A cerebellum-inspired model predictive control method for redundant robots

Abstract

The application provides a cerebellum-inspired model predictive control method for a redundant robot, and belongs to the technical field of robot control, and comprises the following steps: S1: for a redundant robot, a cerebellum-inspired model is designed as a substitute model, and linearization processing along a trajectory is performed on the cerebellum-inspired model; S2: an online training algorithm and an error correction algorithm are designed for the cerebellum-inspired model, and system output of the redundant robot is predicted; S3: for the redundant robot, a model predictive control scheme is designed, and a neural dynamics solver is designed to solve the model predictive control scheme; and S4: the cerebellum-inspired model, the online training algorithm, the error correction algorithm, the model predictive control scheme and the neural dynamics solver are combined to form the cerebellum-inspired model predictive control method for the redundant robot, so that trajectory tracking control of the redundant robot with unknown structural information is realized. The application can realize trajectory tracking control of the redundant robot with unknown structural information, and ensure the accuracy of the redundant robot control.

Description

Technical Field

[0001] The present invention relates to the technical field of robot control, and particularly relates to a cerebellum-inspired model predictive control method for redundant robots. Background Art

[0002] With the development of fields such as control technology, engineering mechanics, and computer applications, robots have become important tools in the industrial field, liberating people from dangerous, complex, and high-precision tasks. Among them, redundant robots with more degrees of freedom in the joint space than in the workspace perform excellently. Although the control of redundant robots is relatively difficult, they can usually complete more complex tasks and have a wider range of applications, so their research has attracted much attention. Existing redundant robot motion control schemes need to introduce additional parameters and reserve a certain margin when dealing with joint constraints at different levels, which will reduce the feasible region of joint angles. Model predictive control, which originated in the industrial field, is an effective means for dealing with complex system constraints. It has many advantages such as directly considering constraints and optimizing system performance, and can be applied to the trajectory tracking control of redundant robots.

[0003] However, the research on many redundant robots depends on the structural information and parameters of the robots, which limits their application to robots with unknown structural information. On the one hand, there may be a certain error between the actual parameters of the robot and the calibrated parameters, especially for low-cost robots and handmade robots. During the movement of the robot, this error will accumulate and amplify, affecting the stability of the system. On the other hand, in order to complete different tasks, it is usually necessary to equip the robot with different end tools or perform secondary hardware development. In these cases, the structural information of the robot will change. Therefore, it is crucial to study how to accurately control redundant robots with unknown structural information. Existing research has found that the echo state network has certain similarities with the cerebellum. It has a simple structure and is easy to train, and is good at processing time series data, and can be used as a candidate computational model for the cerebellum. In recent years, cerebellum-inspired computing is an emerging research topic and has been initially applied in the field of robotics. Therefore, a cerebellum-inspired model based on the echo state network can be used as an alternative model for robots with unknown structural information to further solve their control problems. However, existing cerebellum-inspired models are still difficult to solve problems such as low prediction accuracy and difficult processing of non-linear characteristics.

[0004] Facing such a background, there is an urgent need to propose a cerebellum-inspired model predictive control method for redundant robots to control redundant robots with unknown structural information. Summary of the Invention

[0005] In view of this, the present invention provides a cerebellum-inspired model predictive control method for redundant robots to control redundant robots with unknown structural information to achieve high-precision trajectory tracking control.

[0006] The technical solution adopted by the present invention is as follows:

[0007] A cerebellum-like inspired model predictive control method for redundant robots can achieve trajectory tracking control of redundant robots with unknown structural information, including the following steps:

[0008] S1: For the redundant robot, design a cerebellum-like model as its surrogate model, and perform linearization processing of the cerebellum-like model along the trajectory;

[0009] S2: Design an online training algorithm and an error correction algorithm for the cerebellum-like model, and predict the system output of the redundant robot;

[0010] S3: For the redundant robot, design a model predictive control scheme, and design a neural dynamics solver to solve it;

[0011] S4: Combine the cerebellum-like model, the online training algorithm, the error correction algorithm, the model predictive control scheme, and the neural dynamics solver to form a cerebellum-like inspired model predictive control method for redundant robots, and achieve trajectory tracking control of redundant robots with unknown structural information.

