A physical human-robot interaction control method based on impedance iterative learning

Abstract

The application provides a physical human-computer interaction control method based on impedance iterative learning, and comprises the following steps: establishing an Euler-Lagrange dynamics model of a five-link parallel robot; establishing a human-computer system interaction force model according to a trajectory tracking error of the parallel robot; designing a robot model reference adaptive control based on the Euler-Lagrange dynamics model; designing a human-computer interaction force iterative learning strategy based on the human-computer system interaction force model and the robot model reference adaptive control; and testing the control of the five-link parallel robot by using the human-computer interaction force iterative learning strategy. The physical human-computer interaction control method based on impedance iterative learning provided by the application can reduce the dependence on system information and ensure stable and safe human-computer interaction by realizing variable impedance adjustment.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of robot control, and particularly relates to a physical human-robot interaction control method based on impedance iterative learning. BACKGROUND

[0002] Parallel robots have the advantages of high speed, high precision and high rigidity, and are widely used in the fields of precision machining, measurement engineering and aerospace. Parallel robots play an extremely important role in production automation, and need to have certain flexibility in order to respond to changes in the external environment. Active compliance control is an important link to achieve this goal. The earliest active compliance control research can be traced back to the 1950s. At that time, Goertzs equipped an electro-hydraulic master-slave manipulator with a force feedback device in order to adapt to the harsh environment of a radioactive experimental workshop. When the operator operates on the master manipulator, the contact force between the slave manipulator and the environment can be felt, which is essentially force telepresence.

[0003] Impedance control, as the most widely used compliance control method, adjusts the motion of the robot by establishing the dynamic relationship between the motion of the robot and the external force, so as to realize the dynamic adjustment of the robot and the environment. However, the current impedance control method cannot well guarantee the consistent convergence of the tracking error, and cannot realize the stability of the impedance control system. SUMMARY

[0004] To solve the above problems, the application provides a physical human-robot interaction control method based on impedance iterative learning. The application adopts the following technical scheme:

[0005] The application provides a physical human-robot interaction control method based on impedance iterative learning, which comprises the following steps: S1, establishing an Euler-Lagrange dynamics model of a five-bar parallel robot; S2, establishing a human-robot system interaction force model according to the trajectory tracking error of the parallel robot; S3, designing a robot model reference adaptive control based on the Euler-Lagrange dynamics model; S4, designing a human-robot interaction force iterative learning strategy based on the human-robot system interaction force model and the robot model reference adaptive control; and S5, controlling and testing the five-bar parallel robot by using the human-robot interaction force iterative learning strategy.

[0006] In the physical human-robot interaction control method based on impedance iterative learning provided by the application, the Euler-Lagrange dynamics model in S1 can have the following characteristics:

[0007]

[0008] In the formula, x∈R n is a position vector of a robot end effector, M(x)∈R n×nThe inertia matrix of the robot, The Coriolis and centrifugal force matrix of the robot, G(x)∈R n The gravity vector of the robot, u∈R n The workspace control input force of the robot, u e ∈R n The human-robot interaction force.

[0009] In the physical human-robot interaction control method based on impedance iterative learning provided by the application, the trajectory tracking error in S2 can also have the following characteristics:

[0010] e k =x r -x k (2)

[0011] In the formula, x k represents the value of the kth iteration, and x r represents the reference trajectory; the human-robot system interaction force model is:

[0012]

[0013] In the formula, and respectively represent the stiffness matrix and the damping matrix of the interaction force in the kth iteration process; the stiffness matrix and the damping matrix are functions of the following expressions:

[0014]

[0015]

[0016] In the formula, K h (t) and B h (t) are both iteration-independent terms, which play a leading role in ; K d,k (t) and B d,k (t) are both iteration-dependent terms; based on formulas (2)-(5), the human-robot system interaction force model is simplified as:

[0017]

[0018] In the formula, F0(t)=-K h (t)x r .

