Adaptive robust admittance control method based on optimal impedance selection

Abstract

The application discloses an adaptive robust admittance control method based on optimal impedance selection, wherein step 1 is to establish a five-bar parallel robot dynamics model; step 2 is to design a composite learning strategy to estimate environmental impedance; step 3 is to design optimal stiffness and damping expected by the robot based on the estimated environmental impedance; and step 4 is to design adaptive robust admittance control based on time delay estimation to make the robot track the admittance trajectory with set performance. The control method has the beneficial effects that the accuracy of existing robots in impedance selection is enhanced, the convergence of impedance errors is realized, the stability of adaptive robust admittance control is ensured, and the human-machine interaction is soft, safe and reliable. The application can be used for soft control of robots.

Description

Technical Field

[0001] This invention relates to a robot control method, and more particularly to an adaptive robust admittance control method. Background Technology

[0002] Currently, force / position hybrid control and impedance / admittance control, as powerful active compliance control methods, have been widely applied in fields such as assembly, grinding, polishing, and human-machine interaction. The performance of robot-environment interaction via impedance / admittance control largely depends on environmental dynamics and the desired impedance, highlighting the importance of selecting the desired impedance. The desired stiffness is designed to be proportional to the inverse of the environmental stiffness; however, selecting the desired impedance requires knowledge of the environmental impedance, which is often unknown in many application scenarios. In robot dynamics models, uncertainties and disturbances exist in robot modeling, and impedance errors are sensitive to uncertainties defined as follows. The convergence of impedance errors is crucial for the stability of impedance control and the successful implementation of compliance, safety, and reliability in human-machine interaction.

[0003] A robot admittance control system based on an adaptive optimization method is disclosed in the prior art, with Chinese patent application number CN2018101272389 and publication date of 2018-06-29. This control system constructs a state-space force observer based on the generalized momentum method and the dynamic equations of the robotic arm. Using an adaptive optimal control method, it obtains an optimal admittance model adapted to external torque and inputs the observed torque into the admittance model to obtain a corrected reference trajectory adapted to the external torque. However, this control method cannot obtain the optimal desired impedance, cannot provide good robustness to uncertainties and disturbances, and cannot overcome the shortcomings of existing robot impedance control. It cannot achieve optimal impedance selection, stability of impedance control, or compliant, safe, and reliable human-machine interaction. Summary of the Invention

[0004] The purpose of this invention is to provide an adaptive robust admittance control method for parallel robots based on optimal impedance selection, which enhances the accuracy of impedance selection in existing robots, achieves impedance error convergence, and ensures the stability of adaptive robust admittance control and compliant, safe, and reliable human-machine interaction.

[0005] To achieve the above objectives, this invention provides an adaptive robust admittance control method for parallel robots based on optimal impedance selection, comprising the following steps:

[0006] Step 1: Establish a model of the five-bar parallel robot and its interactive forces;

[0007] Step 2: Design a composite learning strategy and estimate environmental impedance;

[0008] Step 3: Based on the estimated environmental impedance, design the optimal stiffness and damping of the robot.

[0009] Step 4: Design an adaptive robust admittance control based on time delay estimation to enable the robot to track the admittance trajectory with the set performance.

[0010] Compared with the prior art, the beneficial effects of the present invention are as follows: a composite learning strategy is constructed to estimate environmental impedance, an optimization algorithm is designed to obtain the desired optimal stiffness and damping of the robot, an adaptive robust admittance control based on time delay estimation is designed, the accuracy of the existing robot in impedance selection is enhanced, the convergence of environmental impedance is achieved, and the stability of the adaptive robust admittance control and compliant, safe and reliable human-machine interaction are guaranteed. The present invention can be used for compliant control of robots.

[0011] As a further improvement of the present invention, the dynamic model of the five-bar parallel robot in step 1 is as follows:

[0012] (1)

[0013] in: Location of human-computer interaction points Velocity of human-computer interaction point Acceleration at the human-computer interaction point; It is the inertia matrix; It is the matrix of Coriolis force and centrifugal force; It is the gravity vector. For friction, To control the input, Human-computer interaction force; rewrite the robot dynamics model as follows:

[0014] (2)

[0015] in It is a constant matrix; For the uncertain term defined as follows:

[0016]

[0017] The external resistance model is as follows:

[0018] (3)

[0019] in Indicates environmental stiffness. Representing environmental damping; based on the interaction force model, the desired interaction force model can be expressed as:

[0020] (4)

[0021] in Represents the expected trajectory. To represent the desired interaction force and improve the compliance of the robot's interaction with the environment, the following dynamic impedance model is established:

[0022] (5)

[0023] in This indicates the robot's trajectory tracking error; Let be diagonal positive definite matrices, and let represent the desired inertia matrix, stiffness matrix, and damping matrix, respectively.

