Bilateral control based robot teaching method, system, device and storage medium

Abstract

The application discloses a bilateral control-based mechanical arm teaching method, system, device and storage medium, which is applied to the technical field of mechanical control and the method comprises the following steps: acquiring force sensor readings of the master robot and the slave robot; performing gravity compensation on the force sensor readings; judging whether the motion state of the mechanical arm is stable according to the contact force of the master robot and the contact force of the slave robot; inputting the difference between the contact force of the master robot and the contact force of the slave robot into a mobility model; converting Cartesian space position information into joint information according to inverse kinematics, and sending the joint information to the mechanical arms of the master robot and the slave robot, so that the master robot and the slave robot move; and remote operation drag teaching of mobility control can enable an operator to drag the master mechanical arm end with low impedance for teaching and collect data of interaction of the robot independent of the environment.

Description

Technical Field

[0001] This invention relates to the field of mechanical control technology, and in particular to a teaching method, system, device and storage medium for a robotic arm based on bilateral control. Background Technology

[0002] With the rapid development of robotics technology, its applications are becoming increasingly widespread. Robots can replace humans in performing numerous repetitive tasks or operating in dangerous or harsh working environments. Traditional robot skill acquisition is mainly achieved through robot programming or kinesthetic teaching. Robot programming refers to setting the robot's motion / force trajectory through programming, but robot behavior is often not easily scriptable. For example, in tasks involving complex contact environments, it is difficult to design motion planning algorithms with high adaptability and stability. Kinesthetic teaching overcomes some of the shortcomings of robot programming and effectively acquires skills, but operators still need to be in hazardous working environments. Furthermore, in addition to applying forces to complete tasks, operators also need to resist the dynamic forces of the tool. The lack of a reliable remote operation mechanism to independently record the contact forces of the tool to complete tasks leads to the collection of overly large contact forces, which is suboptimal.

[0003] Remote operation teaching means that an operator can remotely control a slave robot to perform tasks by controlling the movement of the master robot. Two-way remote operation can provide force feedback to complete the teaching of contact tasks. Remote operation teaching overcomes the shortcomings of robot programming or kinematic teaching. Two-way control methods are mainly divided into four types: position control, force control, position-force control, and force-position hybrid control. The position-force two-way method is a commonly used method in remote operating systems. The slave robot tracks the position of the master robot, and the master robot tracks the feedback force of the slave robot interacting with the environment.

[0004] When robot agility is achieved using admittance control, significant changes in external stiffness can cause the robot to bounce or oscillate. Adjusting the admittance parameters can reduce this bounce or oscillation, but these changes inject energy into the system, compromising its passivity. The bounce or oscillation during admittance teleoperation occurs because the teleoperation system cannot perfectly execute the admittance model. Due to the response time and error of the robot's end effector, the robot's behavior differs from the nominal admittance model, and this difference undermines the system's passivity.

[0005] To overcome these shortcomings, this application proposes a robotic arm teaching method, system, device, and storage medium based on bilateral control. The teleoperation drag teaching based on admittance control enables the operator to drag the end effector of the main robotic arm with low impedance for teaching and to collect data on robot interaction independent of the environment. Summary of the Invention

[0006] The purpose of this application is to provide a method, system, device, and storage medium for teaching a robotic arm based on bilateral control, and to address the following problem.

[0007] To achieve the above objectives, this application provides the following technical solution:

[0008] This application provides a robotic arm teaching method based on bilateral control, including:

[0009] Acquire force sensor readings from the end effector of the main robot and the slave robot;

[0010] Gravity compensation is applied to the force sensor readings to obtain the contact force between the master robot and the slave robot;

[0011] The stability of the robotic arm's motion state is determined based on the contact force between the master robot and the slave robot. If it is unstable, the parameters of the admittance model are adjusted.

[0012] The difference between the contact force of the master robot and the contact force of the slave robot is calculated and input into the admittance model. The admittance model is then used to convert the contact forces of the master robot and the slave robot into Cartesian spatial position information.

[0013] The Cartesian spatial position information is converted into joint information based on inverse kinematics and sent to the robotic arms of the master robot and the slave robot, causing the robotic arms of the master robot and the slave robot to move.