[0019] In the physical human-robot interaction control method based on impedance iterative learning provided by the application, the error sliding surface defined according to the trajectory error can also have the following characteristics:

[0020]

[0021] where k1 is a positive control parameter; the Euler-Lagrange dynamics model is parameterized as:

[0022]

[0023] where theta is a constant vector; according to the expression of the Euler-Lagrange dynamics model and the parameterized Euler-Lagrange dynamics model, the error sliding mode surface is converted as:

[0024]

[0025] The adaptive control strategy of the control input u is designed as: k

[0026]

[0027] where k2>0, and are the estimations of theta and u e,k respectively; according to the adaptive control strategy of the control input u k , the corresponding dynamics expression of the error sliding mode surface r k is substituted and simplified to obtain the simplified dynamics expression of the error sliding mode surface r k :

[0028]

[0029] where

[0030] In the physical human-robot interaction control method based on impedance iterative learning provided by the application, the method can further have the following characteristics: The following differential adaptive rate is updated:

[0031]

[0032]

[0033] where r0 is a learning rate, and r0>0; proj(t) is a projection, and specifically:

[0034] In the physical human-robot interaction control method based on impedance iterative learning provided by the application, the estimations of F0(t), K h (t) and B h (t) in the formula (6) are The fully saturated adaptive parameter update law is designed as:​

[0035]

[0036]

[0037]

[0038]

[0039]

[0040]

[0041] wherein t∈[0,T] and r1,r2,r3>0; are feedforward force auxiliary matrix, stiffness auxiliary matrix and damping auxiliary matrix, respectively;

[0042] Under the definition of saturation function, F0>0,

[0043]

[0044] wherein F(t) is a function expression, and refers to and F0 is a given constant.

[0045] Inventive action and effect

[0046] According to the physical human-robot interaction control method based on impedance iterative learning of the application, the convergence of the reference trajectory tracking error is ensured by designing impedance control, and then the convergence of the impedance error and the stability of the impedance control are ensured. In addition, the impedance curve in the application is not limited to periodicity, iterative independence or slow change, which is different from the requirement of the impedance curve in the traditional controller. In addition, since the repetitive learning control algorithm is adopted, the initial value of each operation of the system is consistent with the initial value of the previous operation. Finally, the adaptive iterative learning control strategy can handle the parameter uncertainty of the system, and the periodic adaptive learning control method can solve the parameter uncertainty with time delay in the input saturation nonlinear system.

[0047] The physical human-robot interaction control method based on impedance iterative learning of the application can reduce the dependence on system information and ensure stable and safe human-robot interaction through variable impedance adjustment. BRIEF DESCRIPTION OF DRAWINGS

[0048] Figure 1 The flow chart of the physical human-robot interaction control method based on impedance iterative learning of the embodiment of the application;

[0049] Figure 2A structural schematic diagram of a five-bar parallel robot of an embodiment of the present application; and

[0050] Figure 3 An impedance error diagram of the five-bar parallel robot of the embodiment of the present application. DETAILED DESCRIPTION

[0051] In order to make the technical means, creative features, purposes and effects of the present application easy to understand, the following describes in detail a physical human-robot interaction control method based on impedance iterative learning of the present application in combination with embodiments and drawings.

[0052] [EMBODIMENT]

[0053] Figure 1 A flowchart of the physical human-robot interaction control method based on impedance iterative learning of the embodiment of the present application.

[0054] As shown in Figure 1 , a physical human-robot interaction control method based on impedance iterative learning includes the following steps:

[0055] S1, an Euler-Lagrange dynamics model of a five-bar parallel robot is established.

[0056] As shown in Figure 2 , A0 is a HRI point, A1 A2 A3 A4 A0 are five joint points, and q1 q2 q3 q4 are angle degrees.

[0057] The Euler-Lagrange dynamics model in S1 is:

[0058]

[0059] In the formula, x∈R n is a position vector of a robot end effector, M(x)∈R n×n is an inertia matrix of the robot, is a Coriolis and centrifugal force matrix of the robot, G(x)∈R n is a gravity vector of the robot, u∈R n is a control input force of the robot workspace, and u e ∈R n is a human-robot interaction force.

