Dynamic-movement-primitive-based adaptive skill learning method for dual-arm robot

Abstract

A dynamic-movement-primitive-based adaptive skill learning method for a dual-arm robot. The method comprises: acquiring demonstration data, establishing dynamic movement primitive models, enabling, by means of the dynamic movement primitive models, dual arms to respectively learn shape features of trajectories from the demonstration data, generating corresponding trajectory shape functions, and obtaining initial trajectory control weights; acquiring new task target points, and combining the new task target points with the initial trajectory control weights and the trajectory shape functions, which are obtained by means of learning, so as to generate initial trajectories similar to demonstration trajectories; optimizing the initial trajectories to obtain optimized trajectory shapes, and obtaining optimized trajectory control weights; and substituting the optimized trajectory control weights into the dynamic movement primitive models, and performing adaptive adjustment by using adaptive time scaling factors based on trajectory change rates, so as to generate optimized trajectories of the dual arms, such that the efficient and accurate completion of a task by a robot can be ensured.

Description

An Adaptive Skill Learning Method for Dual-Arm Robots Based on Dynamic Motion Primitives

[0001] This application claims priority to Chinese Patent Application No. CN202411698119.0, filed on November 26, 2024, entitled “An Adaptive Skill Learning Method for a Dual-Arm Robot Based on Dynamic Motion Elements”, the entire contents of which are incorporated herein by reference. Technical Field

[0002] This invention belongs to the field of dual-arm robot skill learning technology, and in particular relates to an adaptive skill learning method for dual-arm robots based on dynamic motion primitives. Background Technology

[0003] Dual-arm robots, with their superior operational flexibility and high-precision repeatability, have been widely used in numerous complex task scenarios. However, current skill learning methods rely on manual teaching by experts, that is, teaching robots to complete specific tasks by demonstrating actions. While this method allows robots to master basic operating steps in the initial stage, it often requires re-teaching when encountering new tasks or changing working environments. This manual teaching-dependent mode is inefficient and greatly limits the adaptability of dual-arm robots in complex and changing environments. Whenever 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.

[0004] Dynamic Movement Primitives (DMPs), as an effective skill learning framework, enable robots to acquire diverse motion patterns by learning motion trajectories demonstrated by experts. However, the skill generalization ability of DMPs in dual-arm tasks faces several challenges. First, the generalized trajectory may deviate significantly from the original taught trajectory, resulting in insufficient accuracy when the robot reproduces 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 and affecting the continuity and stability of the task. Furthermore, due to differences in the movement paths and distances of the two arms, the movement rhythms of the left and right arms may be asynchronous, making collaborative operation impossible. Therefore, optimizing the DMP model to improve the accuracy of trajectory reproduction and feasibility under kinematic constraints is crucial for enhancing the synchronization, coordination, and operational efficiency of dual-arm robots. Simultaneously, an end-effector alignment control mechanism is needed to ensure the consistency and synchronization of the two arms in collaborative tasks, enabling efficient and automated execution of dual-arm robots. Summary of the Invention

[0005] To address the above technical problems, this invention provides an adaptive skill learning method for dual-arm robots based on dynamic motion primitives.

[0006] The technical solution adopted by this invention to solve its technical problem is:

[0007] An adaptive skill learning method for a dual-arm robot based on dynamic motion primitives, the method comprising the following steps:

[0008] S100: Acquire teaching data, establish a dynamic motion primitive model, and through the dynamic motion primitive model, both arms learn the shape features of the trajectory from the teaching data. The shape features of the trajectory include the overall trend and local changes of the trajectory, generate the corresponding trajectory shape function, and further calculate the initial trajectory control weights.