[0014] Furthermore, the steps for acquiring force sensor readings from the main robot and the end effector of the robot specifically include the following steps:

[0015] The force sensor readings are acquired by six-dimensional force sensors installed at the end caps of the master robot and the slave robot. These force sensor readings represent the forces and torques in six degrees of freedom in Cartesian space. The force sensor readings of the master and slave robots are f0 and f1, respectively. h and f e .

[0016] Furthermore, the step of performing gravity compensation on the force sensor readings to obtain the contact force between the master robot and the slave robot specifically includes the following steps:

[0017] Calculate the gravity f of the end effector of the master robot and the slave robot. ht and f et The force sensor reading is subtracted from the weight of the end effector to obtain the gravity-compensated contact force f between the master robot and the slave robot. s and f m The calculation formula is:

[0018] f s =f e -f et

[0019] f m =f h -f ht .

[0020] Furthermore, the step of determining whether the motion state of the robotic arm is stable based on the contact force between the master robot and the slave robot, and adjusting the parameters of the admittance model if it is unstable, specifically includes the following steps:

[0021] The initial admittance model of the system is:

[0022]

[0023] Where M0 is the initial virtual mass and B0 is the initial virtual damping, both of which are six-dimensional diagonal matrices; t i i represents the current time; i represents the time step of the program's discrete execution. The command acceleration is calculated for the admittance model; the command position x(t) is obtained by integration. i The master robot and slave robot execute to obtain the actual position x. m (t i ), x s (t i );

[0024] When f s (t i+1 )(x(t i )-x s (t i If ))>ε, then the admittance parameter is not adjusted;

[0025] If the contact force in teleoperation is characterized by admittance oscillation:

[0026] f s (t i+1 )(x(t i )-x s (t i ))≤ε

[0027] Then adjust the admittance parameter, and increment the counter k by one each time an instability is detected.

[0028] Furthermore, the adjustment of the admittance parameter specifically includes the following steps:

[0029] A detection threshold ε is set to detect the abnormal rebound oscillation behavior of the admittance control. When it is necessary to adjust the virtual mass in the admittance model, the rebound oscillation behavior is reduced by increasing the inertia term, M(t). i The adjustment calculation formula is as follows:

[0030]

[0031] B(t i+1 )=RM(t i+1 )

[0032] Where S p (p=0,1,...,k) is the adjustment amount of the virtual mass, β is the forgetting factor, the mass matrix is ​​restored to the initial value M0 after the oscillation disappears, and R is the damping to mass ratio;

[0033] Virtual quality adjustment amount S p The calculation formula is:

[0034] S p =diag{s1,s2,s3,s4,s5,s6}

[0035]

[0036] in T(t) represents the upper bound on the allowable increase of the admittance parameter within a time step, where the subscript j represents the degree of freedom. i ) is in (0,t i The energy dissipated by the system within a certain time period;

[0037] Based on the condition that the system is passive, the system (0,t) i The energy dissipated is greater than (t) i ,t i+1 The energy injected within a time period is expressed by the formula:

[0038]

[0039] Due to the item Establish the inequality:

[0040]

[0041] Based on the upper bound of the existence of the velocity term:

[0042]

[0043] Derive new inequalities:

[0044]

[0045] Adjustment method for deriving M from integrals:

[0046]

[0047] S p (t i )=diag{s1,s2,s3,s4,s5,s6}.

[0048] Furthermore, the step of subtracting the contact force of the master robot and the contact force of the slave robot and inputting the result into the admittance model, and then using the admittance model to convert the contact forces of the master robot and the slave robot into Cartesian spatial position information, specifically includes the following steps:

[0049] After inputting the difference of the contact force into the admittance model, the Cartesian space acceleration is output, and the expression is:

[0050]

[0051] Where M(t) i+1 ), B(t) i+1 These are the inertia matrix and the damping matrix, respectively. Let f be the acceleration of the robot's end effector in Cartesian space. m (t i+1 ), f s (t i+1 ) represents the contact force at the current moment.

[0052] Furthermore, the step of converting the Cartesian spatial position information into joint information based on inverse kinematics and sending it to the robotic arms of the master robot and the slave robot to cause the robotic arms of the master robot and the slave robot to move specifically includes the following steps:

[0053] The Cartesian formula for calculating spatial velocity is:

[0054]

[0055] The joint velocity ΔT is calculated from the inverse matrix of Jacobi, and then integrated with the actual joint position of the robot to obtain the joint position of the robot. The joint position is then sent to the robotic arm servo system.

