An adaptive skill learning method for dual-arm robots based on dynamic motion primitives

Abstract

The invention discloses a dual-arm robot adaptive skill learning method based on dynamic motion primitives, which obtains teaching data, establishes a dynamic motion primitive model, and uses the dynamic motion primitive model to learn the shape characteristics of the trajectory from the teaching data, generate corresponding trajectory shape functions, and obtain initial trajectory control weights; obtain new task target points, combine the learned initial trajectory control weights and trajectory shape functions with the new task target points, and generate an initial trajectory similar to the teaching trajectory; optimize the initial trajectory to obtain an optimized trajectory shape, and obtain an optimized trajectory control weight; bring the optimized trajectory control weight into the dynamic motion primitive model, and use an adaptive time scaling factor based on the trajectory change rate to perform adaptive adjustment to generate an optimized trajectory for the dual arms. Ensure that the robot completes the task efficiently and accurately.

Description

Technical Field

[0001] The present invention belongs to the technical field of dual-arm robot skill learning, and in particular relates to a dual-arm robot adaptive skill learning method based on dynamic motion primitives. Background Art

[0002] Dual-arm robots have been widely used in many complex task scenarios due to their excellent operational flexibility and high-precision repeatability. However, the current way of learning skills relies on manual teaching by experts, that is, teaching robots to complete specific tasks by demonstrating actions. Although this method allows robots to master basic operating steps in the initial stage, when encountering new tasks or changing working environments, re-teaching is often required. This mode that relies on manual teaching is inefficient and greatly limits the adaptability of dual-arm robots in complex and changing environments. Whenever the task conditions or operating positions change, the re-teaching process is not only time-consuming and labor-intensive, but also constitutes a bottleneck for achieving efficient automation. Therefore, improving the adaptability and task expansion capabilities of dual-arm robots in dynamic environments has become an urgent need to promote their wider application.

[0003] Dynamic Movement Primitives (DMP) is an effective skill learning framework that enables robots to acquire diverse motion patterns by learning the motion trajectories demonstrated by experts. However, the skill generalization ability of DMP in dual-arm tasks faces several challenges. First, the generalized trajectory may deviate significantly from the original taught trajectory, resulting in the robot being unable to guarantee sufficient accuracy when reproducing the trajectory, thus affecting its ability to imitate and execute complex tasks. Second, some generalized trajectories may violate the robot's kinematic constraints, making trajectory planning infeasible, which in turn affects the continuity and stability of the task. In addition, due to the differences in the motion paths and distances of the two arms, the movement rhythms of the left and right arms may be out of sync, making it impossible to achieve collaborative operation. Therefore, optimizing the DMP model to improve the accuracy of trajectory reproduction and the feasibility under kinematic constraints has become the key to improving the synchronization coordination and operation efficiency of dual-arm robots. At the same time, the end alignment control mechanism is also required to ensure the consistency and synchronization of the two arms in collaborative tasks in order to achieve efficient and automated execution of the two arms. Summary of the invention

[0004] In view of the above technical problems, the present invention provides a dual-arm robot adaptive skill learning method based on dynamic motion primitives.

[0005] The technical solution adopted by the present invention to solve the technical problem is:

[0006] A dual-arm robot adaptive skill learning method based on dynamic motion primitives, the method comprising the following steps:

[0007] S100: Acquire teaching data and establish a dynamic motion primitive model. Through the dynamic motion primitive model, the two arms learn the shape characteristics of the trajectory from the teaching data respectively. The shape characteristics of the trajectory include the overall trend and local changes of the trajectory, generate the corresponding trajectory shape function, and further calculate to obtain the initial trajectory control weight;

[0008] S200: obtaining a new task target point, combining the learned initial trajectory control weight and trajectory shape function with the new task target point, and generating an initial trajectory similar to the teaching trajectory;

[0009] S300: Optimizing the initial trajectory to obtain an optimized trajectory shape, obtaining an optimized trajectory control weight, ensuring the coordination and consistency of the trajectory at different lengths and speeds, and correcting kinematic infeasibility;

[0010] S400: Bringing the optimized trajectory control weights into the dynamic motion primitive model, and adaptively adjusting them using an adaptive time scaling factor based on the trajectory change rate to generate an optimized trajectory for both arms.

