A Cartesian impedance control method for robots with controlled energy and power

Abstract

The present invention provides a Cartesian impedance control method for a robot with controlled energy and power. In this method, the contact between the robot and the environment is considered, and a Cartesian impedance controller is constructed in combination with a "mass-spring-damper" impedance model; a time-varying stiffness factor is designed to limit the robot's kinetic energy, and a time-varying damping factor is designed to limit the power transmitted by the robot; an energy tank is designed to associate task power, and the energy discharge rate in the energy tank is adjusted by a power scaling factor; the time-varying stiffness factor and the time-varying damping factor are introduced into the impedance controller, and the control torque of each joint of the robot is output; the control torque of each joint of the robot is input into the inner loop of the robot torque control to complete the robot's motion control. The present invention realizes the energy and power control of the robot in impedance mode, which can effectively avoid safety hazards caused by accidental energy release or power overload of the robot, thereby ensuring the safety and stability of the physical human-machine interaction process.

Description

Technical Field

[0001] The present application relates to the field of robot control, and in particular to a robot Cartesian impedance control method with controlled energy and power. Background Art

[0002] As robotics applications continue to expand, more and more tasks require dynamic interaction between robots and their environment. Energy exchange is the primary form of interaction between robots and their environment. This means that robots can actively apply forces to their environment to accomplish tasks like flexible assembly and surface polishing, while the environment can also actively apply forces to the robot to accomplish tasks like compliant interaction and drag-based teaching. Methods such as force-position hybrid control, impedance control, and admittance control are widely used in these scenarios to achieve stable robot-environment interaction.

[0003] However, existing control methods generally focus on constant force control during continuous contact between the robot and the workpiece, ignoring safety. This is especially true when the robot's end-of-line tool suddenly loses contact with the workpiece. The physical impact between the robot and the environment can cause irreversible damage. This impact can not only damage the robot and the workpiece, but can also cause tool failure or reduced work quality. More importantly, in physical human-machine interaction scenarios, sudden energy release can pose a safety threat to the operator. Therefore, online monitoring and limiting the energy and power the controller is allowed to inject into the robot are key to achieving safe force control tasks. Summary of the Invention

[0004] In order to overcome at least one of the shortcomings of the prior art, the present application proposes an energy and power limited robot Cartesian impedance control method to limit the energy and power generated by the robot's own system when performing Cartesian space impedance tasks, thereby ensuring the safety of the interactive environment and humans.

[0005] In a first aspect, the present application provides a method for controlling Cartesian impedance of a robot with controlled energy and power, the method comprising:

[0006] Step S1, constructing a Cartesian impedance controller for the robot according to an impedance model, wherein the impedance model describes the contact relationship between the robot and the environment;

[0007] Step S2, obtaining a time-varying stiffness factor that limits the total energy of the robot and a time-varying damping factor that limits the total power of the robot;

[0008] Step S3, obtaining an energy tank associated with the robot's task power and a power scaling factor that limits the release rate of energy in the energy tank;

[0009] Step S4, correcting the time-varying stiffness factor according to the energy tank characteristics, and using the obtained time-varying stiffness factor and time-varying damping factor to correct the stiffness characteristic matrix and the damping characteristic matrix in the joint space impedance controller, thereby obtaining an energy- and power-controlled joint space impedance controller, and outputting the control torque of each joint of the robot, wherein the joint space impedance controller is obtained by mapping the robot Cartesian impedance controller into the joint space;

[0010] In step S5, the obtained control torque of each joint of the robot is input into the inner loop of the robot torque control to complete the motion control of the robot.

[0011] In conjunction with the optional implementation manner of the first aspect, step S1 specifically includes:

[0012] S11, establishing a dynamic model of the robot according to the robot performing the force control task:

[0013]

[0014] in, is the Cartesian space impedance control force of the robot system; The disturbance force generated by the external environment on the robot; They represent the inertia matrix, Coriolis matrix and gravity term in Cartesian space respectively; Represent the actual position, velocity and acceleration of the robot end respectively;

[0015] S12, the impedance model The corresponding second-order differential equation is expressed as:

[0016]

[0017] in, denote the desired inertia, damping and stiffness characteristic matrices respectively; They represent the actual and expected position deviation, velocity deviation, and acceleration deviation of the robot end, respectively, and are specifically expressed as:

[0018]

[0019] in, They represent the desired position, velocity, and acceleration of the robot end respectively;

[0020] S13, using the inertia matrix of the Cartesian space as the desired inertia characteristic matrix, and obtaining the robot Cartesian impedance controller according to the dynamic model and the impedance model. The expression of the robot Cartesian impedance controller is:

[0021] .