[0060] In the embodiment, when the parallel robot is working, a human hand is placed on a robot end hand support, an arm is rotated at a certain angle around the robot center to the left or to the right, and the robot is analyzed according to a dynamics equation.

[0061] S2, a human-robot system interaction force model is established according to a trajectory tracking error of the parallel robot. In S2, the trajectory tracking error is:

[0062] e k = x r - x k (2)

[0063] where x k denotes the value of the kth iteration, x r denotes the reference trajectory; the human-robot system interaction force model is:

[0064]

[0065] where, and respectively represent the stiffness matrix and the damping matrix of the interaction force in the kth iteration process; the stiffness matrix and the damping matrix are expressed as follows:

[0066]

[0067]

[0068] where K h (t) and B h (t) are both iteration-independent terms, which play a dominant role in ; K d,k (t) and B d,k (t) are both iteration-dependent terms.

[0069] Based on formulas (2)-(5), the human-robot system interaction force model is simplified as:

[0070]

[0071] where F0(t) = -K h (t)x r .

[0072] S3, based on the Euler-Lagrange dynamic model, a robot model reference adaptive control is designed.

[0073] where the error sliding surface defined according to the trajectory error is:

[0074]

[0075] where k1 is a positive control parameter.

[0076] The Euler-Lagrange dynamic model is parameterized as:

[0077]

[0078] where θ is a constant vector.

[0079] Referring to the expression of the Euler-Lagrange dynamics model and the parameterized Euler-Lagrange dynamics model, the error sliding surface is transformed into:

[0080]

[0081] Design control input u k Adaptive control strategy:

[0082]

[0083] In the formula, k2>0, and θ and u respectively e,k The estimate.

[0084] According to the control input u k The adaptive control strategy for the error sliding surface r k Substituting and simplifying the corresponding dynamic expression, we obtain the simplified error sliding surface r. k The corresponding dynamic expression:

[0085]

[0086] In the formula,

[0087] S4, based on the human-machine system interaction force model and robot model reference adaptive control design, proposes an iterative learning strategy for human-machine interaction force.

[0088] in, Updated by the following differential adaptive law:

[0089]

[0090]

[0091] In the formula, r0 is the learning rate, and r0 > 0; proj(t) is a projection, specifically:

[0092]

[0093] In equation (6), F0(t) and K h (t) and B h The estimator of (t) is Design a fully saturated adaptive parameter update law:

[0094]

[0095]

[0096]

[0097]

[0098]

[0099]

[0100] where t∈[0,T] and r1,r2,r3>0. are the feedforward force auxiliary matrix, the stiffness auxiliary matrix and the damping auxiliary matrix, respectively.

[0101] Under the definition of saturation function, F0>0,

[0102]

[0103] where F(t) is a function expression, and is defined as and F0 is a given constant.

[0104] It should be noted that the projection function in formula (11) avoids parameter drift, and the saturation function in formulas (14)-(16) can avoid divergence caused by parameter accumulation in the same direction. The time-invariant vector θ in the time domain is estimated by using the difference update law, and the time-varying impedance parameter in the iteration domain is iteratively learned. After 40 iterations, the actual force and the estimated force are basically consistent, the human-machine system interaction force model after optimization iteration is obtained, and the model tends to be stable. To some extent, the uncertainty of coupling is reduced.

[0105] S5, using the human-machine interaction force iterative learning strategy to control test the five-bar parallel robot.

[0106] In this step, the human-machine interaction force iterative learning strategy determined is used to control system simulation test of the five-bar parallel robot, the motion condition is designed, the interaction force field is preset, the control parameters are adjusted, so that the simulation is normally carried out, and finally the experimental result data is viewed.

[0107] It should be noted that in the process of motion of the five-bar parallel robot, the interaction force is not periodic or slowly time-varying. For the proposed physical human-machine interaction control method based on impedance iterative learning, the parameters K1, K2 and γ0 are set as K1=10, K2=80, and γ0=120. Denote γ1=diag{180,0;0,540}, γ2=500I, and γ3=500I. The simulation results are shown in Figure 3 The physical human-machine interaction control method based on impedance iterative learning proposed in the application makes the tracking error e kAfter five iterations, the error is very close to zero, and the actual trajectory coincides with the desired trajectory after forty iterations; and from Figure 3 It can be seen from the above that the estimated interaction force at iteration time is very close to the actual interaction force after forty iterations compared with the first iteration, which demonstrates the effectiveness of the method of the present application.