[0009] S200: Obtain a new task target point, combine the learned initial trajectory control weights and trajectory shape function with the new task target point to generate an initial trajectory similar to the taught trajectory;

[0010] S300: Optimize the initial trajectory to obtain the optimized trajectory shape, obtain the optimized trajectory control weight, ensure the consistency of the trajectory under different lengths and speeds, and correct kinematic infeasibility;

[0011] S400: The optimized trajectory control weights are input into the dynamic motion primitive model, and an adaptive time scaling factor based on the trajectory change rate is used for adaptive adjustment to generate the optimized trajectory of the two arms.

[0012] Preferably, S100 includes:

[0013] S110: Establish dynamic motion primitive models for the left and right arms respectively to describe their trajectory generation and motion control;

[0014] S120: Collect teaching data: Record the robot end effector trajectory dataset by dragging the robotic arm and using a host computer. and The dataset includes acceleration, velocity, and position;

[0015] S130: Calculate the target shape function based on the collected teaching data;

[0016] S140: Set an optimization problem, and solve the optimization problem based on the dynamic motion primitive model and the target shape function to obtain the weights of the teaching trajectory.

[0017] Preferably, the dynamic motion primitive model in S110 is specifically as follows:

[0018] Among them, yL,0 ,y L ,g L , These represent the initial position, current position, target position, velocity, and acceleration of the left arm, respectively; y R,0 ,y R ,g R , These represent the initial position, current position, target position, velocity, and acceleration of the right arm, respectively, τ. L τ R These are the time scaling factors for the left and right arms, respectively, s L s R These are the phase variables controlling the time progression of the left and right arms, respectively; α y and β y The attraction coefficient and damping coefficient in the spring-damped system represent the position, respectively, and are constants, α. s This represents the convergence rate of the control system, which is a constant.

[0019] f L (s), f R (s) is the shape function in the dynamic motion primitive model, and its form is:

[0020] φ i (s)=exp(-h i (sc i ) 2 (7)

[0021] Where, φ i (s) is based on the width h i and center c i The characteristic Gaussian function is ω; L,i ω R,i The weights are for the left and right arms; N is the number of Gaussian functions.

[0022] S130 specifically refers to:

[0023] Among them, f L,target (s) and f R,target (s) are the target shape functions for the left and right arms, respectively;

[0024] S140 specifically refers to:

[0025] in, The shape function estimated based on the taught trajectory;

[0026] Finally, the formula for calculating the initial weights is expressed as:

[0027] Among them, D i It is a diagonal matrix. s L =[s L,1 ,s L,2 ,…,s L,n ] T ,s R =[s R,1 ,s R,2 ,…,s R,n ] T .

[0028] Preferably, S200 includes:

[0029] S210: Based on the new target point and The learned initial trajectory control weights of the left and right arms The trajectory shape function, combined with the new task target point, estimates the acceleration of the end effectors of the robot's left and right arms;

[0030] Using equations (5), (6) and (12), (13), we obtain:

[0031] in, and These are the shape functions estimated for the left and right arms, respectively.

[0032] Substituting equations (1) and (3) into the equations, we obtain the accelerations of the end effectors of the robot's left and right arms.

[0033] S220: Obtain the acceleration of the end effectors of the robot's left and right arms. Then, numerical integration is used to update the velocity. and position y L y R Specifically:

[0034] in, and These represent the velocities of the left and right arms at the current time point, respectively, based on their initial trajectories. and Let dt represent the accelerations of the left and right arms at the current time point, respectively, based on their initial trajectories. and Let yL and reproduced be the velocities of the left and right arms at the next time point, respectively, based on their initial trajectories. init (t) and yL, reproduced init(t+dt) represent the positions of the left arm's initial trajectory at the current and next time points, respectively. init (t) and yR, reproduced init (t+dt) represent the positions of the right arm's initial trajectory at the current and next time points, respectively;

[0035] S230: Repeat the calculation until the phase variables s of the left and right arms are calculated. L s R When the value changes to 0, the trajectory reaches the target position. and The initial trajectories yL of the left and right arms are obtained, and the reproduction is performed. init yR,reproduced init .