[0024] As a further improvement of the present invention, in step 2, the expression for the human-computer interaction force is:

[0025] (6)

[0026] in: It is a regression vector; It is an unknown vector. ; yes The estimated value; estimator for The estimation error is ;in , Force estimation error The combined error of prediction and error constitutes a composite error, defined as:

[0027] (7)

[0028] (8)

[0029] The prediction error is designed as ;based on and prediction error Constructing a composite learning strategy:

[0030] (9)

[0031] in , j=1,2 is the projection function

[0032] As a further improvement of the present invention, in step 3, based on the external resistance model and the desired human-computer interaction force, the dynamic equation is designed as follows:

[0033] (10)

[0034] in:

[0035] (11)

[0036] (12)

[0037] The optimal stiffness in robot interaction is obtained by constructing an optimization problem:

[0038]

[0039] (13)

[0040] Where i = 1, 2, ..., n; cost function ; Since the weights are positive, according to the minimum principle, the optimal solution is:

[0041] (14)

[0042] in It is a positive constant, and the optimal stiffness of the robot is... = The optimal damping is ;

[0043] in Indicates the damping ratio; the desired design damping is:

[0044] (15)

[0045] Estimated stiffness and damping , They will converge to the optimal stiffness. and damping .

[0046] As a further improvement of the present invention, in step 4, the admittance trajectory is:

[0047] (16)

[0048] Among them: dynamic output satisfy Admittance trajectory tracking error Its filtering error ;

[0049] in It is a positive definite diagonal matrix; when Approaching zero, the desired impedance dynamic characteristics are obtained; the control input is designed as follows:

[0050] (17)

[0051] Among them, control gain It is a positive definite diagonal matrix. The adaptive robust control term to be designed Indicates at time t The value, an estimate based on time delay. Substituting (17) into (2) yields:

[0052] (18)

[0053] Among them, the estimation error And estimation error It is bounded, that is... ,here It is an unknown constant; in order to improve control robustness, the control term Designed as follows:

[0054] (19)

[0055] in It is a saturation function, and It is a small positive parameter. In (19), Updated to:

[0056] (20)

[0057] Where the projection function ensure ,and The upper bound is defined; an adaptive robust admittance controller is designed for the robot under consideration using dynamics; the tracking error of the admittance trajectory is considered. Ultimately, it can be determined by limited. Attached image description:

[0058] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0059] Figure 1 This is a flowchart illustrating the implementation steps of the present invention.

[0060] Figure 2 This is a schematic diagram of the five-bar parallel machine structure of the present invention.

[0061] Figure 3 This is a diagram showing the estimated environmental stiffness values ​​for this invention.

[0062] Figure 4 This is a diagram showing the estimated environmental damping values ​​for this invention.

[0063] Figure 5 This is a diagram showing the environmental stiffness estimation error of the present invention.

[0064] Figure 6 This is a diagram showing the environmental damping estimation error of the present invention.

[0065] Figure 7 This is the interactive force error diagram of the present invention.

[0066] Figure 8 This is a trajectory tracking error diagram of the present invention. Detailed Implementation

[0067] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0068] like Figure 1-8 The adaptive robust admittance control method based on optimal impedance selection, as shown, includes the following steps:

[0069] Step 1, establish the dynamic model of the five-bar parallel robot as follows:

[0070] (1)

[0071] in: Location of human-computer interaction points Velocity of human-computer interaction point Acceleration at the human-computer interaction point; It is the inertia matrix; It is the matrix of Coriolis force and centrifugal force; It is the gravity vector. For friction, To control the input, Human-computer interaction force; rewrite the robot dynamics model as follows:

[0072] (2)

[0073] in It is a constant matrix; and contains uncertainties defined as follows:

[0074]

[0075] The external resistance model is as follows:

[0076] (3)

[0077] Among them, China Indicates environmental stiffness. Representing environmental damping; based on the interaction force model, the desired interaction force model can be expressed as:

[0078] (4)

[0079] in Indicates corresponding to To improve the robot's compliance with its environment and determine its desired trajectory, a dynamic impedance model is established as follows:

[0080] (5)

[0081] in This indicates the robot's trajectory tracking error; Let be diagonal positive definite matrices, and let represent the desired inertia matrix, stiffness matrix, and damping matrix, respectively.

[0082] Step 2, the expression for human-computer interaction force is:

[0083] (6)

[0084] in: It is a regression vector; It is an unknown vector. ; like Figure 3 and Figure 4 As shown, yes The estimated value; estimator for The estimation error is ;in , Force estimation error The combined error of prediction and error constitutes a composite error, defined as:

[0085] (7)

[0086] (8)

[0087] The prediction error is designed as ;based on and prediction error Constructing a composite learning strategy:

[0088] (9)

[0089] in , j=1,2 is the projection function

[0090] Step 3, based on the external resistance model and the desired human-machine interaction force, design the dynamic equation as follows:

[0091] (10)

[0092] in:

[0093] (11)

[0094] (12)

[0095] The optimal stiffness in robot interaction is obtained by constructing an optimization problem:

[0096]

[0097] (13)

[0098] Where i = 1, 2, ..., n; cost function ; Since the weights are positive, according to the minimum principle, the optimal solution is:

[0099] (14)

[0100] in It is a positive constant, and the optimal stiffness of the robot is... = The optimal damping is ;

[0101] in Indicates the damping ratio; the desired design damping is:

[0102] (15)

[0103] like Figure 5 and Figure 6 As shown, the estimated stiffness and damping , They will converge to the optimal stiffness. and damping .

