A robot time-optimal trajectory planning method based on dynamic constraints

Abstract

The application belongs to the technical field of robot control, and specifically discloses a robot time-optimal trajectory planning method based on dynamics constraints, which comprises the following steps: establishing a dynamics model, initializing a genetic algorithm population, and generating a joint space trajectory parameter group; performing genetic operations on the population; evaluating the trajectory execution time of each trajectory parameter group, and judging whether the constraint condition is met; if the condition is not met, iteration is continued, otherwise, multiple trajectory parameter groups are screened as local optimization initial solutions; taking the initial solutions as inputs, constructing a trajectory model based on B-spline curves, and iteratively optimizing the trajectory parameter groups under the constraint condition by using a sequential quadratic programming method; comparing the optimized multiple trajectory schemes, and outputting a group meeting the constraint and having the shortest trajectory time as the final trajectory. The method fuses the global search capability of the genetic algorithm and the local fine optimization capability of the sequential quadratic programming, and can realize the global optimization of the trajectory execution time under complex physical constraints.

Description

Technical Field

[0001] This invention belongs to the field of robot control technology, specifically relating to a time-optimal trajectory planning method for robots based on dynamic constraints. Background Technology

[0002] With the development of intelligent manufacturing and flexible automation, industrial robots are widely used in automobile manufacturing, 3C assembly, metal processing and other fields. Their motion control and trajectory planning technologies are gradually evolving from the traditional teach-and-reproduce mode to high-performance autonomous planning. In high-cycle, high-precision, and high-dynamic-load operation scenarios, robots not only need to fit spatial paths, but also need to achieve optimal running time while meeting dynamic and kinematic constraints, thereby maximizing the system's production efficiency and responsiveness.

[0003] Existing robot trajectory planning methods in industrial applications are mostly based on preset path and time parameters, generating trajectories through interpolation or spline functions, and then adjusting some parameters through offline simulation or finite element optimization to meet kinematic and dynamic constraints.

[0004] While these methods are convenient to implement, they often suffer from problems such as lengthy trajectory execution time, slow response to physical constraints, and lack of global optimality in highly dynamic tasks, making it difficult to meet the trajectory quality requirements of high-speed and high-precision robot systems. On the other hand, traditional optimization methods such as SQP and QP are sensitive to initial values ​​and are prone to getting trapped in local minima; pure genetic algorithms, while possessing certain global search capabilities, have slow convergence speeds and cannot fully guarantee the feasibility of solutions; in robot path optimization problems with complex constraints and multivariate coupling, traditional methods lack the ability to effectively integrate dynamic models and trajectory structure characteristics, and cannot achieve high-efficiency, high-precision time-optimal trajectory output from a global perspective. Summary of the Invention

[0005] This invention addresses the problems in the prior art by providing a time-optimal trajectory planning method for robots based on dynamic constraints, thereby solving the problem mentioned in the background art of not being able to achieve high-efficiency and high-precision time-optimal trajectory output globally.

[0006] The technical solution adopted in this invention is as follows:

[0007] This application provides a time-optimal trajectory planning method for robots based on dynamic constraints, which includes the following steps:

[0008] Step S1: Establish a dynamic model, initialize the population, and generate several sets of trajectory parameters according to preset parameters;

[0009] Step S2: Perform genetic operations on the population to generate a new generation of trajectory parameter sets;

[0010] Step S3: Evaluate the fitness of each trajectory parameter group;

[0011] Step S4: Determine whether the preset termination condition is met;

[0012] If the preset termination condition is not met, return to step S2.

[0013] Otherwise, proceed to step S5;

[0014] Step S5: Select multiple trajectory parameter sets from the current population as initial solutions for subsequent optimization;

[0015] Step S6: Perform local optimization using the selected trajectory parameter groups as initial inputs;

[0016] Step S7: Compare the multiple trajectory parameter sets obtained through local optimization, and determine the set that satisfies the constraints and has the shortest trajectory time as the final output.