[0036] Preferably, S300 includes:

[0037] S310: Normalize the initial trajectories of the left and right arms;

[0038] S320: Optimize the shape of the normalized trajectory based on the optimization function to minimize the shape difference between the reproduced trajectory and the taught trajectory;

[0039] S330: By using the recovery formula, the optimized trajectory is mapped back to the physical coordinate system of the actual task, thereby ensuring that the trajectory executed in the actual task can match the physical requirements;

[0040] S340: Generates a trajectory based on the objective function. The generated trajectory satisfies physical feasibility and kinematic constraints, ensuring that the two arms can coordinate and synchronize during execution.

[0041] Preferably, S310 specifically comprises:

[0042] Among them, y L,0,demo y R,0,demo These represent the starting points for the teaching data of the left and right arms, respectively; g L,demo g R,demo These represent the target points of the teaching data for the left and right arms, respectively. In the normalized space, the initially generated reproduction trajectory and teaching trajectory have been adjusted in the same space.

[0043] The optimized function in S320 is as follows:

[0044] Where y L,scaled (t), y R,scaled (t) is the normalized teaching trajectory;

[0045] The recovery formula in S330 is as follows:

[0046] Preferably, the objective function in S340 is as follows:

[0047] Among them, yL,reproduced temp and yR,reproduced temp Represent the current positions of the updated trajectories of the left and right arms, respectively: yL, end, and reproduced. temp and yR,end,reproduced temp Let λ1 represent the endpoints of the updated trajectories of the left and right arms, respectively, and let λ1 be a constant that encourages alignment of the ends of the two arms.

[0048] The constraints include physical feasibility constraints and weight optimization constraints. The physical feasibility constraints ensure that the generated trajectory is within the robot's reachability range. Specifically, the physical feasibility constraints are:

[0049] The specific weight optimization constraints are as follows:

[0050] Where gL,reproduced and gR,reproduced represent the target positions of the left and right arms, respectively, and yL,0,reproduced and yR,0,reproduced represent the initial positions of the updated trajectories of the left and right arms, respectively. and These represent the current positions of the updated trajectories of the left and right arms, respectively. and These represent the current accelerations of the updated trajectories of the left and right arms, respectively.

[0051] After the above optimization, the weight ω for aligning the endpoints of the completed trajectory is obtained. L,i final ω R,i final .

[0052] Preferably, S400 includes:

[0053] S410: Calculate the rate of change of the optimized trajectory, specifically: Δy L,recover (t)=y L,recover (t)-y L,recover (t-Δt) (28) Δy R,recover (t)=y R,recover (t)-y R,recover (t-Δt) (29)

[0054] Among them, y L,recover (t), y R,recover (t) represent the actual physical positions of the two arms at time step t;

[0055] S420: Substitute the rate of change into the adaptive formula to obtain the time scaling factor τ corresponding to the two arms. L (t) and τ R (t):

[0056] Where k is a constant;

[0057] S430: ω L,i final ω R,i final Substituting equations (14) and (15), and combining equations (14)-(21), (30), and (31), the final trajectory yR is obtained. final yL,reproduced final .

[0058] The aforementioned adaptive skill learning method for dual-arm robots based on dynamic motion primitives first allows the left and right arms to learn from expert teaching data to obtain initial trajectory weights. Then, given a new target point, an initial trajectory is generated. The trajectory is then optimized according to actual needs. Finally, the time scaling parameter is dynamically adjusted using the rate of change to ensure that the trajectories of both arms remain consistent over time, generating optimized trajectories for both arms. Through trajectory normalization, time-space coupling adjustment, and dual-arm synchronization alignment mechanisms, the robot is ensured to complete tasks efficiently and accurately. This effectively solves problems such as trajectory deviation, kinematic infeasibility, and inaccurate end-effector alignment during skill learning and generalization in dual-arm synchronous tasks. Attached Figure Description

[0059] Figure 1 is a flowchart of an adaptive skill learning method for a dual-arm robot based on dynamic motion primitives in one embodiment of the present invention;

[0060] Figure 2 is a flowchart of an adaptive skill learning method for a dual-arm robot based on dynamic motion primitives in another embodiment of the present invention;

[0061] Figure 3 is a diagram of the effect of the original model's two-arm drug dispensing in an embodiment of the present invention; wherein, (a) is a three-dimensional view of the trajectory of the original model at position 1, (b) is a top view of the trajectory of the original model at position 1, (c) is a three-dimensional view of the trajectory of the original model at position 2, and (d) is a top view of the trajectory of the original model at position 2.