[0022] In conjunction with the optional implementation manner of the first aspect, step S2 specifically includes:

[0023] S21, using the Jacobian matrix to map the Cartesian impedance controller to the joint space to obtain a joint space impedance controller, which is specifically expressed as:

[0024]

[0025] in, is the joint space impedance control force; is the joint space gravity term; is the Jacobian matrix of the robot;

[0026] According to the time-varying stiffness factor, the modified stiffness characteristic matrix is ​​obtained , the modified stiffness characteristic matrix Expressed as:

[0027]

[0028]

[0029] in, represents the time-varying stiffness factor; and represent the kinetic energy and elastic potential energy of the robot respectively; represents the total energy of the robot's kinetic energy and elastic potential energy; Indicates the maximum energy allowed to be generated by the robot system;

[0030] According to the time-varying damping factor, the modified damping characteristic matrix is ​​obtained , the modified damping characteristic matrix The expression is:

[0031]

[0032]

[0033] in, represents the time-varying damping factor; Indicates the total power generated by the robot during movement; Indicates the maximum power allowed to be transmitted by the robot system.

[0034] In conjunction with the optional implementation manner of the first aspect, step S3 specifically includes:

[0035] S31, the energy tank The first derivative of Equal to robot mission power , specifically expressed as:

[0036]

[0037] in, It represents the power generated by the robot terminal when performing tasks; and They represent the on / off factors of the energy tank, which are used to control the on / off of energy exchange between the energy tank and the impedance controller;

[0038] S32, the lower limit of energy that can be stored in the energy tank and the corresponding opening and closing conditions:

[0039]

[0040] in, Indicates the lower limit of energy in the energy tank;

[0041] S33, the upper limit of energy that can be stored in the energy tank and the corresponding opening and closing conditions:

[0042]

[0043] in, Indicates the energy limit in the energy tank;

[0044] S34, the power scaling factor , the expression is:

[0045]

[0046] in, Indicates the maximum allowable extraction power of the energy tank;

[0047] According to the power scaling factor and the upper limit of energy that can be stored in the energy tank and the corresponding opening and closing conditions, the modified energy tank is obtained. , the modified energy tank Expressed as:

[0048] .

[0049] In conjunction with the optional implementation manner of the first aspect, step S4 specifically includes:

[0050] S41, when it is impossible to extract energy from the energy tank to maintain the passivity of the time-varying impedance controller, the time-varying stiffness factor Corrected to:

[0051]

[0052] in, represents the modified time-varying stiffness factor;

[0053] S42, according to the revised energy tank , the modified time-varying stiffness factor and time-varying damping factor , construct the energy and power controlled joint space impedance controller, the expression is:

[0054] .

[0055] Compared with the prior art, this application has the following beneficial effects:

[0056] This paper proposes a Cartesian impedance control method for robots, focusing on energy and power management. By scaling stiffness and injecting damping, the robot's energy and power can be adjusted in real time during task execution. The introduction of an energy tank ensures the system remains passive, thus ensuring safety and stability during task execution. This method is widely applicable to force-controlled assembly tasks involving human-machine interaction, offering a simple process and easy engineering implementation. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following is a brief introduction to the drawings required for use in the embodiments. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without creative work.

[0058] Figure 1 The energy and power controlled joint space impedance controller provided by the embodiment of the present application;

[0059] Figure 2 A schematic flow chart of a method for controlling Cartesian impedance of a robot with controlled energy and power provided in an embodiment of the present application;

[0060] Figure 3 A comparison chart of energy changes provided in the embodiments of the present application;

[0061] Figure 4 A power change comparison chart provided in an embodiment of the present application;

[0062] Figure 5 A diagram showing the relationship between the power scaling factor and the robot task power provided in an embodiment of the present application.

