A space domain impedance learning control method for a five-bar parallel robot

Abstract

This invention discloses a spatial domain impedance learning control method for a five-bar parallel robot, comprising the following steps: Step 1, establishing an Eulerian-Lagrange model of the five-bar parallel robot; Step 2, establishing a human-machine system interaction force model based on the trajectory tracking error of the parallel robot; Step 3, estimating impedance dynamics based on the Eulerian-Lagrange model; Step 4, designing an iterative learning strategy for human-machine interaction force based on the human-machine system interaction force model and impedance dynamics; Step 5, conducting control tests on the five-bar parallel robot using the iterative learning strategy for human-machine interaction force. The learning control method proposed in this invention ensures the convergence of tracking errors, considers the uncertainties in robot modeling, and further guarantees the safety of human-machine interaction.

Description

Technical Field

[0001] This invention relates to the field of robot control technology, specifically to a spatial domain impedance learning control method for a five-bar parallel robot. Background Technology

[0002] Currently, five-bar parallel robots are renowned for their high stiffness, compact structure, large load-bearing capacity, and good dynamic response, and are widely used in service robots. Safety is the primary concern in Physical Human-Robot Interaction (PHRI), which can be improved through robot compliance control using impedance regulation. Impedance control is the most widely used compliant force control method, providing robot impedance regulation through the desired spring-damped dynamic relationship between the interaction force and the desired trajectory tracking error. To achieve impedance control in PHRI, two major problems need to be solved: the stability of impedance control and the learning of human impedance. Currently, researchers have constructed various human impedance learning methods based on least squares, recursive least squares, and dynamic primitives, and applied the estimated impedance parameters to impedance control. However, time-varying impedance parameters may disrupt the dynamic stability of the desired variable impedance, thus affecting the stability of human-robot interaction. Summary of the Invention

[0003] This invention is made to solve the above-mentioned problems, and its purpose is to provide a spatial domain impedance learning control method for a five-bar parallel robot.

[0004] This invention provides a spatial domain impedance learning control method for a five-bar parallel robot, characterized by the following steps: Step 1, establishing an Eulerian-Lagrange model of the five-bar parallel robot; Step 2, establishing a human-machine system interaction force model based on the trajectory tracking error of the parallel robot; Step 3, estimating impedance dynamics based on the Eulerian-Lagrange model; Step 4, designing an iterative learning strategy for human-machine interaction force based on the human-machine system interaction force model and impedance dynamics; Step 5, conducting control tests on the five-bar parallel robot using the iterative learning strategy for human-machine interaction force.

[0005] The spatial domain impedance learning control method for a five-bar parallel robot provided by this invention may also have the following feature: wherein, in step 1, the Euler-Lagrange model is:

[0006]

[0007] In the formula, q∈R n Let M(q) be the joint angle vector, and M(q) be the inertia matrix. Let G(q) be the Coriolis torque and centrifugal force matrix, G(q) be the gravitational torque, and τ and τ' be the centrifugal force matrix. h Representing the interaction force and control input respectively, the velocity relationship between the operating space and joint space is as follows:

[0008]

[0009] In the formula, Let J(q) be the velocity of the end effector in the workspace, and J(q) be the Jacobian matrix. The following Cartesian dynamics of the robot are obtained:

[0010]

[0011] In the formula,

[0012] M x =J(q) -T M(q)J(q) -1 ,

[0013] G x =J(q) -T G(q), F x =J(q) -T F, f h =J(q) -T τ h , u=J(q) -T τ,

[0014] The dynamic formula in (3) can be expressed parametrically as follows:

[0015]

[0016] In the formula, W is a regression matrix, and θ is an unknown constant vector satisfying ||θ||≤θ c And θ c It is a normal number.

[0017] The spatial domain impedance learning control method for a five-bar parallel robot provided by this invention may also have the following feature: wherein, in step 2, the trajectory tracking error is:

[0018] e 1,k =x d,k -x 1,k (5)

[0019] e 2,k =x d,k -x 2,k (6)

[0020] e k =e 2,k +k1e 1,k (7)

[0021] In the formula, x i,k Let x represent the value of the k-th iteration. d,kThis represents the reference trajectory, where k1 is the positive gain.