[0012] Furthermore, the specific step S1 is

[0013] S101: Design the following cerebellum-like model:

[0014] c(k + 1) = (1 - a)c(k) + ag(W in u(k) + W gc c(k) + W fb y(k) + w bias );

[0015] x(k + 1) = c(k + 1);

[0016] y(k + 1) = W out x(k + 1);

[0017] Where is the input in the mossy fiber at time k, k represents the update index at the current time t = kτ seconds, and τ is the sampling interval; and are the signals in the granule cells at time k and k + 1; a represents the leakage rate; g(·): is a non-linear activation function, usually selected as g(·) = tanh(·); is the output in the Purkinje cell at time k; respectively represent the weight matrices from mossy fiber to granule cell, from granule cell to granule cell, and from Purkinje cell to granule cell; is the bias term; is the state in the parallel fibers at time k+1; represents the output weight matrix.

[0018] Furthermore, the cerebellum-like model is used as an alternative model for the redundant robot, and the joint angle and joint angle increment of the redundant robot are used as the input vector of the cerebellum-like model. Where, is the joint angular velocity of the redundant robot, and the superscript T represents the transpose operation; the output vector y(k) of the cerebellum-like model is the position of the end effector of the redundant robot.

[0019] S102: Perform linearization processing on the cerebellum-like model along the trajectory, and decompose its output into

[0020]

[0021] Where,

[0022]

[0023]

[0024]

[0025]

[0026]

[0027]

[0028] represents the zero matrix; represents the identity matrix; y(k+i|k) represents the future output at time k+i predicted at time k; represents the control time domain; represents the prediction time domain; z(k+j|k) represents the future control input at time k+j; is obtained by sending the control input z(k-1) at time k-1 to the cerebellum-like model.

[0029] Furthermore, the specific step S2 is as follows

[0030] S201: Design the following online training algorithm for the cerebellum-like model:

[0031] 1) Send the input u(k-1) at time k-1 to the granule cells to obtain the state vector x(k) of the current moment in the parallel fibers;

[0032] 2) Measure the output vector y(k) of the redundant robot at time k;

[0033] 3) Generate a new state matrix X new and a new output matrix Y new : Add the state vector x(k) and the output vector y(k) at time k to the state matrix X and the output matrix Y respectively, and discard the first state vector x(k - k L + k w ) and the first output vector y(k - k L + k w ) in the output matrix Y, where k w represents the flushing time, and k L represents the size of the training data.

[0034]

[0035]

[0036]

[0037]

[0038] 4) Use the ridge regression algorithm to update the output weight matrix W new with X new and Y out : where represents the Tikhonov regularization parameter, and the superscript -1 represents the inverse of the matrix.

[0039] S202: Design the following error correction algorithm for the cerebellum-like model:

[0040] y(k|k - 1) = y li (k|k - 1)+σ(k - 1);

[0041]

[0042] where and represent the correction terms at time k and k - 1, y li (k|k - 1) represents the linearly predicted output obtained in step S102 at time k - 1, y(k|k - 1) represents the corrected predicted output, is the convergence coefficient.

[0043] S203: Predict the system output of the redundant robot as where

[0044]

[0045]

[0046]

[0047] Δz(k+i|k) = z(k+i|k) - z(k+i-1|k) represents the control input increment, where i = 0, 1, ···, N u -1;

[0048] Furthermore, the specific steps of step S3 are as follows

[0049] S301: Design the following model predictive control scheme for the trajectory tracking task and system constraints of the redundant robot:

[0050] Minimize:

[0051] Constraints:

[0052]

[0053]

[0054] where

[0055]

[0056]

[0057]

[0058]

[0059]

[0060] is a positive definite symmetric weight matrix; ||·|| Q 、 represents the weighted two-norm, that is is the desired trajectory of the end effector of the redundant robot at the future k+i moment; is the joint angular acceleration of the redundant robot; θ - 、 are the lower bounds of the joint angle, joint angular velocity, and joint angular acceleration of the redundant robot respectively; θ + 、 are the upper bounds of the joint angle, joint angular velocity, and joint angular acceleration of the redundant robot respectively.