[0063] Icons: 11-second energy change curve; 12-first energy change curve; 13-second power curve; 14-first power curve; 15-parameter curve; 16-task power curve. DETAILED DESCRIPTION

[0064] To make the objectives, technical solutions, and advantages of the embodiments of the present application more clear, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Generally, the components of the embodiments of the present application described and shown in the drawings herein can be arranged and designed in various different configurations.

[0065] Therefore, the following detailed description of the embodiments of the present application provided in the accompanying drawings is not intended to limit the scope of the present application for protection, but merely represents selected embodiments of the present application. All other embodiments obtained by persons of ordinary skill in the art based on the embodiments in the present application without creative work are within the scope of protection of the present application.

[0066] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings.

[0067] In the description of this application, it should be noted that the terms "comprises," "includes," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, article, or apparatus comprising a series of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article, or apparatus comprising the element.

[0068] Based on the above statements, the present invention is further described in detail below in conjunction with the accompanying drawings and examples. It should be understood that these examples are only intended to illustrate the present invention and are not intended to limit the scope of the present invention. After reading this invention, modifications of various equivalent forms of the present invention by those skilled in the art all fall within the scope defined by the appended claims.

[0069] This embodiment provides a method for controlling the Cartesian impedance of a robot with controlled energy and power. Figure 1As shown, this method considers the contact between the robot and the environment and constructs a Cartesian impedance controller in combination with the "mass-spring-damper" impedance model; designs a time-varying stiffness factor to limit the robot's kinetic energy, and designs a time-varying damping factor to limit the power transmitted by the robot; designs an energy tank-associated task power, and adjusts the energy discharge rate in the energy tank through a power scaling factor; introduces the time-varying stiffness factor and the time-varying damping factor into the impedance controller, and outputs the control torque of each joint of the robot; inputs the control torque of each joint of the robot into the inner loop of the robot torque control to complete the robot's motion control. The present invention realizes the energy and power control of the robot in the impedance mode, which can effectively avoid the safety hazards caused by accidental energy release or power overload of the robot, thereby ensuring the safety and stability of the physical human-machine interaction process.

[0070] To make the solution provided by this embodiment clearer, the following Figure 2 Each step of the method is described in detail. However, it should be understood that the operations in the flowchart can be implemented in a non-sequential order, and steps that have no logical contextual relationship can be reversed or implemented simultaneously. In addition, those skilled in the art can add one or more other operations to the flowchart, or remove one or more operations from the flowchart, guided by the content of this application. Figure 2 As shown, the method includes:

[0071] Step S1: construct a Cartesian impedance controller for the robot based on the impedance model.

[0072] The impedance model describes the contact relationship between the robot and the environment. Since the robot is in contact with the environment, a "mass-spring-damper" impedance model is combined to construct a Cartesian impedance controller for the robot. In a specific embodiment, the Newton-Euler iteration method is used to establish the dynamic model of the robot based on the robot performing the force control task. The specific expression is:

[0073] (1)

[0074] in, is the robot's Cartesian space impedance control force; The disturbance force generated by the external environment on the robot; They represent the inertia matrix, Coriolis matrix and gravity term in Cartesian space respectively; Represent the actual position, velocity and acceleration of the robot end respectively.

[0075] Based on the dynamic model in the above embodiment, it should be noted that robot impedance control does not directly control force or position. Instead, it maintains a dynamic relationship between force and position similar to mechanical impedance and, by varying the target impedance parameters, enables the robot to exhibit compliant motion characteristics. Therefore, a "mass-spring-damper" impedance model can be used to describe the dynamic contact relationship between the robot and its environment. Its mathematical model can be expressed as the following second-order differential equation:

[0076] (2)

[0077] in, denote the desired inertia, damping and stiffness characteristic matrices respectively; They represent the actual and expected position deviation, velocity deviation, and acceleration deviation of the robot end, respectively, and can be expressed as:

[0078] (3)

[0079] in, They represent the desired position, velocity, and acceleration of the robot end, respectively.

[0080] Next, combine the above equations (1) and (2) and design , and then construct the robot Cartesian impedance controller, the specific expression is:

[0081] (4)

[0082] Based on the robot Cartesian impedance controller obtained in step S1 above, continue to refer to Figure 2 The energy and power controlled robot Cartesian impedance control method provided in this embodiment further includes:

[0083] Step S2: Obtain a time-varying stiffness factor that limits the total energy of the robot and a time-varying damping factor that limits the total power of the robot.

