve NSGA-II algorithm to achieve trajectory optimization. After establishing the objective function, use the improved NSGA-III to optimize it, obtain the global optimal solution of the function, and obtain the optimized trajectory, that is, the trajectory with the best comprehensive performance in terms of obstacle avoidance, dynamic constraints, smoothness, terminal constraints, and time.

[0011] Furthermore, the A* algorithm in step 1 is a heuristic search algorithm, which is implemented by estimating a function. The value of the function needs to be calculated for each step the robot takes, and the node with the smallest function value is the next step of the robot arm.

[0012] The position to be reached, the general expression of the heuristic function is as follows:

[0013] F(n)=g(n)+h(n) (1)

[0014] Among them, g(n) is the actual cost spent by the robot from the initial node of the path to the node b in the path planning; because the robot arm knows the actual time spent from the initial node to the node n and the actual length traveled, the function g(n) value is the actual value; h(n) is the estimated cost spent from the current node n to the end point of the path planning; function F(n) is the total cost in the entire path planning, and the estimated function g(n) is the distance between the end position of the robot arm and the target node, that is,

[0015]

[0016] Furthermore, the step 2 sets the number of trajectory segments to 5, and selects 4 points in the trajectory excluding the starting point and the target point;

[0017] Select generalized joint configuration As a planning space, q x ,q y They represent the positions of the robot's mobile chassis, Respectively represent the 6 joint angles of the robotic arm;

[0018] The trajectory is divided into 5 segments, each segment is represented by a polynomial of degree 2s-1, so the coefficients of the polynomial of each trajectory segment are represented as a 2s*9 matrix c i , assuming that the duration of each trajectory is T i , then the trajectory of this segment is represented by p i (t), the entire trajectory is expressed as the following piecewise function:

[0019]

[0020] Where β(t)=[1,t,…,t 2s-1 ], the expression obtained by further abstraction is as follows:

[0021]

[0022] It is an abstract representation of the entire trajectory. c is determined by the intermediate path points q and the duration T. According to the definition of the MINCO trajectory, it is found that the coefficient matrix c is optimized by optimizing the path points and time, thereby optimizing the entire trajectory.

[0023] Furthermore, if the step 2 is to obtain the configuration information of a certain path point in the trajectory, it can be calculated by the following formula:

[0024]

[0025] Among them, q i,j represents the path point information of the i-th segment at time j, T i,j Represents the duration of the i-th segment at time j. The MINCO spatiotemporal trajectory representation is used to achieve joint optimization of time and space.

[0026] Furthermore, in step 3, the objective function of the trajectory generation problem is formulated as follows:

[0027]

[0028] J T,i =ω T T i (8)

[0029]

[0030] Among them, J s,i represents the smoothing cost of the i-th trajectory, which is obtained by integrating the s-order derivative of the i-th trajectory with respect to q, J T,i represents the time cost of the i-th trajectory, which ensures that the execution time of the trajectory is as small as possible. p,irepresents the additional penalty term for the i-th trajectory, which is set according to the task customization. It takes into account obstacle avoidance, dynamic constraints, and the end position to maintain a specific trajectory. i Indicates that the i-th segment is divided into M i This is a fine discretization operation of the trajectory. Σ (·) represents sparse and dense sampling strategies, ω T ,ω d represents the weight of time and additional penalty term. The specific meaning of d and D depends on the specific additional penalty term. The MINCO trajectory optimization solution is obtained by solving equation (6).

[0031] Furthermore, the improved NSGA-III algorithm in step 4 uses adaptive crossover and mutation probabilities based on Gaussian distribution to improve the efficiency of the algorithm in searching for solutions and simulating population evolution. The adaptive crossover probability p c and adaptive mutation probability p m as follows:

[0032]

[0033] in, represents the minimum and maximum crossover probability, and Indicates the minimum and maximum values ​​of the mutation probability, gen indicates the current population size, and generation indicates the total number of individuals in the population.

[0034] The improved NSGA-III algorithm performs random number crossover processing on the crossover points. In addition to random number crossover, the positions of gene fragments in individuals are exchanged during the crossover process, and the communication mechanism between individuals is enhanced. In each generation, the algorithm will retain a part of excellent individuals, which will still be used in the next generation to ensure that excellent genetic characteristics are retained. In this way, the objective function can jump out of the local minimum and obtain the global optimal solution.