[0056] Its expression is:

[0057]

[0058]

[0059] Where Δt is the time interval of the operating cycle; Δt = t i+1 -t i J -1 This is the inverse of the Jacobian matrix; Let q(t) be the joint command velocity. i+1 ) represents the joint command position.

[0060] This application provides a system for a robotic arm teaching method based on bilateral control, the system comprising:

[0061] Acquisition module: Acquires force sensor readings from the end effectors of the main robot and the slave robot;

[0062] Processing module: Performs gravity compensation on the force sensor readings to obtain the contact force between the master robot and the slave robot;

[0063] Judgment module: Determines whether the motion state of the robotic arm is stable based on the contact force between the master robot and the slave robot. If it is unstable, the parameters of the admittance model are adjusted.

[0064] Input module: The difference between the contact force of the master robot and the contact force of the slave robot is input into the admittance model, and the contact force of the master robot and the slave robot is converted into Cartesian space position information using the admittance model;

[0065] Sending module: Based on inverse kinematics, the Cartesian spatial position information is converted into joint information and sent to the robotic arms of the master robot and the slave robot, so that the robotic arms of the master robot and the slave robot can move.

[0066] This application provides an apparatus comprising a processor and a memory coupled to the processor, wherein the memory stores program instructions for implementing a bilateral control-based robotic arm teaching method; the processor is configured to execute the program instructions stored in the memory to implement bilateral control-based robotic arm teaching.

[0067] This application provides a storage medium storing processor-executable program instructions for executing a robotic arm teaching method based on bilateral control.

[0068] This application provides a method, system, device, and storage medium for teaching a robotic arm based on bilateral control, which has the following beneficial effects:

[0069] (1) The force sensor readings are collected by the six-dimensional force sensor installed at the end of the master and slave robots, and the information of the slave end independently completing the task is collected. Compared with directly dragging the robotic arm to contact the external environment, the collected force sensor readings are more accurate, and remote operation can be used for remote teaching. When the task is severe, the safety of the teaching personnel can be guaranteed.

[0070] (2) Based on the measurable force sensor readings and the robot's current position information, determine whether the admittance teleoperation system is stable. If the admittance oscillation occurs, the contact force obtained during teleoperation will be f. s (t i+1 )(x(t i )-x s (t i If ))>ε, then adjust the admittance parameter; if the contact force obtained during teleoperation is f s (t i+1)(x(t i )-x s (t i If ε ≤ ε, then no parameter adjustment is needed; the admittance model is used to convert the contact force into position information, enabling low-impedance drag teaching, which is more conducive to operators teaching points or trajectories;

[0071] (3) The teaching method used in this invention is based on the position loop of the robotic arm servo system, which is applicable to most robotic arm systems on the market and has a wide range of applications. Attached Figure Description

[0072] Figure 1 This is a flowchart illustrating the robotic arm teaching method based on bilateral control according to Embodiment 1 of this application;

[0073] Figure 2 This is a schematic diagram of attitude calculation for Embodiment 1 of this application;

[0074] Figure 3 This is a pseudocode flowchart of adjusting the admittance parameter in Embodiment 1 of this application;

[0075] Figure 4 This is a schematic diagram of the structure of the robotic arm teaching system based on bilateral control according to Embodiment 2 of this application;

[0076] Figure 5 This is a diagram showing the overall software architecture of the robotic arm teaching system based on bilateral control according to Embodiment 2 of this application;

[0077] Figure 6 This is a block diagram of the bilateral control transfer function in Embodiment 2 of this application;

[0078] Figure 7 This is a schematic diagram of the device structure provided in Embodiment 3 of the present invention;

[0079] Figure 8 This is a schematic diagram of the storage medium structure provided in Embodiment 4 of the present invention. Detailed Implementation

[0080] It should be understood that the specific embodiments described herein are merely illustrative of this application and are not intended to limit this application.

[0081] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0082] Example 1

[0083] Please see Figure 1 This is a flowchart illustrating the robotic arm teaching method based on bilateral control according to Embodiment 1 of this application; the steps include:

[0084] S1: Acquire force sensor readings from the end effector of the main robot and the slave robot.