[0062] Figure 4 is a diagram showing the effect of the improved model's dual-arm drug dispensing in an embodiment of the present invention; wherein, (a) is a three-dimensional view of the trajectory of the improved model at position 1, (b) is a top view of the trajectory of the improved model at position 1, (c) is a three-dimensional view of the trajectory of the improved model at position 2, and (d) is a top view of the trajectory of the improved model at position 2. Detailed Implementation

[0063] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings.

[0064] In one embodiment, as shown in Figures 1 and 2, an adaptive skill learning method for a dual-arm robot based on dynamic motion primitives includes the following steps:

[0065] S100: Acquire teaching data, establish a dynamic motion primitive model, and through the dynamic motion primitive model, both arms learn the shape features of the trajectory from the teaching data. The shape features of the trajectory include the overall trend and local changes of the trajectory, generate the corresponding trajectory shape function, and further calculate the initial trajectory control weights.

[0066] S200: Obtain a new task target point, combine the learned initial trajectory control weights and trajectory shape function with the new task target point to generate an initial trajectory similar to the taught trajectory;

[0067] S300: Optimize the initial trajectory to obtain the optimized trajectory shape, obtain the optimized trajectory control weight, ensure the consistency of the trajectory under different lengths and speeds, and correct kinematic infeasibility;

[0068] S400: The optimized trajectory control weights are input into the dynamic motion primitive model, and an adaptive time scaling factor based on the trajectory change rate is used for adaptive adjustment to generate the optimized trajectory of the two arms.

[0069] Specifically, S100 obtains the initial trajectory control weights, providing a basis for subsequent trajectory reproduction; S200 ensures that the motion trajectory of the two arms remains consistent and operable under different task conditions; and S400 ensures that the trajectory shape matches the accuracy requirements of the target task, ultimately realizing the skill learning of the dual-arm robot in synchronous tasks.

[0070] In one embodiment, S100 includes:

[0071] S110: Establish dynamic motion primitive models for the left and right arms respectively to describe their trajectory generation and motion control;

[0072] S120: Collect teaching data: Record the robot end effector trajectory dataset by dragging the robotic arm and using a host computer. and The dataset includes acceleration, velocity, and position;

[0073] S130: Calculate the target shape function based on the collected teaching data;

[0074] S140: Set an optimization problem, and solve the optimization problem based on the dynamic motion primitive model and the target shape function to obtain the weights of the teaching trajectory.

[0075] In one embodiment, the dynamic motion primitive model in S110 is specifically as follows:

[0076] Among them, y L,0 ,y L ,g L , These represent the initial position, current position, target position, velocity, and acceleration of the left arm, respectively; y R,0 ,y R ,g R , These represent the initial position, current position, target position, velocity, and acceleration of the right arm, respectively, τ. L τ R These are the time scaling factors for the left and right arms, respectively, s L s R These are the phase variables controlling the time progression of the left and right arms, respectively; α y and β y The attraction coefficient and damping coefficient in the spring-damped system represent the position, respectively, and are constants, α. s This represents the convergence rate of the control system, which is a constant.

[0077] f L (s), f R (s) is the shape function in the dynamic motion primitive model, and its form is:

[0078] φ i (s)=exp(-h i (sc i ) 2 (7)

[0079] Where, φ i (s) is based on the width h i and center c i The characteristic Gaussian function is ω; L,i ω R,iThe weights are for the left and right arms; N is the number of Gaussian functions.