[0035] The present invention provides a method for optimizing the comprehensive performance of the spatiotemporal trajectory of a mobile robot based on an improved NSGA-III, which has the following advantages: the method aims to achieve joint optimization of multiple objectives such as obstacle avoidance, smoothness, dynamic safety constraints, task constraints and time optimization, uses MINCO trajectory representation to reduce the complexity of the trajectory optimization problem, and effectively jumps out of the local minimum by improving NSGA-III, significantly improving the comprehensive operating efficiency of the mobile robot. This project is based on the minimum control volume spatiotemporal trajectory representation method (MINCO) and the improved non-dominated sorting genetic algorithm III (NSGA-III) trajectory optimization method, and uses A* to efficiently generate the initial trajectory, providing a better starting point for the subsequent optimization process. On this basis, a multi-objective function model including obstacle avoidance, smoothness, dynamic safety constraints, task constraints and time is constructed in combination with an intelligent optimization method, which further optimizes the effect of trajectory planning. The planning method uses a new trajectory parameterization method MINCO, uses waypoints and time as parameters to describe the motion path of a 9-DOF mobile robot, and accurately controls the position and posture of the robot at different time points, so as to better adapt to complex task requirements. In order to overcome the problem that traditional optimization algorithms are prone to fall into local optimality, NSGA-III is improved to enhance its exploration ability, so that it can more effectively find the global optimal solution in the search space and improve the success rate of solving multi-objective optimization of mobile manipulator operation. In order to solve the problem of slow performance solution of multiple indicators under redundant degrees of freedom, MINCO trajectory representation is adopted to realize gradient iteration of multi-objective optimization with linear complexity operation trajectory, quickly optimize and solve, and achieve comprehensive performance improvement of mobile manipulator.

[0036] In summary, the method of the present invention aims at multiple objectives such as obstacle avoidance, path smoothness, dynamic constraints and time optimization of a mobile manipulator with high degrees of freedom. The space-time trajectory representation can reduce the computational cost in the optimization process by directly controlling waypoints and time, achieve efficient optimization, and use an intelligent optimization algorithm to overcome the difficulty in finding the optimal solution caused by nonlinearity. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 is a schematic diagram of kinematic modeling of a mobile robotic arm;

[0038] Figure 2 Flowchart for improving the NSGA-III algorithm;

[0039] Figure 3 Schematic diagram of the spatiotemporal trajectory optimization framework for a mobile robot;

[0040] Figure 4 is a schematic diagram of the mobile robot arm operation scene and trajectory. DETAILED DESCRIPTION

[0041] In order to better understand the purpose, structure and function of the present invention, the following is a further detailed description of a method for optimizing the spatiotemporal trajectory comprehensive performance of a mobile manipulator based on an improved NSGA-III in conjunction with the accompanying drawings.

[0042] The present invention is a mobile manipulator spatiotemporal trajectory optimization method based on improved NSGA-III. Its greatest feature and innovation is that it can ensure obstacle avoidance, smoothness, and dynamic safety constraints while optimizing the joint time, solving the problem that the complexity and nonlinearity of multi-objective functions are prone to falling into local minima during the optimization process. The design process of this planning method mainly includes the following steps:

[0043] Step 1: Generate the initial path of the mobile robot. Use the A* algorithm to search for a given obstacle avoidance path from the starting point to the end point in a given obstacle environment as the initial trajectory for the subsequent trajectory optimization. This trajectory only generates multiple nodes, including spatial information but not temporal information.

[0044] The A* algorithm is a heuristic search algorithm that is implemented by estimating a function. The value of the function needs to be calculated every time the robot takes a step, and the node with the smallest function value is the position that the robot needs to reach in the next step. The general expression of the heuristic function is as follows:

[0045] F(n)=g(n)+h(n) (1)

[0046] Among them, g(n) is the actual cost of the robot from the initial node of the path to the node b in the path planning; because the robot arm knows the actual time and actual distance from the initial node to the node n, the function g(n) value is the actual value; h(n) is the estimated cost from the current node n to the end of the path planning; function F(n) is the total cost in the entire path planning. The estimated function g(n) is the distance between the end position of the robot arm and the target node, that is

[0047]

[0048] Step 2: Temporal and spatial parameterization of trajectory. The initial path points generated by the A* algorithm are simplified and classified according to the distance to the obstacle and the number of the closest obstacle. Since the number of trajectory segments is set to 5 in the present invention, 4 points in the trajectory excluding the starting point and the target point are selected, and the trajectory of these simplified trajectory points is represented by the MINCO parameter method.