[0085] In this embodiment, the force sensor readings are collected by six-dimensional force sensors installed at the end caps of the master robot and the slave robot. The force sensor readings represent the forces and torques of the six degrees of freedom in Cartesian space. The force sensor readings of the master and slave robots are f0 and f1, respectively. h and f e .

[0086] S2: Perform gravity compensation on the force sensor readings to obtain the contact force between the master robot and the slave robot.

[0087] In this embodiment, the gravity f of the end effector of the master robot and the slave robot is calculated. ht and f et The force sensor reading is subtracted from the weight of the end effector to obtain the gravity-compensated contact force f between the master robot and the slave robot. s and f m The calculation formula is:

[0088] f s =f e -f et

[0089] f m =f h -f ht .

[0090] Please see Figure 2 This is a schematic diagram of attitude calculation in Embodiment 1 of this application;

[0091] The weight and center-of-gravity coordinates of the end effector were measured using the traditional six-point method. For ease of calculation, six orientations were selected. The end effector gravity G and the orientation coordinates of the center of gravity in the tool coordinate system are as follows: The calculation expression is as follows

[0092]

[0093]

[0094]

[0095]

[0096]

[0097] The gravity of the end effector in the tool coordinate system is:

[0098]

[0099] The gravitational torque is:

[0100] N G =L×F G

[0101] in Let be the rotation matrix from the base coordinate system to the tool coordinate system, where t is the tool coordinate system and b is the base coordinate system. Combining the tool gravity and gravitational torque into a six-dimensional vector yields the gravity compensation amount of the end effector.

[0102] f t =[F G N G ]

[0103] The gravity compensation amount f for the end effector of the master robot and the slave robot is calculated using this method. ht f et

[0104] final f m f s The expression is:

[0105] f m =f h -f ht

[0106] f s =f e -f et .

[0107] S3: Determine whether the motion state of the robotic arm is stable based on the contact force between the master robot and the slave robot. If it is unstable, adjust the parameters of the admittance model.

[0108] In this embodiment, the initial admittance model of the system is:

[0109]

[0110] Where M0 is the initial virtual mass and B0 is the initial virtual damping, both of which are six-dimensional diagonal matrices; t i i represents the current time; i represents the time step of the program's discrete execution. The command acceleration is calculated for the admittance model; the command position x(t) is obtained by integration. i The master robot and slave robot execute to obtain the actual position x. m (t i ), x s (t i ).

[0111] When f s (t i+1 )(x(t i )-x s (t i If ))>ε, then the admittance parameter is not adjusted;

[0112] If the contact force in teleoperation is characterized by admittance oscillation:

[0113] f s (t i+1 )(x(t i )-x s (t i ))≤ε

[0114] Then adjust the admittance parameter, and increment the counter k by one each time an instability is detected.

[0115] The adjustment of the admittance parameter specifically includes the following steps:

[0116] A detection threshold ε is set to detect the abnormal rebound oscillation behavior of the admittance control. When it is necessary to adjust the virtual mass in the admittance model, the rebound oscillation behavior is reduced by increasing the inertia term, M(t). i The adjustment calculation formula is as follows:

[0117]

[0118] B(t i+1 )=RM(t i+1 )

[0119] Where S p (p=0,1,...,k) is the adjustment amount of the virtual mass, β is the forgetting factor, the mass matrix is ​​restored to the initial value M0 after the oscillation disappears, and R is the damping to mass ratio.

[0120] Virtual quality adjustment amount S p The calculation formula is:

[0121] S p =diag{s1,s2,s3,s4,s5,s6},

[0122]

[0123] in T(t) represents the upper bound on the allowable increase of the admittance parameter within a time step, where the subscript j represents the degree of freedom. i ) is in (0,t i The energy dissipated by the system within a certain time period.

[0124] Based on the condition that the system is passive, the system (0,t) i The energy dissipated is greater than (t)i ,t i+1 The energy injected within a time period is expressed by the formula:

[0125]

[0126] Due to the item Establish the inequality:

[0127]

[0128] Based on the upper bound of the existence of the velocity term:

[0129]

[0130] Derive new inequalities:

[0131]

[0132] Adjustment method for deriving M from integrals:

[0133]

[0134] S p (t i )=diag{s1,s2,s3,s4,s5,s6}.