[0084] It should be understood that the Jacobian matrix can describe the mapping relationship between the robot end effector velocity and the joint velocity. In force mapping, the transpose or pseudo-inverse of the Jacobian matrix is ​​usually used to convert the end operation force and torque into joint torque. Therefore, in the specific implementation of step S2, the Cartesian impedance controller obtained in the above-mentioned embodiment can be mapped to the joint space using the Jacobian matrix, which can be specifically expressed as:

[0085] (5)

[0086] in, is the joint space impedance control force; is the joint space gravity term; is the Jacobian matrix of the robot;

[0087] In addition, it should be understood that when the robot works in impedance mode, the total energy of the robot system includes the kinetic energy generated by the movement and elastic potential energy generated by interaction with the environment Among them, the robot's kinetic energy is positively correlated with the robot's movement speed, and the robot's elastic potential energy is positively correlated with the stiffness matrix Without changing the robot's desired motion, the robot can be scaled Control the total energy of the robot. Therefore, this embodiment provides a time-varying stiffness factor that limits the total energy of the robot, which can be specifically expressed as:

[0088] (6)

[0089] in, represents the time-varying stiffness factor; represents the total energy of the robot's kinetic energy and elastic potential energy; Represents the maximum energy allowed to be generated by the robot. Using this time-varying stiffness factor, the modified stiffness characteristic matrix can be obtained: , which can be expressed as:

[0090] (7)

[0091] In addition, when the robot is working in impedance mode, the controller can respond to external forces by adjusting the stiffness, damping and inertia parameters of the robot. For a constant stiffness matrix, increasing the damping The system's dissipation capacity can be improved, thereby controlling the total power transmitted by the robot to the environment. Therefore, this embodiment also provides a time-varying damping factor that limits the robot's total power, which can be specifically expressed as:

[0092] (8)

[0093] in, represents the time-varying damping factor; Indicates the total power generated by the robot during movement; Represents the maximum power allowed to be transmitted by the robot system. Using this time-varying damping factor, the modified damping characteristic matrix can be obtained , which can be expressed as:

[0094] (9)

[0095] Based on the variable stiffness factor and time-varying damping factor obtained in step S2 above, continue to refer to Figure 2 The energy and power controlled robot Cartesian impedance control method provided by this embodiment further includes:

[0096] Step S3: obtaining an energy tank associated with the robot's task power and a power scaling factor that limits the release rate of energy in the energy tank.

[0097] It should be noted that the time-varying impedance controller manipulates the system energy, which results in the uncertainty of the derivative sign of its energy storage function and the inability to guarantee the passivity of the system. Therefore, a virtual energy tank is designed in the robot controller. Storage container, used to store the energy of the system and supply or absorb energy when needed to maintain the overall energy balance of the system. The first derivative of Equal to the robot's mission power , which can be specifically expressed as:

[0098] (10)

[0099] in, It represents the power generated by the robot terminal when performing tasks; and They represent the on / off factors of the energy tank, which are used to control the on / off of energy exchange between the energy tank and the impedance controller.

[0100] In this embodiment, in order to prevent the system from extracting energy from the energy tank without limit, the lower limit of the energy that can be stored in the energy tank and the corresponding opening and closing conditions are also provided:

[0101] (11)

[0102] in, Indicates the lower limit of energy in the energy tank;

[0103] In addition, to prevent the energy stored in the energy tank from being too high, the upper limit of the energy that can be stored in the energy tank and the corresponding opening and closing conditions are also provided:

[0104] (12)

[0105] in, Indicates the upper limit of energy that can be stored in the energy tank;

[0106] From the formula (10) in the above embodiment, it can be seen that the injection / discharge rate of the energy tank is related to the mission power A release rate that is too high may cause the energy in the system to increase rapidly, resulting in high acceleration behavior of the robot in a short period of time, which is still accompanied by the risk of system instability. Therefore, this embodiment also provides a power scaling factor , which can be specifically expressed as:

[0107] (13)

[0108] in, Indicates the maximum allowable extraction power of the energy tank. Using the power scaling factor , revised energy tank It can be expressed as:

[0109] (14)

[0110] The energy tank obtained in step S3 above is used to modify the time-varying stiffness factor. Figure 2 The energy and power controlled robot Cartesian impedance control method provided in this embodiment further includes:

[0111] Step S4, correct the time-varying stiffness factor according to the characteristics of the energy tank, and use the obtained time-varying stiffness factor and time-varying damping factor to correct the stiffness characteristic matrix and damping characteristic matrix in the joint space impedance controller to obtain an energy and power controlled joint space impedance controller, and output the control torque of each joint of the robot.