[0080] S130 specifically refers to:

[0081] Among them, f L,target (s) and f R,target (s) are the target shape functions for the left and right arms, respectively;

[0082] S140 specifically refers to:

[0083] in, The shape function estimated based on the taught trajectory;

[0084] Finally, the formula for calculating the initial weights is expressed as:

[0085] Among them, D i It is a diagonal matrix. s L =[s L,1 ,s L,2 ,…,s L,n ] T ,s R =[s R,1 ,s R,2 ,…,s R,n ] T .

[0086] In one embodiment, S200 includes:

[0087] S210: Based on the new target point and The learned initial trajectory control weights of the left and right arms The trajectory shape function, combined with the new task target point, estimates the acceleration of the end effectors of the robot's left and right arms;

[0088] Using equations (5), (6) and (12), (13), we obtain:

[0089] in, and These are the shape functions estimated for the left and right arms, respectively.

[0090] Substituting equations (1) and (3) into the equations, we obtain the accelerations of the end effectors of the robot's left and right arms.

[0091] S220: Obtain the acceleration of the end effectors of the robot's left and right arms. Then, numerical integration is used to update the velocity. and position y L y R Specifically:

[0092] in, and These represent the velocities of the left and right arms at the current time point, respectively, based on their initial trajectories. and Let dt represent the accelerations of the left and right arms at the current time point, respectively, based on their initial trajectories. and Let yL and reproduced be the velocities of the left and right arms at the next time point, respectively, based on their initial trajectories. init (t) and yL, reproduced init (t+dt) represent the positions of the left arm's initial trajectory at the current and next time points, respectively. init (t) and yR, reproduced init (t+dt) represent the positions of the right arm's initial trajectory at the current and next time points, respectively;

[0093] S230: Repeat the calculation until the phase variables s of the left and right arms are calculated. L s R When the value changes to 0, the trajectory reaches the target position. and The initial trajectories yL of the left and right arms are obtained, and the reproduction is performed. init yR,reproduced init .

[0094] In one embodiment, S300 includes:

[0095] S310: Normalize the initial trajectories of the left and right arms;

[0096] S320: The normalized trajectory shape is optimized based on the optimization function to minimize the shape difference between the reproduced trajectory and the taught trajectory; furthermore, after optimization in the normalization space, the distance between the reproduced trajectory and the taught trajectory is minimized, ensuring the similarity between the trajectory shape and the taught trajectory.

[0097] S330: By using the recovery formula, the optimized trajectory is mapped back to the physical coordinate system of the actual task, thereby ensuring that the trajectory executed in the actual task can match the physical requirements;

[0098] S340: Generates a trajectory based on the objective function. The generated trajectory satisfies physical feasibility and kinematic constraints, ensuring that the two arms can coordinate and synchronize during execution.

[0099] Furthermore, to ensure that the generated trajectory is not only reasonable in shape, but also meets physical feasibility and kinematic constraints, the core objective of physical feasibility optimization is to ensure the executability of the trajectory within the robot's kinematic model. Through further optimization, the reproduced trajectory must not only maintain consistency with the target trajectory in shape, but also meet the actual physical constraints of the task environment, ensuring that the two arms can coordinate and synchronize during execution.

[0100] Specifically, since the generated trajectory is usually achieved by setting new target points, it is difficult to directly assess the similarity between the reproduced trajectory and the initial taught trajectory, which poses a challenge to subsequent optimization. To ensure that the trajectory shapes of the left and right arms at different target points remain consistent with the taught trajectory, this 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.

[0101] In one embodiment, S310 specifically includes:

[0102] Among them, y L,0,demo y R,0,demo These represent the starting points for the teaching data of the left and right arms, respectively; g L,demo g R,demo These represent the target points of the teaching data for the left and right arms, respectively. In the normalized space, the initially generated reproduction trajectory and teaching trajectory have been adjusted in the same space.