[0061] S302: Transform the model predictive control scheme of the redundant robot into a non - linear equation by using the Lagrange multiplier method and the non - linear complementary problem function: Where, ι = 6sN u , k = sN u , γ ∈ (0; 1), is the Lagrange multiplier, ω + = max{0; ω}, denotes the Hadamard product, And design the following neural dynamics solver for it:

[0062]

[0063] Where, ρ = νδ, δ is the step size, is the design parameter, denotes the Hadamard division, diag(·) represents the operation of converting a vector into a diagonal matrix. For the control input increment calculated by the solver, that is, the first sN u elements of the variable ′, take its first s elements to obtain the control input increment Δz(k|k) at time k; then, process the control input increment Δz(k|k) at time k to obtain the joint angular velocity and apply it to the redundant robot system.

[0064] Furthermore, the cerebellum - like inspired model predictive control method for the redundant robot described in step S4 is

[0065] S401: Adopt the ridge regression algorithm to obtain the initial output weight matrix W out of the cerebellum - like model and other weight matrices through offline training;

[0066] S402: Use the online training algorithm to update the output weight matrix W out at time k;

[0067] S403: Through the linearization process in step S1, combined with the error correction algorithm in step S2, predict the system output of the redundant robot;

[0068] S404: Use the predicted output and the reference output Update the model predictive control scheme in step S3 and solve it using a neural dynamics solver to obtain the control input increment Δz(k|k), and then calculate the joint angular velocity based on Δz(k|k) and z(k-1). And apply it to the redundant robot system;

[0069] S405: Repeat steps S402 - S404 at time k+1 until the task ends.

[0070] The beneficial effects of the present invention are as follows: The present invention provides a cerebellum-inspired model predictive control method for redundant robots, which can achieve trajectory tracking control of redundant robots with unknown structural information, directly handle the joint constraints of redundant robots, avoid the reduction of the joint feasible region, and improve the prediction accuracy and tracking accuracy of redundant robots through the online training algorithm of the cerebellum-inspired model, ensuring the accuracy of control. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] To further illustrate the purpose and technical solutions of the present invention, the following drawings are provided for illustration:

[0072] Figure 1 It is a flowchart of a cerebellum-inspired model predictive control method for a redundant robot;

[0073] Figure 2 It is a two-dimensional plan view of the actual trajectory and the desired trajectory of the end effector of the redundant robot in the embodiment of the present invention;

[0074] Figure 3 It is a tracking error diagram of the end effector of the redundant robot in the embodiment of the present invention in the X, Y, and Z directions;

[0075] Figure 4 It is a joint angle diagram of the redundant robot in the embodiment of the present invention;

[0076] Figure 5 It is a joint angular velocity diagram of the redundant robot in the embodiment of the present invention;

[0077] Figure 6 It is a three-dimensional motion process diagram of the redundant robot in the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0078] To make the purpose and technical solutions of the present invention clearer and more understandable, the present invention will be described in detail below with reference to the drawings and embodiments.

[0079] This embodiment is based on a 7-degree-of-freedom redundant robot, and its initial joint angles are set to [0, -0.785472, 0, -2.35425, 0, 1.57164, 0.785465] TRadians, the upper and lower limits of the joint angle are set to θ + = [2.8973, 1.7628, 2.8973; -0.0698; 2.8973, 3.7525, 2.8973] T Radians, θ - = [-2.8973, -1.7628, -2.8973, -3.0718, -2.8973; -0.0175, -2.8973] T Radians, the upper and lower limits of the joint angular velocity are set to Radians per second, the upper and lower limits of the joint angular acceleration are set to Radians per second squared, the sampling interval τ is set to 0.01 seconds, the prediction horizon N and the control horizon N u Are both set to 3, the weight matrix Q is set to 10I 9×9 , the weight matrix V1 is set to I 21×21 , the weight matrix V2 is set to I 21×21 , and the remaining relevant parameters are set as follows: γ = 0.95, ρ = 1, m = 14, n = 340, l = 3, k w = 10, k L = 360, λ = 10 -8 , a = 0.4.