[0112] The joint space impedance controller is obtained by mapping the robot Cartesian impedance controller to the joint space. In the specific implementation of step S4, when the system cannot extract energy from the energy tank to maintain the passivity of the time-varying impedance controller, the equation (4) is obtained as Needs further revision:

[0113] (15)

[0114] in, represents the modified time-varying stiffness factor. Finally, the equation (15) obtained is And formula (8) Substitute into formula (5) to obtain the energy and power controlled joint space impedance controller, which is expressed as:

[0115] (16)

[0116] The control torque of each joint of the robot can be obtained by using the joint space impedance controller with controlled energy and power. Figure 2 The energy and power controlled robot Cartesian impedance control method provided in this embodiment further includes:

[0117] In step S5, the obtained control torque of each joint of the robot is input into the inner loop of the robot torque control to complete the motion control of the robot.

[0118] For the above embodiment, this embodiment is also verified in an actual simulation environment. According to the above embodiment, a robot simulation model is established in the Matlab / SimScape simulation environment. The simulation parameters are set as follows: initial Cartesian space stiffness , initial Cartesian space damping , the maximum energy allowed to be generated by the robot system , the maximum power allowed to be transmitted by the robot system , the maximum allowable extraction power of the energy tank , the initial energy of the energy tank , the energy limit of the energy tank , the lower limit of energy tank The simulation process simulates the movement of the end effector of the seven-degree-of-freedom robot from the force contact state to the free state in the impedance mode.

[0119] like Figure 3 As shown, the first energy variation curve 12 shows the energy variation of the robot under the energy and power controlled impedance controller, while the second energy variation curve 11 shows the energy variation of the robot under the conventional impedance controller. As can be seen from the comparison, the Cartesian impedance control method for the energy and power controlled robot provided in this embodiment can ensure that the total energy of the robot system does not exceed the preset energy threshold.

[0120] like Figure 4 As shown, the first power curve 14 illustrates the power variation of the robot under the energy and power controlled impedance controller, while the second power curve 13 illustrates the power variation of the robot under the conventional impedance controller. As can be seen from the comparison, the Cartesian impedance control method for an energy and power controlled robot provided in this embodiment can ensure that the power transmitted to the environment by the robot system does not exceed a preset power threshold.

[0121] like Figure 5 As shown, the figure shows the power scaling factor The relationship between the parameter curve 15 and the task power curve 16 of the robot task power. It can be seen that the rate of release of the energy tank is scaled by the power scaling factor Limit within the specified threshold.

[0122] Finally, it should be noted that the above-described embodiments of the present invention are merely examples for the purpose of clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Those skilled in the art will appreciate that other variations or modifications may be made based on the above description. It is not necessary and impossible to enumerate all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention are intended to be included within the scope of protection of the claims of the present invention.

[0123] It should be understood that the devices and methods disclosed in the above embodiments may also be implemented in other ways. The device embodiments described above are merely illustrative. For example, the flowcharts and block diagrams in the accompanying drawings show the possible architectures, functions, and operations of the devices, methods, and computer program products according to multiple embodiments of the present application. In this regard, each box in the flowchart or block diagram may represent a module, a program segment, or a portion of code, which contains one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions marked in the box may also occur in an order different from that marked in the accompanying drawings. For example, two consecutive boxes may actually be executed substantially in parallel, or they may sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or flowchart, and the combination of boxes in the block diagram and / or flowchart, may be implemented using a dedicated hardware-based system that performs a specified function or action, or may be implemented using a combination of dedicated hardware and computer instructions.