[0104] Step 4, the admittance trajectory is:

[0105] (16)

[0106] Among them: dynamic output satisfy Admittance trajectory tracking error Its filtering error ;

[0107] in It is a positive definite diagonal matrix; when Approaching zero, the desired impedance dynamic characteristics are obtained; the control input is designed as follows:

[0108] (17)

[0109] Among them, control gain It is a positive definite diagonal matrix. The adaptive robust control term to be designed Indicates at time t The value, an estimate based on time delay. Substituting (17) into (2) yields:

[0110] (18)

[0111] Where the estimation error And estimation error It is bounded, that is... ;here It is an unknown constant; in order to improve control robustness, the control term Designed as follows:

[0112] (19)

[0113] in It is a saturation function, and It is a small positive parameter; in (19), Updated to:

[0114] (20)

[0115] Where the projection function ensure ,and The upper bound is defined; an adaptive robust admittance controller is designed for the robot under consideration using dynamics; the tracking error of the admittance trajectory is considered. Ultimately, it can be determined by limited.

[0116] Step 5: Perform simulation using MATLAB and find that... Figure 7 As shown, the force error in human-computer interaction eventually converges to a small neighborhood of 0, which is very close to the actual force; it was found that... Figure 8 As shown, under the designed robust adaptive admittance control, the tracking error of the robot's admittance trajectory eventually converges to a small neighborhood of 0, achieving a satisfactory control effect.

[0117] This invention is not limited to the above embodiments. Based on the technical solutions disclosed herein, those skilled in the art can make some substitutions and modifications to some of the technical features without creative effort, and all such substitutions and modifications are within the protection scope of this invention.

Claims

1. An adaptive robust admittance control method for parallel robots based on optimal impedance selection, characterized in that: Includes the following steps: Step 1: Establish a model of the five-bar parallel robot and its interactive forces; Step 2: Design a composite learning strategy and estimate environmental impedance; Step 3: Based on the estimated environmental impedance, design the optimal stiffness and damping of the robot. Step 4: Design an adaptive robust admittance control based on time delay estimation to enable the robot to track the admittance trajectory with the set performance. The dynamic model of the five-bar parallel robot in step 1 is as follows: ； in: Location of human-computer interaction points Velocity of human-computer interaction point Acceleration at the human-computer interaction point; It is the inertia matrix; It is the matrix of Coriolis force and centrifugal force; It is the gravity vector. For friction, To control the input, Human-computer interaction force; rewrite the robot dynamics model as follows: ； in It is a constant matrix; For the uncertain term defined as follows: ； The external resistance model is as follows: ； in Indicates environmental stiffness. Representing environmental damping; based on the interaction force model, the desired interaction force model can be expressed as: ； in Represents the expected trajectory. To improve the compliance of the robot's interaction with the environment, and to determine the desired interaction force, the following dynamic impedance model is established: ； in This indicates the robot's trajectory tracking error; Let f(x) be diagonal positive definite matrices, and let f(x) represent the desired inertia matrix, stiffness matrix, and damping matrix, respectively. In step 2, the expression for human-computer interaction force is: ； in: It is a regression vector; It is an unknown vector. ; yes The estimated value; estimator for The estimation error is ;in , Force estimation error The combined error of prediction and error constitutes a composite error, defined as: ； ； The prediction error is designed as ;based on and prediction error Constructing a composite learning strategy: ； in , Let j=1,2 be the projection function, defined as: 。 2. The adaptive robust admittance control method based on optimal impedance selection according to claim 1, characterized in that: In step 3, based on the external resistance model and the desired human-computer interaction force, the dynamic equation is designed as follows: ； in: ; ； ； The optimal stiffness in robot interaction is obtained by constructing an optimization problem: ； ； Where i = 1, 2, ..., n; cost function ; Since the weights are positive, according to the minimum principle, the optimal solution is: ； in It is a positive constant, and the optimal stiffness of the robot is... = Optimal damping is ; in Indicates the damping ratio; the desired design damping is: ； Estimated stiffness and damping They will converge to the optimal stiffness. and damping .

3. The adaptive robust admittance control method based on optimal impedance selection according to claim 2, characterized in that: In step 4, the admittance trajectory is: ； Among them: dynamic output satisfy Admittance trajectory tracking error Its filtering error ; in It is a positive definite diagonal matrix, when Approaching zero, the desired impedance dynamic characteristics are obtained; the control input is designed as follows: ； Among them, control gain It is a positive definite diagonal matrix. The adaptive robust control term to be designed Indicates at time t The value, an estimate based on time delay. ； Will: ; Substitute: ; get: ； Where the estimation error And estimation error It is bounded, that is... ;here It is an unknown constant; in order to improve control robustness, the control term Designed as follows: ； in It is a saturation function, and It is a small positive parameter; in middle, Updated to: ； Where the projection function ensure ,and The upper bound is defined; an adaptive robust admittance controller is designed for the robot under consideration using dynamics; the tracking error of the admittance trajectory is considered. Ultimately, it can be determined by limited.

Images