[0011] Preferably, S100 includes:

[0012] S110: establishing dynamic motion primitive models for the left arm and the right arm respectively to describe trajectory generation and motion control thereof;

[0013] S120: Collect teaching data: drag the robot arm and use the host computer to record the robot end effector trajectory data set and ,The data set includes acceleration, velocity, and position;

[0014] S130: Calculating the target shape function in combination with the collected teaching data;

[0015] S140: Setting an optimization problem, solving the optimization problem based on the dynamic motion primitive model and the target shape function to obtain the weight of the teaching trajectory.

[0016] Preferably, the dynamic motion primitive model in S110 is specifically:

[0017] ;

[0018] ;

[0019] ;

[0020] ;

[0021] in, , , , , Respectively represent the initial position, current position, target position, speed and acceleration of the left arm; , , , , Represent the initial position, current position, target position, speed and acceleration of the right arm respectively. , are the time scaling factors for the left and right arms, respectively, are the phase variables controlling the time course of the left and right arms, respectively; and The attraction coefficient and damping coefficient in the spring-damper system represent the position respectively, which are constants. Represents the convergence speed of the control system, which is a constant;

[0022] , is the shape function in the dynamic motion primitive model, which has the form:

[0023] ;

[0024] ;

[0025] ;

[0026] in, The width and Center is a Gaussian function characterized by , are the weights corresponding to the left arm and the right arm; is the number of Gaussian functions;

[0027] S130 is specifically:

[0028] ;

[0029] ;

[0030] in, and are the target shape functions for the left and right arms, respectively;

[0031] S140 is as follows:

[0032] ;

[0033] ;

[0034] in, is the shape function estimated according to the teaching trajectory;

[0035] Finally, the calculation formula of the initial weight is expressed as:

[0036] ;

[0037] ;

[0038] in, is a diagonal matrix, .

[0039] Preferably, S200 includes:

[0040] S210: Based on the new target point and , the initial trajectory control weights of the left and right arms are learned , , trajectory shape function, combined with the new task target point, estimates the acceleration of the robot's left and right arm end effectors;

[0041] Using equations (5), (6) and (12), (13), we can obtain:

[0042] ;

[0043] ;

[0044] in, and The shape functions estimated for the left and right arms respectively;

[0045] Substituting into equations (1) and (3), we can obtain the acceleration of the robot's left and right arm end effectors: , :

[0046] ;

[0047] ;

[0048] S220: Get the acceleration of the robot's left and right arm end effectors , Then, numerical integration is used to update the velocity , and location , , specifically:

[0049] ;

[0050] ;

[0051] ;

[0052] ;

[0053] in, and are the speeds of the left and right arms at the current time point of the initial trajectory, and are the accelerations of the initial trajectories of the left and right arms at the current time point, represents the time step, and are the speeds of the left and right arms at the next time point after the initial trajectory, and are the positions of the left arm’s initial trajectory at the current time point and the next time point, respectively. and are the positions of the initial trajectory of the right arm at the current time point and the next time point respectively;

[0054] S230: Repeat the calculation until the phase variables of the left arm and the right arm , Becomes 0, the trajectory reaches the target position and , get the initial trajectory of the left arm and the right arm , .

[0055] Preferably, S300 includes:

[0056] S310: Normalizing the initial trajectories of the left and right arms;

[0057] S320: Optimizing the normalized trajectory shape based on the optimization function to minimize the shape difference between the reproduced trajectory and the taught trajectory;

[0058] S330: Mapping the optimized trajectory back to the physical coordinate system of the actual task through a recovery formula, thereby ensuring that the trajectory executed in the actual task can match the physical requirements;

[0059] S340: Generate a trajectory based on the objective function, where the generated trajectory satisfies physical feasibility and kinematic constraints, ensuring that the two arms can be coordinated and synchronized during execution.