[0103] The optimized function in S320 is as follows:

[0104] Where y L,scaled (t), y R,scaled (t) is the normalized teaching trajectory;

[0105] The recovery formula in S330 is as follows:

[0106] In one embodiment, the objective function in S340 is specifically:

[0107] Among them, yL,reproduced temp and yR,reproduced temp Represent the current positions of the updated trajectories of the left and right arms, respectively: yL, end, and reproduced. temp and yR,end,reproduced temp Let λ1 represent the endpoints of the updated trajectories of the left and right arms, respectively, and let λ1 be a constant that encourages alignment of the ends of the two arms.

[0108] The constraints include physical feasibility constraints and weight optimization constraints. The physical feasibility constraints ensure that the generated trajectory is within the robot's reachability range. Specifically, the physical feasibility constraints are:

[0109] The specific weight optimization constraints are as follows:

[0110] Where gL,reproduced and gR,reproduced represent the target positions of the left and right arms, respectively, and yL,0,reproduced and yR,0,reproduced represent the initial positions of the updated trajectories of the left and right arms, respectively. and These represent the current positions of the updated trajectories of the left and right arms, respectively. and These represent the current accelerations of the updated trajectories of the left and right arms, respectively.

[0111] After the above optimization, the weight ω for aligning the endpoints of the completed trajectory is obtained. L,i final ω R,i final .

[0112] Furthermore, after completing trajectory generation and physical feasibility optimization, ensuring the synchronization of the two arm trajectories is the final step for task success. During execution, the dual-arm robot must guarantee coordinated movements of both arms; otherwise, task failure may occur. In this process, the DMP method provides an adaptive time scaling mechanism to ensure the synchronization of the arms' movements during task execution. By calculating the rate of change of the left and right arm trajectories and dynamically adjusting the time scaling parameters based on the rate of change, the robot ensures that the trajectories of both arms remain consistent over time. In this way, the robot can avoid one arm moving too fast or too slow during task execution, thereby achieving synchronized coordination between the two arms.

[0113] In one embodiment, S400 includes:

[0114] S410: Calculate the rate of change of the optimized trajectory, specifically: Δy L,recover (t)=y L,recover (t)-y L,recover (t-Δt) (28) Δy R,recover (t)=y R,recover (t)-y R,recover (t-Δt) (29)

[0115] Among them, y L,recover (t), y R,recover(t) represent the actual physical positions of the two arms at time step t;

[0116] S420: Substitute the rate of change into the adaptive formula to obtain the time scaling factor τ corresponding to the two arms. L (t) and τ R (t):

[0117] Where k is a constant;

[0118] S430: ω L,i final ω R,i final Substituting equations (14) and (15), and combining equations (14)-(21), (30), and (31), the final trajectory yR is obtained. final yL,reproduced final .

[0119] Figures 3 and 4 show the simulation results. Figure 3 shows the effect of the original model, where the trajectory shape is strange and the end points are not aligned. Figure 4 shows the effect of the invention, where the shape is reasonable and the end points are aligned, effectively demonstrating the effectiveness of the method of the invention.

[0120] The aforementioned adaptive skill learning method for dual-arm robots based on dynamic motion primitives has the following advantages:

[0121] (1) Based on the improved trajectory generation capability of the original dynamic motion primitive model, this 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 operational accuracy while improving the coordination and stability between multiple motion primitives.

[0122] (2) This invention achieves high-precision operation of a robot in complex experimental environments by applying a dual-arm robot to laboratory drug preparation tasks. It significantly enhances the synchronous coordination ability of the left and right arms in drug preparation tasks, ensuring precise cooperation and synchronized operation, thus improving the robot's efficiency and accuracy in delicate tasks. Simultaneously, the system improves the generalization ability of its skills, enabling the robot to flexibly respond to different task scenarios, effectively enhancing its adaptability and automation level.