[0049] Select generalized joint configuration As a planning space. q x ,q y They represent the positions of the robot's mobile chassis, They represent the six joint angles of the robotic arm respectively.

[0050] The trajectory is divided into 5 segments, each segment is represented by a polynomial of degree 2s-1, so the coefficients of the polynomial of each trajectory segment are represented as a 2s*9 matrix c i Assume that the duration of each trajectory is T i , then the trajectory of this segment is represented by p i (t), the entire trajectory can be expressed as the following piecewise function:

[0051]

[0052] Where β(t)=[1,t,…,t 2s-1 ]. The expression obtained by further abstraction is as follows:

[0053]

[0054] It is an abstract representation of the entire trajectory, and c is determined by the intermediate path points q and the duration T. According to the definition of the MINCO trajectory, it can be found that by optimizing the path points and time to optimize the coefficient matrix c, the entire trajectory is optimized. Compared with the Bezier curve, this trajectory representation method can intuitively optimize the path points and time continuous variables.

[0055] If you want to obtain the configuration information of a certain path point in the trajectory, you can easily calculate it through the following formula:

[0056]

[0057] Among them, q i,j represents the path point information of the i-th segment at time j, T i,j Represents the duration of the i-th segment at time j. Using MINCO spatiotemporal trajectory representation, joint optimization of time and space can be achieved, and this trajectory representation method can keep the trajectory locally smooth through linear complexity operations.

[0058] Step 3: Establish multi-objective functions and add specific task constraints. In order to generate smooth, safe and dynamically constrained trajectories for the mobile robot to complete specific tasks, we formulate the objective function of the trajectory generation problem as follows:

[0059]

[0060] J T,i =ω T T i (8)

[0061]

[0062] Among them, J s,i represents the smoothing cost of the i-th trajectory, which is obtained by integrating the s-order derivative of the i-th trajectory with respect to q. T,i represents the time cost of the i-th trajectory, which ensures that the execution time of the trajectory is as small as possible. p,i M represents the additional penalty term for the i-th segment of the trajectory, which can be customized according to the task. In the present invention, this term considers obstacle avoidance, dynamic constraints, and the terminal posture maintaining a specific trajectory. i Indicates that the i-th segment is divided into M i This is a fine discretization operation of the trajectory, which is beneficial for more refined iteration of the trajectory cost to avoid skipping the global minimum. Σ (·) represents sparse and dense sampling strategies. ω T ,ω d represents the weight of time and additional penalty term, and the specific meaning of d and D depends on the specific additional penalty term. By solving equation (6), the MINCO trajectory optimization solution can be obtained.

[0063] Step 4: Improve NSGA-II algorithm to achieve trajectory optimization. After establishing the above objective function, use improved NSGA-III to optimize it, obtain the global optimal solution of the function, and obtain the optimized trajectory, that is, the trajectory with the best comprehensive performance in terms of obstacle avoidance, dynamic constraints, smoothness, terminal constraints, and time.

[0064] The NSGA-III algorithm is improved by using adaptive crossover and mutation probabilities based on Gaussian distribution to improve the efficiency of the algorithm in searching for solutions and simulating population evolution. c and adaptive mutation probability p m as follows:

[0065]

[0066] in, Indicates the minimum and maximum crossover probability. and Indicates the minimum and maximum values ​​of the mutation probability. gen indicates the current population size, and generation indicates the total number of individuals in the population.

[0067] The improved NSGA-III algorithm performs random number crossover processing on the crossover points. In addition to random number crossover, the positions of gene fragments in individuals are exchanged during the crossover process. This method helps to maintain certain characteristics of individuals while introducing new genetic variations. In addition, the communication mechanism between individuals is enhanced. In each generation, the algorithm will retain a part of excellent individuals, which will still be used in the next generation to ensure that excellent genetic characteristics are retained. In this way, the objective function jumps out of the local minimum and obtains the global optimal solution.

[0068] Example:

[0069] refer to Figure 1a , Figure 1b ,First, the mobile manipulator is modeled to facilitate the establishment of the ,objective function. The mobile manipulator is approximated as a set of collision spheres. l p l,m represents the center position of the mth sphere of the link l, where l∈{0,1,2,3,4,5,6}, and when l is 0, it refers to the chassis of the mobile robot. These spheres are in the world coordinate system The center of can be obtained through the forward kinematics of the mobile manipulator:

[0070]

[0071] Among them, m∈{1,…,m l},m l represents the number of spheres covered by connecting rod l, Represents the coordinate system from link l to the world Homogeneous transformation of . l Represents the radius of the sphere covering the link l.