[0060] Preferably, S310 specifically includes:

[0061] ;

[0062] ;

[0063] in, , Respectively represent the starting points of the left arm and right arm teaching data; , Represent the target points of the left arm and right arm teaching data respectively; in the normalized space, the initially generated reproduction trajectory and teaching trajectory have been adjusted in the same space;

[0064] The optimization function in S320 is as follows:

[0065] ;

[0066] in , is the normalized teaching trajectory;

[0067] The recovery formula in S330 is as follows:

[0068] ;

[0069] ;

[0070] Preferably, the objective function in S340 is specifically:

[0071] ;

[0072] in, and represent the current positions of the updated trajectories of the left and right arms, respectively. and Represent the end points of the updated trajectories of the left and right arms, respectively. A constant to encourage alignment of the ends of the arms;

[0073] The constraints include physical feasibility constraints and weight optimization constraints. The physical feasibility constraints ensure that the generated trajectory is within the reach of the robot. The physical feasibility constraints are as follows:

[0074] ;

[0075] The weight optimization constraints are as follows:

[0076] ;

[0077] ;

[0078] in, and denote the target positions of the left and right arms respectively, and denote the initial positions of the updated trajectories of the left and right arms, respectively. and represent the current positions of the updated trajectories of the left and right arms, respectively; and represents the current acceleration of the updated trajectory of the left and right arms respectively;

[0079] After the above optimization problems, the weights for aligning the end points of the completed trajectory are obtained. , .

[0080] Preferably, S400 includes:

[0081] S410: Calculate the change rate of the optimized trajectory, specifically:

[0082] ;

[0083] ;

[0084] S420: Bring the rate of change into the adaptive formula:

[0085] ;

[0086] ;

[0087] in is a constant;

[0088] S430: , Substitute into equations (14) and (15), and then connect equations (14)-(21), (30), and (31) to obtain the final trajectory. , .

[0089] The above-mentioned adaptive skill learning method for a dual-arm robot based on dynamic motion primitives first allows the left and right arms to learn expert teaching data respectively to obtain the initial weight of the trajectory, then generates the initial trajectory after a new target point is given, and then optimizes the trajectory according to actual needs. Finally, the time scaling parameter is dynamically adjusted using the rate of change to ensure that the dual-arm trajectory remains consistent in the time process and generate the optimized trajectory of the dual arms. Through trajectory normalization, time-space coupling adjustment and dual-arm synchronous alignment mechanism, the robot is ensured to complete the task efficiently and accurately, effectively solving the problems of trajectory deviation, kinematic infeasibility and inaccurate end alignment when the dual-arm robot is handling dual-arm synchronous tasks. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] Figure 1 A flowchart of a dual-arm robot adaptive skill learning method based on dynamic motion primitives in one embodiment of the present invention;

[0091] Figure 2 A flowchart of a dual-arm robot adaptive skill learning method based on dynamic motion primitives in another embodiment of the present invention;

[0092] Figure 3 The diagram is a two-arm dispensing effect diagram of the original model in one embodiment of the present invention; wherein (a) is a three-dimensional view of the trajectory display of the original model at position 1, (b) is a top view of the trajectory display of the original model at position 1; (c) is a three-dimensional view of the trajectory display of the original model at position 2, and (d) is a top view of the trajectory display of the original model at position 2;

[0093] Figure 4 The diagram is a two-arm dispensing effect diagram of an improved model in one embodiment of the present invention; wherein, (a) is a three-dimensional view showing the trajectory of the improved model at position 1, (b) is a top view showing the trajectory of the improved model at position 1; (c) is a three-dimensional view showing the trajectory of the improved model at position 2, and (d) is a top view showing the trajectory of the improved model at position 2. DETAILED DESCRIPTION

[0094] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings.