[0017] Furthermore, step S1 includes the following steps:

[0018] Step S1-1: Construct a dynamic model based on the structural parameters of the target robot;

[0019] Step S1-2: Determine the dimensions and boundary conditions of the trajectory parameters based on the number of joints and the number of trajectory segments;

[0020] Boundary conditions include the location range of B-spline control points, the temporal distribution range of nodes, and the number of individuals and encoding length of the genetic algorithm population;

[0021] Steps S1-3: Use quintic B-spline curves to describe the trajectory in the joint space of the robot, and represent each trajectory as a sequence of control points and a node time vector to form the trajectory parameter set of a single individual in the population.

[0022] Steps S1-4: Based on the trajectory structure and value range, generate multiple trajectory parameter sets in a random perturbation or uniform distribution manner to serve as the initial population for the genetic algorithm.

[0023] Furthermore, in step S1-1, the dynamic model is as follows:

[0024]

[0025] in, The location of the joint; The velocity of the joint; This refers to the acceleration of the joint; This represents the torque vector of the joint; The inertia matrix; The centripetal force matrix; It is the gravity vector; External interference The friction vector; The external force acting on the end effector; It is a Jacobian matrix.

[0026] Furthermore, in step S2, samples are selected from the trajectory parameter set in the population, and the trajectory control points and time nodes are combined and recombined using a set crossover strategy. Perturbations are added to the control points or time nodes in the trajectory parameter set with a preset probability to generate a new generation of trajectory parameter set.

[0027] Furthermore, in step S3, the fitness evaluation is based on the trajectory execution time, and it is determined whether each set of trajectory parameters meets the speed constraint, torque constraint and trajectory accuracy constraint.

[0028] Furthermore, in step S4, the termination condition is set to... and / or ;

[0029]

[0030] in, It is a Lagrange function; Let x be the gradient of the Lagrange function with respect to the independent variable x. , To optimize the condition threshold, it can be set by the user. Let i be the i-th Lagrange multiplier vector. Let i be the i-th constraint function. To constrain the change in the target, The optimal solution for the constrained objective.

[0031] Furthermore, in step S5, the elite solution set of the genetic algorithm is defined as:

[0032]

[0033] in Sort by fitness in ascending order = This is the minimum Euclidean distance. As a diversity threshold, 5% to 10% of the solution space diameter is selected;

[0034] in, For candidate solutions, For individuals who have been selected into the elite group, Sort all solutions in the population by fitness in ascending order. Let K be the fitness function, K be the elite size threshold, and E be the set of elite solutions that have met the conditions.

[0035] Furthermore, the local optimization in step S6 includes:

[0036] Multiple constraints are set, including dynamic constraints, kinematic constraints, and trajectory accuracy constraints, to construct a local sequence planning time optimization model;

[0037] The velocity value of the i-th planning point is obtained by using a joint motion trajectory model derived from a quintic B-spline curve. The speed constraint is that the absolute value of the speed at all times does not exceed the rated limit:

[0038]

[0039] in It is the upper limit of the joint's rated speed. This represents the total exercise time.

[0040] Given the kinematic constraints at each point during the motion. Defined as:

[0041]

[0042] in, Represents the joint number. Number the constraints;

[0043] By sampling points from the actual curve, the distance from each sampling point to the reference curve is calculated sequentially, representing the trajectory accuracy error. According to the trajectory accuracy constraints:

[0044]

[0045] in, This indicates the error setting value in different regions of the trajectory. A value of 1 indicates a strong constraint in the operating condition segment; A value of 2 indicates a weak constraint in the transition section.

[0046] Set trajectory accuracy constraints at each point during the motion process :

[0047] .