[0072] Then, with regard to the additional penalty items mentioned above, this patent mainly divides them into three parts according to practical problems: obstacle avoidance and self-obstacle avoidance, dynamic feasibility constraints, and the task constraint of minimizing the deviation between the end position and the target position.

[0073] Obstacle avoidance and self-collision avoidance are taken as one of the additional penalty items. In order to ensure that there is no collision between the obstacle and the robot, we establish an ESDF graph and define the ESDG value of the collision sphere as D ESDF (·).

[0074] If you want to avoid collision with obstacles, you need D ESDF (·) is greater than the radius r of each sphere l :

[0075]

[0076] Among them, l∈{0,1,2,3,4,5,6}, m∈{1,…,m l}.

[0077] To avoid self-collision, define the following inequality constraints:

[0078]

[0079] Among them, l′∈{0,…,l-1}, l∈{0,1,2,3,4,5,6}, i∈{1,…,m l′},j∈{1,…,m l}

[0080] The dynamic feasibility constraint is used as another additional penalty term. The dynamic feasibility constraint can be divided into the feasibility constraint of the mobile chassis and the feasibility constraint of the robot joint. For the mobile chassis, the angular velocity and acceleration of the left and right wheels are restricted as follows:

[0081]

[0082] Among them, ω l(r) , α l(r) Represent the angular velocity and acceleration of the left and right wheels of the mobile chassis respectively. The following constraints are imposed on the angle, velocity and acceleration of each joint of the robot arm:

[0083] g θ (q l )=q l -q l,max (17)

[0084] g θ (q l )=q l,min -q l (18)

[0085]

[0086] Among them, q l represents the angle of the connecting rod l, q l,max and q l,min is the maximum and minimum allowable angle of the connecting rod l, ω l,max and α l,max is the maximum value allowed for the angular velocity and angular acceleration of the connecting rod l.

[0087] The task constraint of minimizing the deviation between the end position and the target position is taken as the last additional penalty term. The objective function formula is as follows:

[0088]

[0089] in, is the position of the end effector, is the end position of the end effector, d p is the allowable deviation value of the first two.

[0090] Figure 2 The optimization flow chart of the improved NSGA-III is recorded and displayed. As can be seen from the flow chart, the present invention focuses more on the improvement of the crossover method, which can increase more exploration and thus jump out of the local minimum. A flow chart of the spatiotemporal trajectory optimization method of a mobile manipulator based on the improved NSGA-III is shown in the figure. Figure 3 As shown in the figure, it mainly includes A* initial trajectory generation module, initial trajectory simplification module, space-time trajectory MINCO characterization trajectory module, multi-objective function construction module and improved NSGA-III optimization module. The robot trajectory planning idea is relatively clear and easy to implement. Figure 4a , Figure 4b Schematic diagram of the mobile robot arm operation scene and trajectory.

[0091] It is to be understood that the present invention is described by some embodiments, and it is known to those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the scope of protection of the present invention.

Claims

1. A method for optimizing the comprehensive performance of spatiotemporal trajectory of a mobile manipulator based on improved NSGA-III, characterized in that: The steps include: Step 1: Generate the initial path of the mobile robot: Use the A* algorithm to search for a given obstacle avoidance path from the starting point to the end point in a given obstacle environment as the initial trajectory for the subsequent trajectory optimization. This trajectory only generates multiple nodes, including spatial information but not time information; Step 2: Temporal and spatial parameterization of trajectory: Simplify the initial path points generated by the A* algorithm, classify them according to the distance to the obstacle and the number of the closest obstacle, and use the MINCO parameter method to represent the trajectory of these simplified trajectory points; Step 3: Establish a multi-objective function and add specific task constraints to generate a smooth, safe trajectory that satisfies dynamic constraints for the mobile robot to complete a specific task; Step 4: Improve NSGA-II algorithm to achieve trajectory optimization. After establishing the objective function, use the improved NSGA-III to optimize it, obtain the global optimal solution of the function, and obtain the optimized trajectory, that is, the trajectory with the best comprehensive performance in terms of obstacle avoidance, dynamic constraints, smoothness, terminal constraints, and time.