[0095] In one embodiment, Figure 1 and Figure 2 As shown, a dual-arm robot adaptive skill learning method based on dynamic motion primitives, the method comprises the following steps:

[0096] S100: Acquire teaching data and establish a dynamic motion primitive model. Through the dynamic motion primitive model, the two arms learn the shape characteristics of the trajectory from the teaching data respectively. The shape characteristics of the trajectory include the overall trend and local changes of the trajectory, generate the corresponding trajectory shape function, and further calculate to obtain the initial trajectory control weight;

[0097] S200: obtaining a new task target point, combining the learned initial trajectory control weight and trajectory shape function with the new task target point, and generating an initial trajectory similar to the teaching trajectory;

[0098] S300: Optimizing the initial trajectory to obtain an optimized trajectory shape, obtaining an optimized trajectory control weight, ensuring the coordination and consistency of the trajectory at different lengths and speeds, and correcting kinematic infeasibility;

[0099] S400: Bringing the optimized trajectory control weights into the dynamic motion primitive model, and adaptively adjusting them using an adaptive time scaling factor based on the trajectory change rate to generate an optimized trajectory for both arms.

[0100] Specifically, the initial trajectory control weight is obtained in S100, which provides a basis for subsequent trajectory reproduction. S200 can ensure that the motion trajectory of the dual arms remains consistent and operable under different task conditions. S400 can ensure that the trajectory shape is consistent with the accuracy requirements of the target task, and ultimately realize the skill learning of the dual-arm robot in synchronous tasks.

[0101] In one embodiment, S100 includes:

[0102] S110: establishing dynamic motion primitive models for the left arm and the right arm respectively to describe their trajectory generation and motion control;

[0103] S120: Collect teaching data: drag the robot arm and use the host computer to record the robot end effector trajectory data set and ,The data set includes acceleration, velocity, and position;

[0104] S130: Calculating a target shape function in combination with the collected teaching data;

[0105] S140: Setting an optimization problem, solving the optimization problem based on the dynamic motion primitive model and the target shape function to obtain the weight of the teaching trajectory.

[0106] In one embodiment, the dynamic motion primitive model in S110 is specifically:

[0107] ;

[0108] ;

[0109] ;

[0110] ;

[0111] in, , , , , Respectively represent the initial position, current position, target position, speed and acceleration of the left arm; , , , , Represent the initial position, current position, target position, speed and acceleration of the right arm respectively. , are the time scaling factors for the left and right arms, respectively, are the phase variables controlling the time course of the left and right arms, respectively; and The attraction coefficient and damping coefficient in the spring-damper system represent the position respectively, which are constants. Represents the convergence speed of the control system, which is a constant;

[0112] , is the shape function in the dynamic motion primitive model, which has the form:

[0113] ;

[0114] ;

[0115] ;

[0116] in, The width and Center is a Gaussian function characterized by , are the weights corresponding to the left arm and the right arm; is the number of Gaussian functions;

[0117] S130 is specifically:

[0118] ;

[0119] ;

[0120] in, and are the target shape functions for the left and right arms, respectively;

[0121] S140 is specifically:

[0122] ;

[0123] ;

[0124] in, is the shape function estimated according to the teaching trajectory;

[0125] Finally, the calculation formula of the initial weight is expressed as:

[0126] ;

[0127] ;

[0128] in, is a diagonal matrix, .

[0129] In one embodiment, S200 includes:

[0130] S210: Based on the new target point and , the initial trajectory control weights of the left and right arms are learned , , trajectory shape function, combined with the new task target point, estimates the acceleration of the robot's left and right arm end effectors;

[0131] Using equations (5), (6) and (12), (13), we can obtain:

[0132] ;

[0133] ;

[0134] in, and The shape functions estimated for the left and right arms respectively;

[0135] Substituting into equations (1) and (3), we can obtain the acceleration of the robot's left and right arm end effectors: , :

[0136] ;

[0137] ;

[0138] S220: Get the acceleration of the robot's left and right arm end effectors , Then, numerical integration is used to update the velocity , and location , , specifically:

[0139] ;

[0140] ;

[0141] ;

[0142] ;

[0143] in, and are the speeds of the left and right arms at the current time point of the initial trajectory, and are the accelerations of the initial trajectories of the left and right arms at the current time point, represents the time step, and are the speeds of the left and right arms at the next time point after the initial trajectory, and are the positions of the left arm’s initial trajectory at the current time point and the next time point, respectively. and are the positions of the initial trajectory of the right arm at the current time point and the next time point respectively;

[0144] S230: Repeat the calculation until the phase variables of the left arm and the right arm , Becomes 0, the trajectory reaches the target position and , get the initial trajectory of the left arm and the right arm , .