[0022] The spatial domain impedance learning control method for a five-bar parallel robot provided by this invention may also have the following feature: In step 2, the specific process of establishing the human-machine system interaction force model is as follows: x d,k As a reference trajectory for physical human-computer interaction, where k represents the k-th iteration, the interaction force is extended as follows:

[0023]

[0024] In the formula, f f,k (t), K k (t), D k (t) represent the feedforward force, stiffness matrix, and damping matrix, respectively. For ease of impedance learning, f h,k (x k This can be represented as:

[0025]

[0026] In the formula, f k (t):=f f,k (t)-K k (t)x d,k This represents the corrected feedforward force, assuming the existence of constant matrices f*, K*, and D*:

[0027] f k (t)≤f*,K k (t)≤K*,D k (t)≤D* (10)

[0028] In the formula, each element on the left side of "≤" does not exceed the corresponding element on the right side of "≤". The dynamics of human-computer interaction force and impedance change with the robot's position and are presented in the following form:

[0029] f k (t):=f(x k (t),x d,k (t)),K k (t):=K(x k (t)),

[0030] D k (t):=D(x k (t)). (11)

[0031] Define the spatial coordinates s as:

[0032]

[0033] The length traveled by the robot in the k-th iteration is represented by ▽, which is defined as a spatial differentiator in the following form:

[0034]

[0035] From (11) we get Furthermore, it has the following relationship with spatial and temporal differentials:

[0036]

[0037] Based on (13), (1) is transformed from time-domain dynamics to space-domain dynamics, and the expression is as follows:

[0038] ||x 2,k ||▽x 1,k =x 2,k ,

[0039] M(x 1,k )||x 2,k ||▽x 2,k =-C(x) 1,k ,x 2,k )x 2,k -G(x 1,k )-F(x 2,k )+f h,k +u k (15)

[0040] The spatial domain impedance learning control method for a five-bar parallel robot provided by this invention may also have the following feature: In step 3, the specific process of estimating the impedance dynamics is as follows: For the five-bar parallel robot, the desired trajectory x... d,k satisfy:

[0041]

[0042] The initial state value of the k-th iteration is set to the termination value of the (k-1)-th iteration, that is:

[0043] x 1,k (0)=x 1,k-1 (S),x 2,k (0)=x 2,k-1 (S) (17)

[0044] Based on the dynamic formulas in (1) and (15), e k The dynamic formula is expressed as:

[0045]

[0046] In the formula, W k for A simplified expression. Design a repetitive learning control input u.k for:

[0047]

[0048] In the formula, k2 is the positive gain. and θ and f respectively h,k The estimator, the estimator The definition is as follows:

[0049]

[0050] In the formula, They are f k (s), K k (s), D k The estimated impedance dynamics of (s) and the relevant estimation error are expressed as follows:

[0051]

[0052] The spatial domain impedance learning control method for the five-bar parallel robot provided by this invention may also have the following features: In step 4, the specific process of designing the human-machine interaction force iterative learning strategy is as follows: Substituting (19) into (18) yields:

[0053]

[0054] Since vector θ is a constant, it can be estimated using the following differential update law:

[0055]

[0056] In the formula, β0 is the learning rate, and proj θ (·) is the projection function, defined as:

[0057]

[0058] To estimate the time-varying term, the estimators of f(s), K(s), and D(s) are respectively Design the following fully saturated adaptive parameter update law:

[0059]

[0060]

[0061]

[0062] In the formula, s∈[0,S], Let k be an auxiliary matrix, and when k < 0, we have:

[0063] β2, β2, and β3 are all positive gains, and under the definition of the saturation function, F0 > 0:

[0064]

[0065] In the formula, F(t) is a function expression, referring to... F0 is a given constant.

[0066] The role and effect of invention

[0067] According to the spatial domain impedance learning control method for a five-bar parallel robot of the present invention, the specific process is as follows: Step 1, establish the Eulerian-Lagrange model of the five-bar parallel robot; Step 2, establish the human-machine system interaction force model based on the trajectory tracking error of the parallel robot; Step 3, estimate the impedance dynamics based on the Eulerian-Lagrange model; Step 4, design an iterative learning strategy for human-machine interaction force based on the human-machine system interaction force model and impedance dynamics; Step 5, conduct control tests on the five-bar parallel robot using the iterative learning strategy for human-machine interaction force.

[0068] Therefore, compared with the prior art, this invention proves the uniform convergence of the tracking error based on Lyapunov-like analysis, and verifies the effectiveness of tracking error control through simulation and experiment on repetitive tracking tasks of parallel robots.

[0069] Furthermore, the repetitive learning control method proposed in this invention ensures the uniform convergence of tracking errors and takes into account the uncertainties of robot modeling.