[0048] Furthermore, it allows for short-term exceedances of the rated speed, but not the overload speed limit; a standard speed limit is set. and overload speed limit And set the overload speed gain coefficient. ,in:

[0049]

[0050] Absolute speed The overload speed limit must not be exceeded at any time. If the speed is between the standard limit and the overload limit, that is... Set the duration length The preset overload time cannot be exceeded. ;

[0051] Configure the allowable torque constraint overload setting, and the overload gain coefficient of the torque constraint. A more conservative safety margin than the speed constraint is used in the setting, that is... ;

[0052]

[0053] in, For the duration of overload, For real-time joint torque, The allowable overload torque of the joint. This is a dynamic torque constraint.

[0054] Furthermore, constructing a local sequence programming time optimization model includes:

[0055] We set up a sequential quadratic programming problem, incorporating the three constraints mentioned above, with the goal of achieving time optimization:

[0056]

[0057] in, The objective function is non-convex. As the first nonlinear constraint, For the second nonlinear constraint, Let x be an n-dimensional real vector, m be the number of the first constraint, and p be the number of the second constraint;

[0058] The time optimization algorithm model is given as follows:

[0059]

[0060] in The time-optimal objective function is... The inequality constraint function in the optimization process includes three inequalities: velocity, torque, and trajectory accuracy.

[0061] As can be seen from the above technical solutions, the advantages of the present invention are:

[0062] By employing a phased, hybrid optimization strategy, a genetic algorithm is introduced into the global search layer to generate diverse trajectory candidate solutions. Constrained Sequential Quadratic Programming (SQP) is used for iterative optimization of trajectory parameters during the local refinement stage, thus balancing global exploration with local accuracy. The trajectory is parameterized in joint space using quintic B-splines. Combined with the established complete dynamic model, multiple constraints on velocity, torque, and accuracy are uniformly considered during trajectory optimization, ensuring that the obtained trajectory not only has the shortest execution time but also meets the physical feasibility and trajectory continuity requirements for actual execution. Furthermore, this method constructs an overload limit and overload duration mechanism, allowing flexible scheduling of high-dynamic actions within a set safety margin, improving the overall timeliness and robustness of the trajectory. Compared to existing methods, this invention can effectively reduce trajectory execution time, improve motion smoothness, enhance the interpretability and deployment reliability of optimization results, and is applicable to the general trajectory planning needs of various types of industrial robotic arm systems. Attached Figure Description

[0063] To more clearly illustrate the technical solution of the present invention, the accompanying drawings used in the description will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0064] Figure 1 A flowchart illustrating the steps of a time-optimal trajectory planning method for robots based on dynamic constraints;

[0065] Figure 2 This is a schematic diagram of key points of the end effector trajectory in the embodiment;

[0066] Figure 3 This is a schematic diagram illustrating the principle of continuous torque overload time constraint in the embodiment.

[0067] Figure 4 This is a schematic diagram illustrating the trajectory accuracy constraint principle in the embodiment. Detailed Implementation

[0068] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0069] Please see Figure 1 As shown, this invention provides a time-optimal trajectory planning method for robots based on dynamic constraints, comprising the following steps:

[0070] Step S1: Establish a dynamic model, initialize the population, and generate several sets of trajectory parameters according to preset parameters;

[0071] Step S1-1: Construct a dynamic model based on the structural parameters of the target robot;

[0072] The dynamic model is as follows:

[0073]

[0074] in, The location of the joint; The velocity of the joint; This refers to the acceleration of the joint; This represents the torque vector of the joint; The inertia matrix; The centripetal force matrix; It is the gravity vector; External interference The friction vector; The external force acting on the end effector; It is a Jacobian matrix;

[0075] Step S1-2: Determine the dimensions and boundary conditions of the trajectory parameters based on the number of joints and the number of trajectory segments;

[0076] Boundary conditions include the location range of B-spline control points, the temporal distribution range of nodes, and the number of individuals and encoding length of the genetic algorithm population;

[0077] Steps S1-3: Use quintic B-spline curves to describe the trajectory in the joint space of the robot, and represent each trajectory as a sequence of control points and a node time vector to form the trajectory parameter set of a single individual in the population.