[0145] In one embodiment, S300 includes:

[0146] S310: Normalizing the initial trajectories of the left and right arms;

[0147] S320: optimizing the normalized trajectory shape based on the optimization function to minimize the shape difference between the reproduced trajectory and the taught trajectory; further, after optimization in the normalized space, the distance between the current trajectory and the taught trajectory is minimized, ensuring the similarity between the trajectory shape and the taught trajectory;

[0148] S330: Mapping the optimized trajectory back to the physical coordinate system of the actual task through a recovery formula, thereby ensuring that the trajectory executed in the actual task can match the physical requirements;

[0149] S340: Generate a trajectory based on the objective function, where the generated trajectory satisfies physical feasibility and kinematic constraints, ensuring that the two arms can be coordinated and synchronized during execution.

[0150] Furthermore, in order to ensure that the generated trajectory is not only reasonable in shape, it must also satisfy physical feasibility and kinematic constraints. The core goal of physical feasibility optimization is to ensure the executableness of the trajectory in the robot kinematic model. Through further optimization, the reproduced trajectory must not only be consistent with the target trajectory in shape, but also meet the actual physical constraints in the task environment to ensure that the two arms can coordinate and synchronize during execution.

[0151] Specifically, since the generated trajectory is usually achieved by setting a new target point, it is difficult to directly evaluate the similarity between the reproduced trajectory and the initial taught trajectory, which brings challenges to subsequent optimization. In order to ensure that the trajectory shapes of the left and right arms at different target points are consistent with the taught trajectory, the present invention designs a dynamic scaling formula to adjust the reproduced trajectory. In this way, the reproduced trajectory and the taught trajectory can be compared and optimized under the same standard.

[0152] In one embodiment, S310 specifically includes:

[0153] ;

[0154] ;

[0155] in, , Respectively represent the starting points of the left arm and right arm teaching data; , Represent the target points of the left arm and right arm teaching data respectively; in the normalized space, the initially generated reproduction trajectory and teaching trajectory have been adjusted in the same space;

[0156] The optimization function in S320 is as follows:

[0157] ;

[0158] in , is the normalized teaching trajectory;

[0159] The recovery formula in S330 is as follows:

[0160] ;

[0161] ;

[0162] In one embodiment, the objective function in S340 is specifically:

[0163] ;

[0164] in, and represent the current positions of the updated trajectories of the left and right arms, respectively. and Represent the end points of the updated trajectories of the left and right arms, respectively. A constant to encourage alignment of the ends of the arms;

[0165] The constraints include physical feasibility constraints and weight optimization constraints. The physical feasibility constraints ensure that the generated trajectory is within the reach of the robot. The physical feasibility constraints are as follows:

[0166] ;

[0167] The specific weight optimization constraints are:

[0168] ;

[0169] ;

[0170] in, and denote the target positions of the left and right arms respectively, and denote the initial positions of the updated trajectories of the left and right arms, respectively. and represent the current positions of the updated trajectories of the left and right arms, respectively; and represents the current acceleration of the updated trajectory of the left and right arms respectively;

[0171] After the above optimization problems, the weights for aligning the end points of the completed trajectory are obtained. , .

[0172] Furthermore, after completing trajectory generation and physical feasibility optimization, the synchronization of the two-arm trajectory is the last step for the success of the task. During the execution of the dual-arm robot, the movements of the left and right arms must be coordinated, otherwise the task may fail. In this process, the DMP method provides an adaptive time scaling mechanism to ensure the synchronization of the movements of the two arms when performing tasks. By calculating the rate of change of the left and right arm trajectories and dynamically adjusting the time scaling parameters according to the rate of change, the trajectories of the two arms are ensured to be consistent in the time process. In this way, the robot can avoid one arm being too fast or too slow during the task execution, thereby achieving synchronization of the two arms.