[0135] S4: The difference between the contact force of the master robot and the contact force of the slave robot is calculated and input into the admittance model. The admittance model is then used to convert the contact forces of the master robot and the slave robot into Cartesian spatial position information.

[0136] In this embodiment, after the difference of the contact force is input into the admittance model, the Cartesian space acceleration is output, and the expression is:

[0137]

[0138] Where M(t) i+1 ), B(t) i+1 These are the inertia matrix and the damping matrix, respectively. Let f be the acceleration of the robot's end effector in Cartesian space. m (t i+1 ), f s (t i+1 ) represents the contact force at the current moment.

[0139] Since the force sensor reading is the input for calculating position information, the proposed detection method can effectively reduce the impact of admittance rebound oscillation.

[0140] S5: Convert the Cartesian spatial position information into joint information based on inverse kinematics, and send it to the robotic arms of the master robot and the slave robot to make the robotic arms of the master robot and the slave robot move.

[0141] In this embodiment, the Cartesian space velocity calculation formula is:

[0142]

[0143] The joint velocity ΔT is calculated from the inverse matrix of Jacobi, and then integrated with the actual joint position of the robot to obtain the joint position of the robot. The joint position is then sent to the robotic arm servo system.

[0144] Its expression is:

[0145]

[0146]

[0147] Where Δt is the time interval of the operating cycle; Δt = t i+1 -t i J -1 This is the inverse of the Jacobian matrix; Let q(t) be the joint command velocity. i+1 ) represents the joint command position.

[0148] In summary, Embodiment 1 of this application detects oscillations by comparing the magnitudes of the contact forces at the master and slave ends. In admittance control, force is the cause of robot motion; therefore, detecting force sensor readings is an effective method for detecting rebound oscillations. Based on passive theory, while ensuring the passivity of the system, an adjustment method for the inertial term M is obtained. The difference between the contact forces is then input into the admittance model, and the contact forces are converted into Cartesian spatial position information using the admittance model. Finally, the Cartesian spatial position information is converted into joint information based on inverse kinematics and sent to the robotic arm servo system to move the master and slave robotic arms. Teleoperation drag teaching based on admittance control allows operators to drag the end effector of the master robotic arm with low impedance for teaching and collect data on robot interaction independent of the environment. It has a wide range of applications and can be used in most robotic arms on the market that are controlled by the position loop of a servo system.

[0149] Example 2

[0150] Please see Figure 4 This is a schematic diagram of the structure of the robotic arm teaching system based on bilateral control according to Embodiment 2 of this application; the specific content includes:

[0151] Acquisition module: Acquires force sensor readings from the end effectors of the main robot and the slave robot;

[0152] Processing module: Performs gravity compensation on the filtered force sensor readings to obtain the contact force between the master and slave robots;

[0153] Judgment module: Determines whether the motion state of the robotic arm is stable based on the contact force between the master robot and the slave robot. If it is unstable, the parameters of the admittance model are adjusted.

[0154] Input module: The difference between the contact force of the master robot and the contact force of the slave robot is input into the admittance model, and the contact force of the master robot and the slave robot is converted into Cartesian space position information using the admittance model;

[0155] Sending module: Based on inverse kinematics, the Cartesian spatial position information is converted into joint information and sent to the robotic arms of the master robot and the slave robot, so that the robotic arms of the master robot and the slave robot can move.

[0156] Please see Figure 5 This is a software architecture diagram of the robotic arm teaching system based on bilateral control according to Embodiment 2 of this application; the diagram describes the implementation process of the admittance teleoperation system, the teacher's operating force after gravity compensation, and the environmental contact force f. m f s As input to admittance control, it is used to determine whether the robot oscillates and to calculate position commands. Inverse kinematics is used to calculate joint motion commands and send them to the joint servos of the master and slave robots for execution. The master and slave robots execute the position commands and interact with the environment and the teacher to obtain the interaction force f. h f e Repeat this process.