[0070] Furthermore, in this invention, only the desired trajectory is periodic; repositioning of the initial location is not required. In traditional iterative impedance learning control, it is assumed that the feedforward force, stiffness matrix, damping matrix, and desired trajectory all change periodically over time. However, this assumption is too stringent for robot-assisted rehabilitation and other physical human-machine interactions. On one hand, the robot's desired path may be spatially periodic, and the time required for the robot to complete one spatial cycle is uncertain. On the other hand, the dynamics of human-machine interaction forces and impedance are closely related to the human-machine position and posture; therefore, spatial periodicity is more suitable for impedance learning control than temporal periodicity. This invention can be used to improve the safety of physical human-machine interactions. Attached Figure Description

[0071] Figure 1 This is a flowchart of the spatial domain impedance learning control method for a five-bar parallel robot in an embodiment of the present invention;

[0072] Figure 2 This is a structural diagram of a five-bar parallel robot according to an embodiment of the present invention;

[0073] Figure 3 This is an impedance error diagram of the five-bar parallel robot in an embodiment of the present invention;

[0074] Figure 4 This is an estimated stiffness diagram of the spatial domain impedance learning control method for a five-bar parallel robot in an embodiment of the present invention.

[0075] Figure 5 This is the control input diagram of the spatial domain impedance learning control method for a five-bar parallel robot in an embodiment of the present invention. Detailed Implementation

[0076] To make the technical means, creative features, objectives and effects of this invention easy to understand, the following embodiments, in conjunction with the accompanying drawings, specifically illustrate a spatial domain impedance learning control method for a five-bar parallel robot according to this invention.

[0077] In this embodiment, a spatial domain impedance learning control method for a five-bar parallel robot is provided.

[0078] Figure 1 This is a flowchart of the spatial domain impedance learning control method for a five-bar parallel robot in an embodiment of the present invention.

[0079] like Figure 1 As shown, the spatial domain impedance learning control method for a five-bar parallel robot involved in this embodiment includes the following steps:

[0080] Step S1: Establish the Euler-Lagrange linkage for the five-bar parallel robot.

[0081] Figure 2 This is a structural diagram of a five-bar parallel robot according to an embodiment of the present invention.

[0082] In this embodiment, the Euler-Lagrange model is:

[0083]

[0084] In the formula, q∈R n Let M(q) be the joint angle vector, and M(q) be the inertia matrix. Let G(q) be the Coriolis torque and centrifugal force matrix, G(q) be the gravitational torque, and τ and τ' be the centrifugal force matrix. h These represent the interaction force and the control input, respectively.

[0085] The velocity relationship between the operating space and the joint space is as follows:

[0086]

[0087] In the formula, Let J(q) be the velocity of the end effector in the workspace, and J(q) be the Jacobian matrix. The following Cartesian dynamics of the robot are obtained:

[0088]

[0089] In the formula,

[0090] M x =J(q) -T M(q)J(q) -1 ,

[0091] G x =J(q) -T G(q), F x =J(q) -T F, f h =J(q) -T τ h , u=J(q) -T τ,

[0092] The dynamic formula in (3) can be expressed parametrically as follows:

[0093]

[0094] In the formula, W is a regression matrix, and θ is an unknown constant vector satisfying ||θ||≤θ c And θ c It is a normal number.

[0095] Step S2: Based on the trajectory tracking error of the parallel robot, establish a human-machine system interaction force model.

[0096] Figure 3 This is an impedance error diagram of the five-bar parallel robot in an embodiment of the present invention.

[0097] like Figure 3 As shown, in this embodiment, the trajectory tracking error is:

[0098] e 1,k =x d,k -x 1,k (5)

[0099] e 2,k =x d,k -x 2,k (6)

[0100] e k =e 2,k +k1e 1,k (7)

[0101] In the formula, x i,k Let x represent the value of the k-th iteration. d,k This represents the reference trajectory, where k1 is the positive gain.

[0102] The specific process of establishing a human-computer system interaction force model is as follows:

[0103] x d,k As a reference trajectory for Physical Human-Computer Interaction (PHRI), where k represents the k-th iteration, the interaction forces are extended as follows:

[0104]

[0105] In the formula, f f,k (t), K k (t), D k (t) represent the feedforward force, stiffness matrix, and damping matrix, respectively. For ease of impedance learning, f h,k (x k This can be represented as:

[0106]

[0107] In the formula, f k (t):=f f,k (t)-K k (t)x d,k This represents the corrected feedforward force, assuming the existence of constant matrices f*, K*, and D*:

[0108] f k (t)≤f*,K k (t)≤K*,D k (t)≤D* (10)

[0109] In the formula, each element on the left side of “≤” does not exceed the corresponding element on the right side of “≤”.