[0173] In one embodiment, S400 includes:

[0174] S410: Calculate the change rate of the optimized trajectory, specifically:

[0175] ;

[0176] ;

[0177] S420: Bring the rate of change into the adaptive formula:

[0178] ;

[0179] ;

[0180] in is a constant;

[0181] S430: , Substitute into equations (14) and (15), and then connect equations (14)-(21), (30), and (31) to obtain the final trajectory. , .

[0182] Figure 3 and Figure 4 This is a simulation effect diagram. Figure 3 This shows the effect of the original model, where the trajectory has a strange shape and the end points are not aligned. Figure 4 For the effect of the invention, the shape is reasonable and the ends are aligned, which effectively reflects the effectiveness of the method of the invention.

[0183] The above dual-arm robot adaptive skill learning method based on dynamic motion primitives has the following beneficial effects:

[0184] (1) Based on improving the trajectory generation capability of the original dynamic motion primitive model, the present invention further enhances the coupling effect of two independent dynamic motion primitive models. This improvement enables the dual-arm robot to complete tasks more smoothly during collaborative operation, ensuring operation accuracy while improving the coordination and stability between multiple motion primitives.

[0185] (2) The present invention realizes high-precision operation of the robot in a complex experimental environment through the application of the dual-arm robot in the laboratory medicine dispensing task. The dual-arm robot significantly enhances the synchronous coordination ability of the left and right arms in the medicine dispensing task, ensuring that the two arms can accurately cooperate and perform operations synchronously, and improving the execution efficiency and accuracy of the robot in delicate tasks. At the same time, the system improves the generalization ability of skills, enabling the robot to flexibly respond to different task scenarios, effectively improving its adaptability and automation level.

[0186] The above is a detailed introduction to a dual-arm robot adaptive skill learning method based on dynamic motion primitives provided by the present invention. This article uses specific examples to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the core idea of ​​the present invention. It should be pointed out that for ordinary technicians in this technical field, without departing from the principles of the present invention, the present invention can also be improved and modified, and these improvements and modifications also fall within the scope of protection of the claims of the present invention.