[0080] Now, it is set that within 20 seconds, the end effector of the redundant robot is controlled to track an epicycloid. For this scenario, this embodiment provides "a cerebellum-like heuristic model predictive control method for a redundant robot", combined with Figure 1 , this method includes the following steps:

[0081] Step 1: For the redundant robot, design a cerebellum-like model as its surrogate model and perform linearization processing of the cerebellum-like model along the trajectory; specifically

[0082] (101) Design the following cerebellum-like model:

[0083] c(k + 1) = 0.6c(k) + 0.4tanh(W in u(k) + W gc c(k) + W fb y(k) + w bias ),

[0084] x(k + 1) = c(k + 1),

[0085] y(k + 1) = W out x(k + 1);

[0086] Among them, is the input in mossy fibers at time k, where k represents the update index at the current time t = 0.01k seconds; and are the signals in granule cells at time k and time k + 1; is the output in Purkinje cells at time k; represent the weight matrices from mossy fibers to granule cells, from granule cells to granule cells, and from Purkinje cells to granule cells respectively; is the bias term; is the state in parallel fibers at time k + 1; represents the output weight matrix.

[0087] Furthermore, take the cerebellar-like model as the alternative model of the redundant robot, and use the joint vector of the joint angle and the joint angle increment of the redundant robot as the input vector of the cerebellar-like model where, is the joint angular velocity of the redundant robot, and the superscript T represents the transpose operation; the output vector y(k) of the cerebellar-like model is the position of the end effector of the redundant robot.

[0088] (102) Perform linearization processing on the cerebellar-like model along the trajectory, and decompose its output into

[0089]

[0090] where,

[0091]

[0092]

[0093]

[0094]

[0095]

[0096]

[0097] y(k + i|k) represents the future output at time k + i predicted at time k; z(k + j|k) represents the future control input at time k + j; is obtained by sending the control input z(k - 1) at time k - 1 to the cerebellar-like model.

[0098] ​

[0099] (201) Design the following online training algorithm for the cerebellum-like model:

[0100] 1) Send the input u(k - 1) at time k - 1 to the granule cells to obtain the state vector x(k) at the current time in the parallel fibers;

[0101] 2) Measure the output vector y(k) of the redundant robot at time k;

[0102] 3) Generate a new state matrix X new and a new output matrix Y new : Add the state vector x(k) and the output vector y(k) at time k to the state matrix X and the output matrix Y respectively, and discard the first state vector x(k - 350) in the state matrix X and the first output vector y(k - 350) in the output matrix Y, where,

[0103]

[0104]

[0105]

[0106]

[0107] 4) Adopt the ridge regression algorithm to update the output weight matrix W new using X new and Y out :

[0108]

[0109] (202) Design the following error correction algorithm for the cerebellum-like model:

[0110] y(k|k - 1) = y li (k|k - 1) + σ(k - 1),

[0111] σ(k) = σ(k - 1) + y(k) - y(k - 1) - y li (k|k - 1)

[0112] + y li (k - 1|k - 2) + (y(k) - y(k|k - 1)),

[0113] where, and represent the correction terms at time k and k - 1, y li(k|k - 1) represents the linearized predicted output obtained through step (102) at time k - 1, and y(k|k - 1) represents the corrected predicted output.

[0114] (203) The system output of the redundant robot is where

[0115]

[0116]

[0117]

[0118] Δz(k + i|k) = z(k + i|k) - z(k + i - 1|k) represents the control input increment,

[0119] Step 3: For the redundant robot, design a model predictive control scheme and design a neural dynamics solver to solve it. Specifically,

[0120] (301) For the trajectory tracking task and system constraints of the redundant robot, design the following model predictive control scheme:

[0121] Minimize:

[0122] Constraint conditions:

[0123] <​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​is the desired trajectory of the redundant robot's end effector at the future k+i moment; is the joint angular acceleration of the redundant robot; θ - 、 are the lower bounds of the joint angle, joint angular velocity, and joint angular acceleration of the redundant robot respectively; θ + 、 are the upper bounds of the joint angle, joint angular velocity, and joint angular acceleration of the redundant robot respectively.