[0157] Please see Figure 6 The diagram below shows the bilateral control transfer function block diagram of Embodiment 2 of this application. In admittance control, the time delay of force sensor readings has a significant impact on the interactive stability of the admittance environment. In traditional position-force bilateral control, each control loop of the master arm and slave arm is connected in series to construct a bilateral control loop. Therefore, through the total phase lag of the bilateral control loop in single-arm control, the force sensor reading provided by the tracking arm always lags behind that of the tracked arm. The time delay of the force affects the interactive stability of admittance control. To improve the impact of this time delay on stability, the master arm and slave arm are placed in a single control loop for parallel control.

[0158] In summary, Embodiment 2 of this application acquires force sensor readings from the master robot and slave robot via an acquisition module, performs filtering and gravity compensation, and determines the motion state of the robotic arm based on the obtained contact force. If the admittance oscillation occurs during teleoperation, the contact force is expressed as f. s (t i+1 )(x(t i )*x s (ti If ))>ε, then adjust the admittance parameter; if the admittance oscillation in teleoperation is expressed as f s (t i+1 )(x(t i )-x s (t i If ε ≤ ε, then the admittance parameter is not adjusted; and the contact force is converted into Cartesian spatial position information using the admittance model; the Cartesian spatial position information is converted into joint information according to inverse kinematics and sent to the robotic arm servo system to make the master and slave robotic arms move.

[0159] Example 3

[0160] Please see Figure 7 This is a schematic diagram of the device structure in Embodiment 3 of this application. The device 50 includes a processor 51 and a memory 52 coupled to the processor 51.

[0161] The memory 52 stores program instructions for implementing the above-described bilateral control-based robotic arm teaching method.

[0162] The processor 51 is used to execute program instructions stored in the memory 52 to implement teaching of the robotic arm based on bilateral control.

[0163] The processor 51 can also be referred to as a CPU (Central Processing Unit).

[0164] Processor 51 may be an integrated circuit chip with signal processing capabilities. Processor 51 may also be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), an off-the-shelf programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. A general-purpose processor may be a microprocessor or any conventional processor.

[0165] Example 4

[0166] Please see Figure 8This is a schematic diagram of the storage medium in Embodiment 4 of this application. The storage medium in this embodiment stores a program file 61 capable of implementing all the above methods. This program file 61 can be stored in the storage medium in the form of a software product, including several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute all or part of the steps of the methods of various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks, or devices such as computers, servers, mobile phones, and tablets.

[0167] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, apparatus, article, or method that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, apparatus, article, or method. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, apparatus, article, or method that includes that element.

[0168] The above description is only a preferred embodiment of this application and does not limit the patent scope of this application. Any equivalent structural or procedural changes made based on the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

[0169] Although embodiments of this application have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of this application, the scope of which is defined by the appended claims and their equivalents.

[0170] Of course, the present invention may have many other embodiments. Based on this embodiment, other embodiments obtained by those skilled in the art without any creative effort are all within the scope of protection of the present invention.

Claims

1. A robotic arm teaching method based on bilateral control, characterized in that, include: Acquire force sensor readings from the end effector of the main robot and the slave robot; Gravity compensation is applied to the force sensor readings to obtain the contact force between the master robot and the slave robot; The stability of the robotic arm's motion state is determined based on the contact force between the master robot and the slave robot. If it is unstable, the parameters of the admittance model are adjusted. The contact forces of the master robot and the slave robot are summed and then input into the admittance model. The admittance model is then used to convert the contact forces of the master robot and the slave robot into Cartesian spatial position information. The Cartesian spatial position information is converted into joint information based on inverse kinematics and sent to the robotic arms of the master robot and the slave robot, so that the robotic arms of the master robot and the slave robot can move. The step of determining whether the motion state of the robotic arm is stable based on the contact force between the master robot and the slave robot, and adjusting the parameters of the admittance model if it is unstable, specifically includes the following steps: The initial admittance model of the system is: in For the initial virtual quality, For the initial virtual damping, both are six-dimensional diagonal matrices; The current time; The time steps for discrete execution of the program; Command acceleration calculated for the admittance model; The command position is obtained through integration. The master robot and the slave robot execute to obtain the actual position. ; If admittance oscillations manifest as robot contact force during teleoperation... If so, the admittance parameter is not adjusted; If admittance oscillations manifest as robot contact force during teleoperation: Then adjust the admittance parameter, and increment the counter k by one each time an instability is detected; The adjustment of the admittance parameter specifically includes the following steps: Set detection threshold To detect abnormal rebound oscillation behavior in admittance control, when it is necessary to adjust the virtual mass in the admittance model, the rebound oscillation behavior is reduced by increasing the inertia term. The adjustment calculation formula is as follows: in The adjustment amount for virtual quality. The forgetting factor is used to restore the mass matrix to its initial value after the oscillations disappear. , R The ratio of damping to mass; Virtual quality adjustment amount The calculation formula is: in This is the upper bound on the allowable increase of the admittance parameter within a time step, where the subscript j represents the degree of freedom. In order to be in Energy dissipated by the system over a period of time; Based on the condition that the system is passive, the system The energy dissipated is greater than The energy injected within a time period is expressed by the following formula: Due to the item Establish the inequality: Based on the upper bound of the existence of the velocity term: Derive new inequalities: Adjustment method for deriving M from integrals: 。 2. The robotic arm teaching method based on bilateral control according to claim 1, characterized in that, The steps for acquiring force sensor readings from the main robot and the end effector of the robot specifically include the following steps: The force sensor readings are acquired by six-dimensional force sensors installed at the end caps of the master robot and the slave robot. These force sensor readings represent the forces and torques in six degrees of freedom in Cartesian space. The force sensor readings of the master and slave robots are respectively... and .