[0124] The above descriptions are merely examples of various embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any modifications or substitutions that can be readily conceived by a person skilled in the art within the technical scope disclosed in the present application should be included within the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A method for controlling Cartesian impedance of a robot with controlled energy and power, characterized in that: The method comprises: Step S1, constructing a Cartesian impedance controller for the robot according to an impedance model, wherein the impedance model describes the contact relationship between the robot and the environment; Step S2, obtaining a time-varying stiffness factor that limits the total energy of the robot and a time-varying damping factor that limits the total power of the robot. Step S2 specifically includes: S21, using the Jacobian matrix to map the Cartesian impedance controller to the joint space to obtain a joint space impedance controller, which is specifically expressed as: in, is the joint space impedance control force; is the joint space gravity term; is the Jacobian matrix of the robot; According to the time-varying stiffness factor, the modified stiffness characteristic matrix is ​​obtained , the modified stiffness characteristic matrix Expressed as: in, represents the time-varying stiffness factor; and represent the kinetic energy and elastic potential energy of the robot respectively; represents the total energy of the robot's kinetic energy and elastic potential energy; Indicates the maximum energy allowed to be generated by the robot system; According to the time-varying damping factor, the modified damping characteristic matrix is ​​obtained , the modified damping characteristic matrix The expression is: in, represents the time-varying damping factor; Indicates the total power generated by the robot during movement; Indicates the maximum power allowed to be delivered by the robot system; Step S3, obtaining an energy tank associated with the robot's task power and a power scaling factor that limits the release rate of energy in the energy tank, specifically comprising: S31, the energy tank The first derivative of Equal to robot mission power , specifically expressed as: in, It represents the power generated by the robot terminal when performing tasks; and They represent the on / off factors of the energy tank, which are used to control the on / off of energy exchange between the energy tank and the impedance controller; S32, the lower limit of energy that can be stored in the energy tank and the corresponding opening and closing conditions: in, Indicates the lower limit of energy in the energy tank; S33, the upper limit of energy that can be stored in the energy tank and the corresponding opening and closing conditions: in, Indicates the energy limit in the energy tank; S34, the power scaling factor , the expression is: in, Indicates the maximum allowable extraction power of the energy tank; According to the power scaling factor and the upper limit of energy that can be stored in the energy tank and the corresponding opening and closing conditions, the modified energy tank is obtained. , the modified energy tank Expressed as: ； Step S4, correcting the time-varying stiffness factor according to the energy tank characteristics, and using the obtained time-varying stiffness factor and time-varying damping factor to correct the stiffness characteristic matrix and the damping characteristic matrix in the joint space impedance controller, thereby obtaining an energy- and power-controlled joint space impedance controller, and outputting the control torque of each joint of the robot, wherein the joint space impedance controller is obtained by mapping the robot Cartesian impedance controller into the joint space; In step S5, the obtained control torque of each joint of the robot is input into the inner loop of the robot torque control to complete the motion control of the robot.

2. The method according to claim 1, characterized in that The step S1 specifically includes: S11, establishing a dynamic model of the robot according to the robot performing the force control task: in, is the Cartesian space impedance control force of the robot system; The disturbance force generated by the external environment on the robot; They represent the inertia matrix, Coriolis matrix and gravity term in Cartesian space respectively; Represent the actual position, velocity and acceleration of the robot end respectively; S12, the impedance model The corresponding second-order differential equation is expressed as: in, denote the desired inertia, damping and stiffness characteristic matrices respectively; They represent the actual and expected position deviation, velocity deviation, and acceleration deviation of the robot end, respectively, and are specifically expressed as: in, They represent the desired position, velocity, and acceleration of the robot end respectively; S13, using the inertia matrix of the Cartesian space as the desired inertia characteristic matrix, and obtaining the robot Cartesian impedance controller according to the dynamic model and the impedance model. The expression of the robot Cartesian impedance controller is: 。 3. The method according to claim 1, characterized in that The step S4 specifically includes: S41, when it is impossible to extract energy from the energy tank to maintain the passivity of the time-varying impedance controller, the time-varying stiffness factor Corrected to: in, represents the modified time-varying stiffness factor, represents the total energy of the robot's kinetic energy and elastic potential energy, Indicates the maximum energy the robot is allowed to generate. and represent the kinetic energy and elastic potential energy of the robot respectively; S42, according to the revised energy tank , the modified time-varying stiffness factor and time-varying damping factor , construct the energy and power controlled joint space impedance controller, the expression is: 。

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