[0078] Steps S1-4: Based on the trajectory structure and value range, generate multiple trajectory parameter sets using random perturbation or uniform distribution to serve as the initial population for the genetic algorithm.

[0079] Step S2: Perform genetic operations on the population to generate a new generation of trajectory parameter sets;

[0080] Samples are selected from the trajectory parameter set in the population, and the trajectory control points and time nodes are combined and recombined using a set crossover strategy. Perturbations are added to the control points or time nodes in the trajectory parameter set with a preset probability to generate a new generation of trajectory parameter set.

[0081] Step S3: Evaluate the fitness of each trajectory parameter group;

[0082] The fitness assessment is based on trajectory execution time and determines whether each set of trajectory parameters meets the velocity constraint, torque constraint, and trajectory accuracy constraint.

[0083] Step S4: Determine whether the preset termination condition is met;

[0084] If the preset termination condition is not met, return to step S2.

[0085] Otherwise, proceed to step S5;

[0086] The termination condition is set as follows: and / or ;

[0087]

[0088] in, It is a Lagrange function; Let x be the gradient of the Lagrange function with respect to the independent variable x. , To optimize the condition threshold, it can be set by the user. Let i be the i-th Lagrange multiplier vector. Let i be the i-th constraint function. To constrain the change in the target, The optimal solution for the constrained objective;

[0089] Step S5: Select multiple trajectory parameter sets from the current population as initial solutions for subsequent optimization;

[0090] Define the elite solution set of the genetic algorithm as:

[0091]

[0092] in Sort by fitness in ascending order = This is the minimum Euclidean distance. As a diversity threshold, 5% to 10% of the solution space diameter is selected;

[0093] in, For candidate solutions, For individuals who have been selected into the elite group, Sort all solutions in the population by fitness in ascending order. Let K be the fitness function, K be the elite size threshold, and E be the set of elite solutions that have met the conditions.

[0094] Step S6: Perform local optimization using the selected trajectory parameter groups as initial inputs;

[0095] The relationship between joint and distal end transformation is obtained using forward kinematics;

[0096]

[0097] Using quintic B-spline curves, the position, velocity, and acceleration parameters of the robotic arm's end effector are derived:

[0098]

[0099] For active joints, discrete joint path points are transformed into continuous and smooth trajectory functions using quintic B-splines. Then, the first derivative of the function in each joint space is used to obtain the velocity curve, and the second derivative is used to obtain the acceleration curve.

[0100]

[0101]

[0102] At the start and end points of the loading and unloading robotic arm, the velocity, acceleration, and jerk must all be 0, and the corresponding joint space start and end points should also meet the above requirements. An initial trajectory for optimization was constructed using a quintic B-spline curve, and the continuity of the robot's position, velocity, and acceleration during movement was achieved.

[0103] Local optimization in step S6 includes:

[0104] Multiple constraints are set, including dynamic constraints, kinematic constraints, and trajectory accuracy constraints, to construct a local sequence planning time optimization model;

[0105] The velocity value of the i-th planning point is obtained by using a joint motion trajectory model derived from a quintic B-spline curve. The speed constraint is that the absolute value of the speed at all times does not exceed the rated limit:

[0106]

[0107] in It is the upper limit of the joint's rated speed. This represents the total exercise time.

[0108] Given the kinematic constraints at each point during the motion. Defined as:

[0109]

[0110] in, Represents the joint number. Number the constraints;

[0111] By sampling points from the actual curve, the distance from each sampling point to the reference curve is calculated sequentially, representing the trajectory accuracy error. According to the trajectory accuracy constraints:

[0112]

[0113] in, This indicates the error setting value in different regions of the trajectory. A value of 1 indicates a strong constraint in the operating condition segment; A value of 2 indicates a weak constraint in the transition section.