2. The method for optimizing the spatiotemporal trajectory comprehensive performance of a mobile manipulator based on an improved NSGA-III according to claim 1 is characterized in that: The A* algorithm in step 1 is a heuristic search algorithm, which is implemented by estimating a function. The value of the function needs to be calculated for each step the robot takes, and the node with the smallest function value is the position that the robot needs to reach in the next step. The general expression of the heuristic function is as follows: F(n)=g(n)+h(n) (1) Among them, g(n) is the actual cost spent by the robot from the initial node of the path to the node b in the path planning; because the robot arm knows the actual time spent from the initial node to the node n and the actual length traveled, the function g(n) value is the actual value; h(n) is the estimated cost spent from the current node n to the end point of the path planning; function F(n) is the total cost in the entire path planning, and the estimated function g(n) is the distance between the end position of the robot arm and the target node, that is, 3. The method for optimizing the spatiotemporal trajectory comprehensive performance of a mobile manipulator based on an improved NSGA-III according to claim 1 is characterized in that: In step 2, the number of trajectory segments is set to 5, and 4 points excluding the starting point and the target point in the trajectory are screened out; Select generalized joint configuration As a planning space, q x ,q y They represent the positions of the robot's mobile chassis, Respectively represent the 6 joint angles of the robotic arm; The trajectory is divided into 5 segments, each segment is represented by a polynomial of degree 2s-1, so the coefficients of the polynomial of each trajectory segment are represented as a 2s*9 matrix c i , assuming that the duration of each trajectory is T i , then the trajectory of this segment is represented by p i (t), the entire trajectory is expressed as the following piecewise function: Where β(t)=[1,t,…,t 2s-1 ], the expression obtained by further abstraction is as follows: It is an abstract representation of the entire trajectory. c is determined by the intermediate path points q and the duration T. According to the definition of the MINCO trajectory, it is found that the coefficient matrix c is optimized by optimizing the path points and time, thereby optimizing the entire trajectory.

4. The method for optimizing the spatiotemporal trajectory comprehensive performance of a mobile manipulator based on an improved NSGA-III according to claim 1 is characterized in that: If the step 2 is to obtain the configuration information of a certain path point in the trajectory, it can be calculated by the following formula: Among them, q i,j represents the path point information of the i-th segment at time j, T i,j Represents the duration of the i-th segment at time j. The MINCO spatiotemporal trajectory representation is used to achieve joint optimization of time and space.

5. The method for optimizing the comprehensive performance of spatiotemporal trajectory of a mobile manipulator based on improved NSGA-III according to claim 1 is characterized in that: The objective function of the trajectory generation problem is formulated as follows in step 3: J T,i =ω T T i (8) Among them, J s,i represents the smoothing cost of the i-th trajectory, which is obtained by integrating the s-order derivative of the i-th trajectory with respect to q, J T,i represents the time cost of the i-th trajectory, which ensures that the execution time of the trajectory is as small as possible. p,i represents the additional penalty term for the i-th trajectory, which is set according to the task customization. It takes into account obstacle avoidance, dynamic constraints, and the end position to maintain a specific trajectory. i Indicates that the i-th segment is divided into M i This is a fine discretization operation of the trajectory. Σ (·) represents sparse and dense sampling strategies, ω T ,ω d represents the weight of time and additional penalty term. The specific meaning of d and D depends on the specific additional penalty term. The MINCO trajectory optimization solution is obtained by solving equation (6).

6. The method for optimizing the comprehensive performance of spatiotemporal trajectory of a mobile manipulator based on improved NSGA-III according to claim 1 is characterized in that: The improved NSGA-III algorithm in step 4 uses adaptive crossover and mutation probabilities based on Gaussian distribution to improve the efficiency of the algorithm in searching for solutions and simulating population evolution. The adaptive crossover probability p c and adaptive mutation probability p m as follows: in, represents the minimum and maximum crossover probability, and Indicates the minimum and maximum values ​​of the mutation probability, gen indicates the current population size, and generation indicates the total number of individuals in the population. The improved NSGA-III algorithm performs random number crossover processing on the crossover points. In addition to random number crossover, the positions of gene fragments in individuals are exchanged during the crossover process, and the communication mechanism between individuals is enhanced. In each generation, the algorithm will retain a part of excellent individuals, which will still be used in the next generation to ensure that excellent genetic characteristics are retained. In this way, the objective function can jump out of the local minimum and obtain the global optimal solution.

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