3. The robotic arm teaching method based on bilateral control according to claim 1, characterized in that, The step of performing gravity compensation on the force sensor readings to obtain the contact force between the master robot and the slave robot specifically includes the following steps: Calculate the gravity of the end effector of the master robot and the slave robot. and The gravity-compensated contact force between the master robot and the slave robot is obtained by subtracting the weight of the end-effector from the force sensor reading. and The calculation formula is: 。 4. The robotic arm teaching method based on bilateral control according to claim 1, characterized in that, The step of summing the contact forces of the master robot and the slave robot and inputting the sum into the admittance model, and then using the admittance model to convert the contact forces of the master robot and the slave robot into Cartesian spatial position information, specifically includes the following steps: After inputting the resultant force of the main robot's contact force and the slave robot's contact force into the admittance model, the Cartesian space acceleration is output, and the expression is: in These are virtual mass and virtual damping, respectively. Let the acceleration of the robot's end effector in Cartesian space be denoted as . The contact force at the current moment.

5. The robotic arm teaching method based on bilateral control according to claim 1, characterized in that, The step of converting the Cartesian spatial position information into joint information based on inverse kinematics and sending it to the robotic arms of the master robot and the slave robot to cause the robotic arms of the master robot and the slave robot to move specifically includes the following steps: The Cartesian formula for calculating spatial velocity is: Will Multiplying the inverse of Jacobi Obtain joint velocity , Multiply by time interval Then compare it with the joint position at the previous moment. Accumulate to obtain the current joint position. The joint position is sent to the robotic arm servo system; Its expression is: ， ， in This refers to the time interval of the running cycle; , This is the inverse of the Jacobian matrix; For joint velocity, This indicates the joint position.

6. A system for teaching a robotic arm based on bilateral control according to claim 1, characterized in that, The system includes: Acquisition module: Acquires force sensor readings from the end effectors of the main robot and the slave robot; Processing module: Performs gravity compensation on the force sensor readings to obtain the contact force between the master robot and the slave robot; Judgment module: Determines whether the motion state of the robotic arm is stable based on the contact force between the master robot and the slave robot. If it is unstable, the parameters of the admittance model are adjusted. Input module: The contact force of the master robot and the contact force of the slave robot are summed and then input into the admittance model. The admittance model is used to convert the contact force of the master robot and the slave robot into Cartesian spatial position information. Sending module: Converts the Cartesian spatial position information into joint information based on inverse kinematics and sends it to the robotic arms of the master robot and the slave robot, causing the robotic arms of the master robot and the slave robot to move.

7. A device, characterized in that, The device includes a processor and a memory coupled to the processor, wherein the memory stores program instructions for implementing the bilateral control-based robotic arm teaching method according to any one of claims 1-5; the processor is used to execute the program instructions stored in the memory to implement bilateral control-based robotic arm teaching.

8. A storage medium, characterized in that, The device stores processor-executable program instructions for performing the bilateral control-based robotic arm teaching method according to any one of claims 1-5.

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