[0110] The dynamics of human-robot interaction force and impedance change with the robot's position, and are presented in the following forms:

[0111] f k (t):=f(x k (t),x d,k (t)),K k (t):=K(x k (t)),

[0112] D k (t):=D(x k (t)). (11)

[0113] Define the spatial coordinates s as:

[0114]

[0115] The length traveled by the robot in the k-th iteration is represented by ▽, which is defined as a spatial differentiator in the following form:

[0116]

[0117] From (11) we get Furthermore, it has the following relationship with spatial and temporal differentials:

[0118]

[0119] Based on (13), (1) is transformed from time-domain dynamics to space-domain dynamics, and the expression is as follows:

[0120]

[0121] Step S3: Estimate the impedance dynamics based on the Euler-Lagrange model. The specific process is as follows:

[0122] For a five-bar parallel robot, the desired trajectory x d,k satisfy:

[0123]

[0124] The initial state value of the k-th iteration is set to the termination value of the (k-1)-th iteration, that is:

[0125] x 1,k (0)=x 1,k-1 (S),x 2,k (0)=x 2,k-1 (S) (17)

[0126] Based on the dynamic formulas in (1) and (15), e k The dynamic formula is expressed as:

[0127]

[0128] In the formula, W k for The simplified form of expression.

[0129] Design a repetitive learning control input u k for:

[0130]

[0131] In the formula, k2 is the positive gain. and θ and f respectively h,k The estimator, the estimator The definition is as follows:

[0132]

[0133] In the formula, They are f k (s), K k (s), D k The estimated impedance dynamics of (s) and the relevant estimation error are expressed as follows:

[0134]

[0135] Step S4: Based on the human-computer system interaction force model and impedance dynamics, design an iterative learning strategy for human-computer interaction force. The specific process is as follows:

[0136] Substituting (19) into (18) gives:

[0137]

[0138] Since vector θ is a constant, it can be estimated using the following differential update law:

[0139]

[0140] In the formula, β0 is the learning rate, and proj θ (·) is the projection function, defined as:

[0141]

[0142] To estimate the time-varying term, the estimators of f(s), K(s), and D(s) are respectively Design the following fully saturated adaptive parameter update law:

[0143]

[0144]

[0145]

[0146] In the formula, s∈[0,S], Let k be an auxiliary matrix, and when k < 0, we have:

[0147] β2, β2, and β3 are all positive gains.

[0148] Under the definition of the saturation function, F0 > 0:

[0149]

[0150] In the formula, F(t) is a function expression, referring to... F0 is a given constant.

[0151] Step S5: Use the human-computer interaction force iterative learning strategy to control and test the five-bar parallel robot. Combine the above steps and conduct simulation experiments. If the control effect meets the requirements, the design is complete.

[0152] Figure 4 This is an estimated stiffness diagram of the spatial domain impedance learning control method for a five-bar parallel robot in an embodiment of the present invention.

[0153] Figure 5 This is the control input diagram of the spatial domain impedance learning control method for a five-bar parallel robot in an embodiment of the present invention.

[0154] Simulation results show that the proposed repetitive learning control brings the tracking error very close to zero after 5 iterations, and the actual trajectory matches the expected trajectory after 40 iterations. Compared to the first iteration, the estimated interaction force at the 40th iteration is very close to the actual force. This demonstrates the effectiveness of iterative learning. However, due to the coupling of uncertainties in robot parameters and impedance, the estimation error of the interaction force does not converge to zero. Based on the simulation results, the proposed impedance-based repetitive learning control can provide variable impedance regulation for physical human-robot interaction and has a uniform asymptotic stability guarantee.

[0155] The role and effect of the embodiments

[0156] According to the spatial domain impedance learning control method for a five-bar parallel robot involved in this embodiment, the specific process is as follows: Step 1, establish the Eulerian-Lagrange model of the five-bar parallel robot; Step 2, establish the human-machine system interaction force model based on the trajectory tracking error of the parallel robot; Step 3, estimate the impedance dynamics based on the Eulerian-Lagrange model; Step 4, design an iterative learning strategy for human-machine interaction force based on the human-machine system interaction force model and impedance dynamics; Step 5, conduct control tests on the five-bar parallel robot using the iterative learning strategy for human-machine interaction force.

[0157] Therefore, compared with the prior art, the above embodiments, based on Lyapunov-like analysis, prove the uniform convergence of the tracking error, and verify the effectiveness of tracking error control through simulation and experiments on repetitive tracking tasks of parallel robots.