[0132] (302) Use the Lagrange multiplier method and the nonlinear complementary problem function to transform the model predictive control scheme of the redundant robot into a nonlinear equation: where,

[0133]

[0134]

[0135] are Lagrange multipliers, ω + = max{0; ω}, denotes the Hadamard product, and design the following neural dynamics solver for it:

[0136]

[0137] where, denotes the Hadamard division, diag(·) represents the operation of converting a vector into a diagonal matrix. For the control input increment calculated by the solver, that is, the first 21 elements of the variable ′, take its first 7 elements to obtain the control input increment Δz(k|k) at the k moment; then, process the control input increment Δz(k|k) at the k moment to obtain the joint angular velocity and apply it to the redundant robot system.

[0138] Step 4: Combine the cerebellar-like model, online training algorithm, error correction algorithm, model predictive control scheme, and neural dynamics solver to form a cerebellar-like inspired model predictive control method for the redundant robot to achieve trajectory tracking control of the redundant robot with unknown structural information. Specifically

[0139] (401) Adopt the ridge regression algorithm to obtain the initial output weight matrix W of the cerebellar-like model through offline trainingout and other weight matrices;

[0140] (402) Update the output weight matrix W at time k using an online training algorithm out ;

[0141] (403) Through the linearization process in Step 1, combined with the error correction algorithm in Step 2, predict the system output of the redundant robot;

[0142] (404) Use the predicted output and the reference output to update the model predictive control scheme in Step 3, and solve it using a neural dynamics solver to obtain the control input increment Δz(k|k), and then calculate the joint angular velocity based on Δz(k|k) and z(k - 1) and apply it to the redundant robot system:

[0143] (405) Repeat steps (402)-(404) at time k + 1 until the task ends.

[0144] In this embodiment, after 20 seconds of simulation on MATLAB software, the simulation results are as Figure 2 shown.<00,00518>are the simulation results of the embodiments of the present invention. Among them, Figure 2 is a two-dimensional plan view of the actual trajectory and the desired trajectory of the end effector of the redundant robot; Figure 3 is the tracking error graph of the end effector of the redundant robot in the X, Y, and Z directions in the embodiments of the present invention; Figure 4 is the joint angle graph of the redundant robot in the embodiments of the present invention; Figure 5 is the joint angular velocity graph of the redundant robot in the embodiments of the present invention; Figure 6 is the three-dimensional motion process graph of the redundant robot in the embodiments of the present invention. It can be seen from Figure 2-6 that the control method of the present invention can effectively perform high-precision trajectory tracking control on a redundant robot with unknown structural information.

[0145] In summary, the method of the present invention effectively realizes the trajectory tracking control of a redundant robot with unknown structural information, ensuring the accuracy of the redundant robot control.

[0146] Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail through the above preferred embodiments, those skilled in the art should understand that various changes can be made in form and details without departing from the scope defined by the claims of the present invention.