[0123] The above provides a detailed description of an adaptive skill learning method for a dual-arm robot based on dynamic motion primitives, as provided by this invention. Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are merely for the purpose of helping to understand the core ideas of this invention. It should be noted that those skilled in the art can make various improvements and modifications to this invention without departing from its principles, and these improvements and modifications also fall within the protection scope of the claims of this invention.

Claims

1. An adaptive skill learning method for a dual-arm robot based on dynamic motion primitives, characterized in that, The method includes the following steps: S100: Acquire teaching data, establish a dynamic motion primitive model, and through the dynamic motion primitive model, both arms learn the shape features of the trajectory from the teaching data. The shape features of the trajectory include the overall trend and local changes of the trajectory, generate the corresponding trajectory shape function, and further calculate the initial trajectory control weights. S200: Obtain a new task target point, combine the learned initial trajectory control weights and trajectory shape function with the new task target point to generate an initial trajectory similar to the taught trajectory; S300: Optimize the initial trajectory to obtain the optimized trajectory shape, obtain the optimized trajectory control weight, ensure the consistency of the trajectory under different lengths and speeds, and correct kinematic infeasibility; S400: The optimized trajectory control weights are input into the dynamic motion primitive model, and an adaptive time scaling factor based on the trajectory change rate is used for adaptive adjustment to generate the optimized trajectory of the two arms.

2. The method according to claim 1, characterized in that, S100 includes: S110: Establish dynamic motion primitive models for the left and right arms respectively to describe their trajectory generation and motion control; S120: Collect teaching data: Record the robot end effector trajectory dataset by dragging the robotic arm and using a host computer. and The dataset includes acceleration, velocity, and position; S130: Calculate the target shape function based on the collected teaching data; S140: Set an optimization problem, and solve the optimization problem based on the dynamic motion primitive model and the target shape function to obtain the weights of the teaching trajectory; 3. The method according to claim 2, characterized in that, The dynamic motion primitive model in S110 is as follows: Among them, y L,0 ,y L ,g L , These represent the initial position, current position, target position, velocity, and acceleration of the left arm, respectively; y R,0 ,y R ,g R , These represent the initial position, current position, target position, velocity, and acceleration of the right arm, respectively, τ. L τ R These are the time scaling factors for the left and right arms, respectively, s L s R These are the phase variables controlling the time progression of the left and right arms, respectively; α y and β y The attraction coefficient and damping coefficient in the spring-damped system represent the position, respectively, and are constants, α. s This represents the convergence rate of the control system, which is a constant. f L (s), f R (s) is the shape function in the dynamic motion primitive model, and its form is: φ i (s)=exp(-h i (sc i ) 2 ) (7) Where, φ i (s) is based on the width h i and center c i The characteristic Gaussian function is ω; L,i ω R,i The weights are for the left and right arms; N is the number of Gaussian functions. S130 specifically refers to: Among them, f L,target (s) and f R,target (s) are the target shape functions for the left and right arms, respectively; S140 specifically refers to: in, The shape function estimated based on the taught trajectory; Finally, the formula for calculating the initial weights is expressed as: Among them, D i It is a diagonal matrix. s L =[s L,1 ,s L,2 ,…,s L,n ] T ,s R =[s R,1 ,s R,2 ,…,s R,n ] T 。 4. The method according to claim 3, characterized in that, S200 includes: S210: Based on the new target point and The learned initial trajectory control weights of the left and right arms The trajectory shape function, combined with the new task target point, estimates the acceleration of the end effectors of the robot's left and right arms; Using equations (5), (6) and (12), (13), we obtain: in, and These are the shape functions estimated for the left and right arms, respectively. Substituting equations (1) and (3) into the equations, we obtain the accelerations of the end effectors of the robot's left and right arms. S220: Obtain the acceleration of the end effectors of the robot's left and right arms. Then, numerical integration is used to update the velocity. and position y L y R Specifically: yL,reproduced init (t+dt)=yL,reproduced init (t)+yL,reproduced init (t+dt)*dt (19) yR,reproduced init (t+dt)=yR,reproduced init (t)+yR,reproduced init (t+dt)*dt (21) in, and These represent the velocities of the left and right arms at the current time point, respectively, based on their initial trajectories. and Let dt represent the accelerations of the left and right arms at the current time point, respectively, based on their initial trajectories. and Let yL and reproduced be the velocities of the left and right arms at the next time point, respectively, based on their initial trajectories. init (t) and yL, reproduced init (t+dt) represent the positions of the left arm's initial trajectory at the current and next time points, respectively. init (t) and yR, reproduced init (t+dt) represent the positions of the right arm's initial trajectory at the current and next time points, respectively; S230: Repeat the calculation until the phase variables s of the left and right arms are calculated. L s R When the value changes to 0, the trajectory reaches the target position. and The initial trajectories yL of the left and right arms are obtained, and the reproduction is performed. init yR,reproduced init .