[0158] Furthermore, the repetitive learning control method proposed in the above embodiments ensures the uniform convergence of the tracking error and takes into account the uncertainty of robot modeling.

[0159] Furthermore, in the above embodiments, only the desired trajectory is periodic, and there is no need to reposition the initial position. Additionally, in traditional iterative impedance learning control, it is assumed that the feedforward force, stiffness matrix, damping matrix, and desired trajectory all change periodically over time. However, this assumption is too stringent for robot-assisted rehabilitation and some other physical human-machine interactions. On the one hand, the path desired by the robot may be spatially periodic, and the time required for the robot to complete one spatial cycle is uncertain. On the other hand, the dynamics of human-machine interaction forces and impedance are closely related to the human-machine position and posture; therefore, spatial periodicity is more suitable for impedance learning control than temporal periodicity. The above embodiments can be used to improve the safety of physical human-machine interactions.

[0160] The above embodiments are preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention.

Claims

1. A spatial domain impedance learning control method for a five-bar parallel robot, characterized in that, Includes the following steps: Step 1: Establish the Euler-Lagrange model of the five-bar parallel robot; In step 1, the Euler-Lagrange model is: In the formula, For joint angle vectors, The inertia matrix, The matrix represents the Coriolis torque and centrifugal force. For gravitational torque, and These represent the interaction force and the control input, respectively. The velocity relationship between the operating space and the joint space is as follows: In the formula, The speed of the end effector in the workspace. Given the Jacobian matrix, the following Cartesian dynamics of the robot are obtained: In the formula, , , , , , The dynamic formula in the equation can be expressed parametrically as follows: In the formula, W is a regression matrix, and θ is an unknown constant vector that satisfies and It is a positive constant; Step 2: Based on the trajectory tracking error of the parallel robot, establish a human-machine system interaction force model; In step 2, the trajectory tracking error is: (5) (6) (7) In the formula, Indicates the iteration number The value of the second time. Indicates the reference trajectory. Positive gain; In step 2, the specific process of establishing the human-computer system interaction force model is as follows: The As a reference trajectory for physical human-computer interaction, where k represents the k-th iteration, the interaction force is extended as follows: In the formula, , , These represent the feedforward force, stiffness matrix, and damping matrix, respectively, for ease of impedance learning. It can be represented as: In the formula, This represents the corrected feedforward force, assuming the existence of a constant matrix. , , : ， ， In the formula, each element on the left side of "≤" does not exceed the corresponding element on the right side of "≤". The dynamics of human-robot interaction force and impedance change with the robot's position, and are presented in the following forms: Define the spatial coordinates s as: The length traveled by the robot in the k-th iteration is represented by ▽, which is defined as a spatial differentiator in the following form: From (11) we get And it has the following relationship with spatial and temporal differentials: Based on (13), (1) is transformed from time-domain dynamics to space-domain dynamics, and the expression is as follows: Step 3: Estimate the impedance dynamics based on the Eulerian-Lagrange model; Step 4: Based on the human-computer system interaction force model and the impedance dynamic design, design an iterative learning strategy for human-computer interaction force; Step 5: Use the human-computer interaction force iterative learning strategy to conduct control tests on the five-bar parallel robot.

2. The spatial domain impedance learning control method for a five-bar parallel robot according to claim 1, characterized in that: in, In step 3, the specific process of estimating the impedance dynamics is as follows: For a five-bar parallel robot, the desired trajectory satisfy: The initial state value of the k-th iteration is set to the termination value of the (k-1)-th iteration, that is: Based on the dynamic formulas in (1) and (15), The dynamic formula is expressed as: In the formula, for The simplified form of expression, Design repetitive learning control input for: In the formula, Positive gain and They are respectively and The estimator, the estimator The definition is as follows: In the formula, , , They are , , The estimated impedance dynamics and the relevant estimation errors are expressed as follows: .

3. The spatial domain impedance learning control method for a five-bar parallel robot according to claim 2, characterized in that: in, In step 4, the specific process of designing the iterative learning strategy for human-computer interaction is as follows: Substituting (19) into (18) gives: Since vector θ is a constant, it can be estimated using the following differential update law: In the formula, β0 is the learning rate. The projection function is defined as follows: In order to estimate the time-varying term, The estimators are respectively , , Design the following fully saturated adaptive parameter update law: In the formula, , For auxiliary matrix, and when At that time, there were: ; , , All are positive gains. Under the definition of the saturation function : In the formula, For function expression, referring to , , , is a given constant.

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