[0114] Set trajectory accuracy constraints at each point during the motion process :

[0115] ;

[0116] It is permissible to exceed the rated speed for short periods, but not the overload speed limit; a standard speed limit is set. and overload speed limit And set the overload speed gain coefficient. ,in:

[0117]

[0118] Absolute speed The overload speed limit must not be exceeded at any time. If the speed is between the standard limit and the overload limit, that is... Set the duration length The preset overload time cannot be exceeded. .

[0119] Configure the allowable torque constraint overload setting, and the overload gain coefficient of the torque constraint. A more conservative safety margin than the speed constraint is used in the setting, that is... ;

[0120]

[0121] in, For the duration of overload, For real-time joint torque, The allowable overload torque of the joint. For dynamic torque constraints;

[0122] Constructing a local sequence planning time optimization model includes:

[0123] We set up a sequential quadratic programming problem, incorporating the three constraints mentioned above, with the goal of achieving time optimization:

[0124]

[0125] in, The objective function is non-convex. As the first nonlinear constraint, For the second nonlinear constraint, Let x be an n-dimensional real vector, m be the number of the first constraint, and p be the number of the second constraint;

[0126] The time optimization algorithm model is given as follows:

[0127]

[0128] in The time-optimal objective function is... The inequality constraint function in the optimization process includes three inequalities: velocity, torque, and trajectory accuracy.

[0129] Step S7: Compare the multiple trajectory parameter sets obtained through local optimization, and determine the set that satisfies the constraints and has the shortest trajectory time as the final output.

[0130] In some embodiments, this application provides a robot time-optimal trajectory planning system based on dynamic constraints, the system comprising:

[0131] The dynamics modeling module, trajectory initialization module, genetic optimization module, fitness evaluation module, termination determination module, initial solution screening module, local optimization module, and result output module are used to realize the time-optimal planning of robot joint trajectories under multiple constraints.

[0132] The dynamics modeling module is used to construct a complete dynamics model of the robot to be planned. This model describes the relationships between inertial forces, gravity, friction, external loads, and driving torques at the joints under different states. In this embodiment, based on the robot's structural parameters, a rigid body chain dynamics structure is established using modeling tools, generating a symbolic representation that can be used for constraint calculations.

[0133] The trajectory initialization module is used to generate multiple trajectory parameter sets according to preset parameters, forming the initial population of the genetic algorithm. In this embodiment, a quintic B-spline function is used to describe the trajectory parameters in the joint space. Each parameter set includes multiple control points and corresponding time nodes, and the population is constructed through uniform distribution and perturbation generation mechanisms.

[0134] The genetic optimization module is used to perform genetic operations on the current population to generate a new generation of trajectory parameter sets. In this embodiment, the genetic operations include individual selection based on set rules, crossover and recombination of control points and time nodes, and probability-triggered small perturbation mutation operations to maintain population diversity.

[0135] The fitness evaluation module is used to evaluate the fitness value of each trajectory parameter group. In this embodiment, the fitness is optimized based on the total execution time of the trajectory, while also detecting whether each trajectory group meets the speed constraint, torque constraint, and trajectory accuracy constraint. Trajectories that do not meet the conditions will be eliminated or assigned a low fitness value.

[0136] The termination determination module is used to determine whether the current population meets the termination conditions. In this embodiment, the termination conditions include the convergence of the fitness function, the population's generation count exceeding the upper limit, or insufficient diversity in the solution space. The genetic phase terminates when any of these conditions are met.

[0137] The initial solution selection module is used to select multiple trajectory parameter sets from the current population as initial solutions for local optimization. In this embodiment, an elite solution set is constructed, and the solutions are selected based on fitness ranking and Euclidean distance distribution to ensure that the selected solutions are representative and widely distributed.