[0108] Effects of the embodiments

[0109] According to the physical human-robot interaction control method based on impedance iterative learning provided by the embodiment, the convergence of the reference trajectory tracking error is ensured by designing the impedance control, and then the convergence of the impedance error and the stability of the impedance control are ensured. In addition, in the present application, the impedance curve is not limited to the characteristics of periodicity, iteration independence or slow change, which are different from the requirements of the impedance curve in the traditional controller. In addition, since the repetitive learning control algorithm is adopted, the initial value of each operation of the system is consistent with the initial value of the previous operation. Finally, by using the adaptive iterative learning control strategy, the parameter uncertainty existing in the system can be processed; and by using the periodic adaptive learning control method, the parameter uncertainty with time delay in the input saturation nonlinear system is solved.

[0110] The above embodiments are only used to illustrate the specific embodiments of the present application, and the present application is not limited to the description range of the above embodiments.

Claims

1. A physical human-robot interaction control method based on impedance iterative learning, characterized in that, The method comprises the following steps: S1, establishing an Euler-Lagrange dynamic model of a five-link parallel robot; S2, establishing a human-robot system interaction force model according to a trajectory tracking error of the parallel robot; S3, designing a robot model reference adaptive control based on the Euler-Lagrange dynamic model; S4, designing a human-robot interaction force iterative learning strategy based on the human-robot system interaction force model and the robot model reference adaptive control; S5, testing the five-link parallel robot by using the human-robot interaction force iterative learning strategy, wherein the Euler-Lagrange dynamic model in S1 is: where x ∈ R n is the robot end effector position vector, M(x) ∈ R n×n is the robot inertia matrix, is the robot Coriolis and centrifugal force matrix, G(x) ∈ R n is the robot gravity vector, u ∈ R n is the robot workspace control input force, u e ∈ R n is the human-robot interaction force, the trajectory tracking error in S2 is: e k = x r - x k (2) wherein x k represents the value of the iteration k, x r represents the reference trajectory; the human-robot system interaction force model is: wherein and represent the stiffness matrix and the damping matrix of the interaction force in the kth iteration process, respectively; the stiffness matrix and the damping matrix are expressed as follows: where K h (t) and B h (t) are both iteration-independent terms, respectively, in K d,k (t) and B d,k (t) are both iteration-dependent terms; based on formulas (2)-(5), the human-robot system interaction force model is simplified as: where F0(t) = -K h (t)x r .

2. The physical human-robot interaction control method based on impedance iterative learning according to claim 1, wherein an error sliding mode surface defined according to a trajectory error is: wherein wherein k1 is a positive control parameter; the Euler-Lagrange dynamic model is parameterized as: wherein θ is a constant vector; the error sliding mode surface is converted into:

3. The physical human-robot interaction control method based on impedance iterative learning according to claim 2, wherein: Design control input u k Adaptive control strategy: where k2> 0, with are estimates of θ and u e,k respectively; According to the control input u k The adaptive control strategy of the error sliding mode surface r k The corresponding dynamic expression is substituted and simplified, and the simplified error sliding mode surface r k The corresponding dynamic expression: In the formulae, wherein r0 is a learning rate, and r0>0; proj(t) is a projection, and specifically: wherein, The is updated by the following differential adaptation rate:

4. The physical human-robot interaction control method based on impedance iterative learning according to claim 1, wherein: under the definition of a saturation function, F0>0, wherein The F0(t), K h (t) and B h (t) in the formula (6) are estimated as Design a full-saturated adaptive parameter update law: In the formula, t∈[0, T], and r1, r2, r3>0; FF, K, C are feedforward force auxiliary matrix, stiffness auxiliary matrix and damping auxiliary matrix respectively. ​ In the formula, F(t) is a function expression, which refers to and F0 is a given constant.

Images