Claims

1. A cerebellar-inspired predictive control method for redundant robots, characterized in that, The method includes the following steps: S1: For redundant robots, a cerebellar-like model is designed as a replacement model, and the cerebellar-like model is linearized along the trajectory, specifically as follows: S101: Design the following cerebellar model: in, yes Input into moss fibers at all times Indicates the current time Index update every second. The sampling interval; and yes Time and Signals in granulocytes at any given moment; Represents the leakage rate; It is a non-linear activation function, usually chosen as . ; yes Output in Purkinje cells at any given time; , , These represent the weight matrices from moss fibers to granular cells, from granular cells to granular cells, and from Purkinje cells to granular cells, respectively; It is a deviation term; yes The state in the parallel fiber at any given moment; This represents the output weight matrix; Furthermore, a cerebellar-like model is used as a replacement model for redundant robots, based on the joint angles of the redundant robots. and joint angle increment The joint vector is used as the input vector of the cerebellar model. ,in, , It is the joint angular velocity of the redundant robot, superscript. Represents the transpose operation; the output vector of the cerebellar model. The location of the redundant robot end effector; S102: Linearize the cerebellar model along the trajectory and decompose its output into... in, ， ， ， ， ， ； Represents a zero matrix; Represents the identity matrix; Representative at Time prediction The future output of a moment; Represents the control time domain; Represents the prediction time domain; represent Future control input at any given moment; It is by... Time control input Obtained from a cerebellar-like model; S2: Design online training and error correction algorithms for cerebellar-like models, and predict the system output of redundant robots, specifically... S201: The following online training algorithm is designed for cerebellar-like models: 1) Input of time The vector is sent to the granule cell to obtain the current state vector in the parallel fiber. ; 2) Measurement Redundancy Robot Output vector at time step ; 3) Generate a new state matrix and the new output matrix :Will State vector at time step and output vector Add to the state matrix respectively and output matrix In, and discard the state matrix. The first state vector in and output matrix The first output vector in ,in, Represents flushing time. This represents the size of the training data. ， ， ， ； 4) Ridge regression algorithm is used. and Update the output weight matrix : ,in, Represents the Tikhonov regularization parameter, superscript Represents the inverse of a matrix; S202: The following error correction algorithm is designed for cerebellar-like models: in, and represent Time and Time correction terms, Representative at The linearized prediction output obtained in step S102 at each time step. This represents the corrected prediction output. It is the convergence coefficient; S203: The predicted system output of the redundant robot is... ,in, This represents the increment of the control input. ; ; S3: For redundant robots, design a model predictive control scheme and a neurodynamics solver to solve it. Specifically: S301: For the trajectory tracking task and system constraints of redundant robots, design the following model predictive control scheme: in, , , It is a positive definite symmetric weight matrix; , , This represents the weighted L2 norm, i.e. , ; For the future The desired trajectory of a time-redundant robot end effector; It is the joint angular acceleration of the redundant robot; , , These are the lower bounds for the joint angle, joint angular velocity, and joint angular acceleration of the redundant robot, respectively. , , These are the upper bounds for the joint angle, joint angular velocity, and joint angular acceleration of the redundant robot, respectively. S302: The model predictive control scheme for a redundant robot is transformed into a nonlinear equation using the Lagrange multiplier method and nonlinear complementary problem functions. ,in, , , , , , , , , , For Lagrange multipliers, , , , , It represents the Hadamah accumulation. , , And the following neurodynamic solver was designed for it: ， in, , Step size, For design parameters, , , , It means Hadama is removed. , , , This represents the operation of transforming a vector into a diagonal matrix; further, it involves the control input increment calculated by the solver. , i.e., variables The former Take the first element. You can get the elements. Incremental control input at any time Then, for Incremental control input at any time The joint angular velocity is obtained through processing. This is applied to redundant robot systems; S4: A cerebellum-inspired model predictive control method for redundant robots is constructed by combining a cerebellum-like model, online training algorithm, error correction algorithm, model predictive control scheme, and neurodynamic solver, to achieve trajectory tracking control of redundant robots with unknown structural information.

2. The cerebellar-inspired predictive control method for redundant robots according to claim 1, characterized in that, The specific steps S4 are as follows: S401: Employs the ridge regression algorithm to obtain the initial output weight matrix of the cerebellar model through offline training. Other weight matrices; S402: Update using online training algorithm Output weight matrix at time step ; S403: Predict the system output of the redundant robot by combining the linearization process in step S1 with the error correction algorithm in step S2; S404: Using Predicted Output and reference output Update the model predictive control scheme in step S3 and solve it using a neurodynamics solver to obtain the control input increment. And then according to and Calculate joint angular velocity And apply it to redundant robot systems; S405: In Repeat steps S402-S404 continuously until the task is completed.

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