[0138] The local optimization module is used to perform local optimization operations on the selected trajectory parameter set. In this embodiment, a sequential quadratic programming algorithm is used to establish a trajectory model based on a quintic B-spline curve, and constraints such as velocity, torque, and trajectory accuracy are set to minimize the trajectory time within the feasible solution space.

[0139] The result output module compares multiple sets of trajectory parameters after local optimization, determines the optimal trajectory, and outputs it. In this embodiment, the set of trajectory parameters that satisfies all constraints and has the shortest trajectory time is selected as the final output result for the robot's execution control system to use.

[0140] This system can be deployed on industrial robot simulation platforms or embedded trajectory control units, supporting trajectory planning tasks in complex paths, high-precision requirements, and high-speed cycle operation scenarios, and has good versatility and engineering adaptability.

[0141] In some embodiments, this application provides a terminal, including:

[0142] The memory is used to store the robot's time-optimal trajectory planning program based on dynamic constraints;

[0143] A processor is configured to implement the steps of the dynamic constraint-based robot time-optimal trajectory planning method when executing the dynamic constraint-based robot time-optimal trajectory planning system.

[0144] In some embodiments, this application provides a computer-readable storage medium that stores computer instructions. When a computer reads the computer instructions in the storage medium, the computer executes the robot time-optimal trajectory planning method based on dynamic constraints.

[0145] It is understood that the systems, devices, modules, or units described in the above embodiments can be implemented by computer chips or entities, or by products with certain functions. A typical implementation device is a computer, which can be a personal computer, a laptop computer, a personal digital assistant, a tablet computer, a wearable device, or any combination of these devices.

[0146] In a typical configuration, a computer includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0147] Memory may include non-persistent storage in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory is an example of computer-readable media.

[0148] Computer-readable media include both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, disk storage, quantum memory, graphene-based storage media or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0149] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0150] It should be understood that although the terms first, second, third, etc., may be used to describe various information in one or more embodiments of this specification, such information should not be limited to these terms. These terms are only used to distinguish information of the same type from one another. For example, first information may also be referred to as second information without departing from the scope of one or more embodiments of this specification, and similarly, second information may also be referred to as first information. Depending on the context, the word "if" as used herein may be interpreted as "when," "in response to a determination," or "when," or "in the event of a determination."

[0151] The above description is merely a preferred embodiment of one or more embodiments of this specification and is not intended to limit the scope of one or more embodiments of this specification. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of one or more embodiments of this specification should be included within the protection scope of one or more embodiments of this specification.

Claims

1. A method for robot time-optimal trajectory planning based on dynamics constraints, characterized in that, The method comprises the following steps: Step S1, establishing a dynamic model, initializing a population, and generating a plurality of trajectory parameter groups according to preset parameters; Step S2, performing a genetic operation on the population to generate a new generation of trajectory parameter groups; In step S2, sample selection is performed on the trajectory parameter groups in the population, a set crossover strategy is used to combine and recombine the trajectory control points and time nodes, and a preset probability is used to add disturbance to the control points or time nodes in the trajectory parameter groups to generate a new generation of trajectory parameter groups; Step S3, evaluating the fitness of each trajectory parameter group; Step S4, determining whether a preset termination condition is met; If the preset termination condition is not met, return to step S2; Otherwise, step S5 is performed; In step S4, the termination condition is set to and / or ; wherein, is a Lagrangian function; is a gradient of the Lagrangian function with respect to the argument x, , is an optimization condition threshold value, which can be set by a user, is an i-th Lagrange multiplier vector, is an i-th constraint function, is a variation of a constraint target, is an optimal solution of the constraint target; Step S5, selecting a plurality of trajectory parameter groups from the current population as initial solutions for subsequent optimization; In step S5, the elite solution set of the genetic algorithm is defined as: wherein, sorted in ascending order of fitness, = min distance between two individuals in the population, is the minimum Euclidean distance, is the diversity threshold, which is 5%~10% of the diameter of the solution space; wherein, is a candidate solution, is an individual that has been selected into the elite set, is the fitness of all solutions in the population sorted in ascending order, is a fitness function, K is an elite size threshold, and E is a set of elite solutions that have been satisfied. Step S6, performing local optimization with the selected trajectory parameter groups as initial inputs; The local optimization in step S6 includes: Setting multiple constraints, including dynamic constraints, kinematic constraints, and trajectory accuracy constraints, to construct a local sequence planning time optimization model; The joint movement trajectory model is obtained through five B-spline curves, and a velocity value of the ith planning point is obtained The velocity constraint is that the absolute value of the velocity at all times does not exceed the rated limit value: wherein is the upper limit of the rated speed of the joint, is the total time of motion; Kinematic constraints at points in a given motion process are defined as: wherein, represents the joint number, is the constraint number; The distance from the sampling point to the reference curve is solved according to the actual curve sampling point, and the trajectory precision error is obtained According to the trajectory precision constraint requirement: wherein, represents the error setting value in different regions of the trajectory, and = 1 is strong constraint for the working section; = 2 is weak constraint for the transition section; Setting trajectory accuracy constraints at points during a motion : ； Step S7, comparing the plurality of trajectory parameter groups obtained by local optimization to determine a trajectory parameter group that meets the constraint conditions and has the shortest trajectory time as the final output.