5. The method according to claim 4, characterized in that, The S300 includes: S310: Normalize the initial trajectories of the left and right arms; S320: Optimize the shape of the normalized trajectory based on the optimization function to minimize the shape difference between the reproduced trajectory and the taught trajectory; S330: By using the recovery formula, the optimized trajectory is mapped back to the physical coordinate system of the actual task, thereby ensuring that the trajectory executed in the actual task can match the physical requirements; S340: Generates a trajectory based on the objective function. The generated trajectory satisfies physical feasibility and kinematic constraints, ensuring that the two arms can coordinate and synchronize during execution.

6. The method according to claim 5, characterized in that, S310 specifically refers to: Among them, y L,0,demo y R,0,demo These represent the starting points for the teaching data of the left and right arms, respectively; g L,demo g R,demo These represent the target points of the teaching data for the left and right arms, respectively. In the normalized space, the initially generated reproduction trajectory and teaching trajectory have been adjusted in the same space. The optimized function in S320 is as follows: Where y L,scaled (t), y R,scaled (t) is the normalized teaching trajectory; The recovery formula in S330 is as follows:

7. The method according to claim 6, characterized in that, The objective function in S340 is as follows: Among them, yL,reproduced temp and yR,reproduced temp Represent the current positions of the updated trajectories of the left and right arms, respectively: yL, end, and reproduced. temp and yR,end,reproduced temp λ1 represents the endpoints of the updated trajectories of the left and right arms, respectively, and is a constant that encourages alignment of the ends of the two arms. The constraints include physical feasibility constraints and weight optimization constraints. The physical feasibility constraints ensure that the generated trajectory is within the robot's reachability range. Specifically, the physical feasibility constraints are: The specific weight optimization constraints are as follows: Where gL,reproduced and gR,reproduced represent the target positions of the left and right arms, respectively, and yL,0,reproduced and yR,0,reproduced represent the initial positions of the updated trajectories of the left and right arms, respectively. and These represent the current positions of the updated trajectories of the left and right arms, respectively. and These represent the current accelerations of the updated trajectories of the left and right arms, respectively. After the above optimization, the weight ω for aligning the endpoints of the completed trajectory is obtained. L,i final ω R,i final ; 8. The method according to claim 7, characterized in that, The S400 includes: S410: Calculate the rate of change of the optimized trajectory, specifically: Dy L,recover (t)=y L,recover (t)-y L,recover (t-Δt) (28) Dy R,recover (t)=y R,recover (t)-y R,recover (t-Δt) (29) Among them, y L,recover (t), y R,recover (t) represent the actual physical positions of the two arms at time step t; S420: Substitute the rate of change into the adaptive formula to obtain the time scaling factor τ corresponding to the two arms. L (t) and τ R (t): Where k is a constant; S430: ω L,i final ω R,i final Substituting equations (14) and (15), and combining equations (14)-(21), (30), and (31), the final trajectory yR is obtained. final yL,reproduced final .

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