Claims

1. A dual-arm robot adaptive skill learning method based on dynamic motion primitives, characterized in that: The method comprises the following steps: S100: Acquire teaching data and establish a dynamic motion primitive model. Through the dynamic motion primitive model, the two arms learn the shape characteristics of the trajectory from the teaching data respectively. The shape characteristics of the trajectory include the overall trend and local changes of the trajectory, generate the corresponding trajectory shape function, and further calculate to obtain the initial trajectory control weight; S200: obtaining a new task target point, combining the learned initial trajectory control weight and trajectory shape function with the new task target point, and generating an initial trajectory similar to the teaching trajectory; S300: Optimizing the initial trajectory to obtain an optimized trajectory shape, obtaining an optimized trajectory control weight, ensuring the coordination and consistency of the trajectory at different lengths and speeds, and correcting kinematic infeasibility; S400: Bringing the optimized trajectory control weights into the dynamic motion primitive model, and adaptively adjusting them using an adaptive time scaling factor based on the trajectory change rate to generate the optimized trajectory of the two arms; S100 includes: S110: establishing dynamic motion primitive models for the left arm and the right arm respectively to describe their trajectory generation and motion control; S120: Collect teaching data: drag the robot arm and use the host computer to record the robot end effector trajectory data set and ,The data set includes acceleration, velocity, and position; S130: Calculating a target shape function in combination with the collected teaching data; S140: setting an optimization problem, solving the optimization problem based on a dynamic motion primitive model and a target shape function to obtain a weight of a teaching trajectory; The dynamic motion primitive model in S110 is as follows: ； ； ； ； in, , , , , Respectively represent the initial position, current position, target position, speed and acceleration of the left arm; , , , , Represent the initial position, current position, target position, speed and acceleration of the right arm respectively. , are the time scaling factors for the left and right arms, respectively, are the phase variables controlling the time course of the left and right arms, respectively; and The attraction coefficient and damping coefficient in the spring-damper system represent the position respectively, which are constants. Represents the convergence speed of the control system, which is a constant; , is the shape function in the dynamic motion primitive model, which has the form: ； ； ； in, The width and Center is a Gaussian function characterized by , are the weights corresponding to the left arm and the right arm; is the number of Gaussian functions; S130 is specifically: ； ； in, and are the target shape functions for the left and right arms, respectively; S140 is specifically: ； ； in, is the shape function estimated according to the teaching trajectory; Finally, the calculation formula of the initial weight is expressed as: ； ； in, is a diagonal matrix, ; S200 includes: S210: Based on the new target point and , the initial trajectory control weights of the left and right arms are learned , , trajectory shape function, combined with the new task target point, estimates the acceleration of the robot's left and right arm end effectors; Using equations (5), (6) and (12), (13), we can obtain: ； ； in, and The shape functions estimated for the left and right arms respectively; Substituting into equations (1) and (3), we can obtain the acceleration of the robot's left and right arm end effectors: , : ； ； S220: Get the acceleration of the robot's left and right arm end effectors , Then, numerical integration is used to update the velocity , and location , , specifically: ； ； ； ； in, and are the speeds of the left and right arms at the current time point of the initial trajectory, and are the accelerations of the initial trajectories of the left and right arms at the current time point, represents the time step, and are the speeds of the left and right arms at the next time point after the initial trajectory, and are the positions of the left arm’s initial trajectory at the current time point and the next time point, respectively. and are the positions of the initial trajectory of the right arm at the current time point and the next time point respectively; S230: Repeat the calculation until the phase variables of the left arm and the right arm , Becomes 0, the trajectory reaches the target position and , get the initial trajectory of the left arm and the right arm , ; S300 includes: S310: Normalizing the initial trajectories of the left and right arms; S320: Optimizing the normalized trajectory shape based on the optimization function to minimize the shape difference between the reproduced trajectory and the taught trajectory; S330: Mapping the optimized trajectory back to the physical coordinate system of the actual task through a recovery formula, thereby ensuring that the trajectory executed in the actual task can match the physical requirements; S340: Generate a trajectory based on the objective function, where the generated trajectory satisfies physical feasibility and kinematic constraints, ensuring that the two arms can be coordinated and synchronized during execution; S310 is specifically: ； ； in, , Respectively represent the starting points of the left arm and right arm teaching data; , Represent the target points of the left arm and right arm teaching data respectively; in the normalized space, the initially generated reproduction trajectory and teaching trajectory have been adjusted in the same space; The optimization function in S320 is as follows: ； in , is the normalized teaching trajectory; The recovery formula in S330 is as follows: ； ； The specific objective function in S340 is: ； in, and represent the current positions of the updated trajectories of the left and right arms, respectively. and Represent the end points of the updated trajectories of the left and right arms, respectively. A constant to encourage alignment of the ends of the arms; The constraints include physical feasibility constraints and weight optimization constraints. The physical feasibility constraints ensure that the generated trajectory is within the reach of the robot. The physical feasibility constraints are as follows: ； The specific weight optimization constraints are: ； ； in, and denote the target positions of the left and right arms respectively, and denote the initial positions of the updated trajectories of the left and right arms, respectively. and represent the current positions of the updated trajectories of the left and right arms, respectively; and represents the current acceleration of the updated trajectory of the left and right arms respectively; After the above optimization problems, the weights for aligning the end points of the completed trajectory are obtained. , ; S400 includes: S410: Calculate the change rate of the optimized trajectory, specifically: ； ； S420: Bring the rate of change into the adaptive formula: ； ； in is a constant; S430: , Substitute into equations (14) and (15), and then connect equations (14)-(21), (30), and (31) to obtain the final trajectory. , .

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