2. The method of claim 1, wherein, In step S1, the following steps are included: Step S1-1, constructing a dynamic model based on the structural parameters of the target robot; Step S1-2, determining the dimension and boundary conditions of the trajectory parameters according to the number of joints and the number of trajectory segments; The boundary conditions include the position range of the B-spline control points, the node time distribution range, and the individual number and coding length of the genetic algorithm population; Step S1-3, using a quintic B-spline curve to describe the trajectory in the joint space of the robot, representing each trajectory as a control point sequence and a node time vector, and constructing a trajectory parameter group for a single individual in the population; Step S1-4, generating a plurality of trajectory parameter groups as the initial population of the genetic algorithm according to the trajectory structure and value range in a random disturbance or uniform distribution manner.

3. The method of claim 2, wherein, In step S1-1, the dynamic model is: wherein, is the position of the joint; is the velocity of the joint; is the acceleration of the joint; is the torque vector of the joint; is the inertia matrix; is the centripetal force matrix; is the gravity vector; is the external disturbance, is the friction vector; is the external force acting on the end effector; is the Jacobian matrix.

4. The method of claim 1, wherein, In step S3, the fitness evaluation targets the trajectory execution time and determines whether each trajectory parameter group meets the speed constraint, torque constraint, and trajectory accuracy constraint.

5. The method of claim 1, wherein, Allowing a short time to exceed the rated speed, but not to exceed the upper limit of the overload speed, setting the standard speed limit and the overload speed limit and setting the overload speed gain coefficient wherein: absolute speed may not exceed the overload speed limit at any time if the speed is between the standard limit and the overload limit, i.e. the duration length is set may not exceed the preset preset overload time ; A torque-constrained overload setting is provided, the torque-constrained overload gain factor At set-up, a more conservative safety margin than the speed constraint is employed, i.e. ; wherein, is the overload duration, is the real-time joint torque, is the joint allowable overload torque, is the dynamics torque constraint.

6. The method of claim 5, wherein, Constructing a local sequence planning time optimization model includes: Set up sequence quadratic programming, add kinematic constraints , dynamic torque constraints and trajectory accuracy constraints Targeting time optimality: wherein, is a non-convex objective function, is a first non-linear constraint, is a second non-linear constraint, is an n-dimensional real vector of x, m is a first constraint number, and p is a second constraint number. Giving a time optimization algorithm model: where is the time optimal objective function, is the inequality constraint function in optimization, including three inequalities of velocity, torque and trajectory accuracy.

Images