A Control Method for Space Dual-Arm Robots Based on Machine Learning and LQR Control

Abstract

This invention relates to the field of robot control technology, and particularly to a control method for a space dual-arm robot based on machine learning and LQR control. It includes: constructing a dynamic model of the space dual-arm robot in a space environment; observing the trajectory of the space dual-arm robot and constructing a following error; combining the following error with a deep learning model to obtain the prediction error for the control of the space dual-arm robot; and designing LQR optimal control based on the prediction error. Unlike traditional controllers that rely solely on current state feedback, this invention predicts future deviations and performs control compensation in advance, significantly improving the adaptability of the dynamic system to external changes.

Description

Technical Field

[0001] This invention relates to the field of robot control technology, and in particular to a control method for a space dual-arm robot based on machine learning and LQR control. Background Technology

[0002] Space dual-arm robots, as important tools for orbital operation and maintenance tasks, exhibit complex nonlinear dynamic characteristics in free-floating environments. Existing technologies mainly rely on traditional control methods based on precise modeling, such as LQR and robust control, which can handle some known uncertainties. However, they still fall short in addressing the following challenges: the high-dimensional complexity of dynamic modeling makes model parameterization methods difficult to adapt to complex nonlinear scenarios; the dynamic changes and noise effects of the mission's operating environment make it difficult for traditional methods to effectively achieve online adaptive control; and the control delay problem remains unresolved. Summary of the Invention

[0003] This invention discloses a control method for a space dual-arm robot based on machine learning and LQR control. The specific method is as follows:

[0004] Construct a dynamic model of a space dual-arm robot in the space environment;

[0005] Observe the trajectory of a dual-arm robot in space and construct the following error;

[0006] By combining the error with a deep learning model, the prediction error for the control of a spatial dual-arm robot can be obtained.

[0007] Based on the prediction error, LQR optimal control is designed to control the space dual-arm robot.

[0008] Furthermore, the dynamic model of the space dual-arm robot in the space environment includes base inertia terms, coupling terms between the robotic arms, joint dynamic terms, and end-effector force terms. The specific formulas of the dynamic model are constructed as follows:

[0009] The Lagrange equation is:

[0010]

[0011] Where L = KP is the Lagrange function, K is the kinetic energy, P is the potential energy, and τ is the generalized force.

[0012] For a space dual-arm robot, a generalized velocity variable is defined. in, To describe the linear velocity of the base motion With angular velocity Generalized variables; and These are the angular velocities of the joints of the two robotic arms, respectively.

[0013] Then the kinetic and potential energy of the generalized coordinate x are:

[0014]

[0015] In a microgravity environment, G(x) can be neglected; substituting L=KP into the Lagrange equation and introducing joint force / external force terms, we obtain the dynamic equations of the dual-arm robot:

[0016]

[0017] In the formula: M is the inertia matrix of the space dual-arm robot; C is the nonlinear term; To control the control force and torque of the robotic arm; J e For the Jacobian matrix of the end effector of a dual-arm robot, it maps the velocity in the joint space to the velocity in the maneuvering space; This represents the contact force and torque acting on the ends of both arms, and f e Accurately measured by a force sensor installed at the end of the robotic arm;

[0018] The inertia matrix M(z) is in the form of:

[0019]

[0020] M 12 (z1,x2) and M 21 (x1, x2) represents the coupling inertial characteristics between the two robotic arms; M b For the inertia of the floating base; M b,i M i,b Let M1(x1) represent the coupling inertia between the base and the robotic arm; M2(x2) are the inertia matrices of the first and second robotic arms, respectively, specifically expressed as follows:

[0021]

[0022] Among them, J i (x j The Jacobian matrix of the j-th link; j The inertia tensor of the j-th link; The Jacobian matrix of the centroid of the j-th link; m j The mass of the j-th link;

[0023] Terminal Jacobian matrix J e Related joint velocity and end-effector velocity The expression is:

[0024]

[0025] The terminal Jacobian matrix Je It is a block matrix, in the form of:

[0026]

[0027] J e1 (x1) and J e2 (x2) is the end Jacobian matrix of the first and second robotic arms:

[0028]

[0029] J v (x i ) and J ω (x i ) represents the Jacobian matrix of the linear and angular velocities at the terminal.

[0030] Based on the dynamic equations of the space dual-arm robot, the system's state equations can be expressed as:

[0031]

[0032] in,

[0033] It is a state matrix;

[0034] It is the control input matrix;

[0035] It is the external force input matrix.

[0036] Furthermore, the following method is used to construct the following tracking error:

[0037] The actual state x of the space dual-arm robot is obtained by measurements from various sensors;

[0038] The actual state is expressed in generalized coordinates. The desired state is

[0039] The formula for following error is:

[0040] e(t) = x(t) - x d (t)

[0041] If the expected following error is within the target range, then

[0042] ∥e(t)∥≤∈

[0043] Where ∈ represents the error tolerance of the spatial dual-arm robot.

[0044] Furthermore, the prediction error of the spatial dual-arm robot control is obtained using the following method:

[0045] Collect data on the state of the dual-arm space robot system, the input force at the end of the robotic arm, and the following error to construct a training dataset D:

[0046]

[0047] in, f is a system state variable; ei Input force to the end effector of the robotic arm; The tracking error is represented by N; N is the total number of data points.

[0048] Train a nonlinear mapping using training dataset D make:

[0049]

[0050] Where θ are model parameters, the objective is to minimize the difference between the prediction error and the actual error;

[0051] During training, the loss function is optimized by minimizing it, and the loss function is constructed as follows:

[0052]

[0053] During training, when the actual error e i With prediction error If the deviation is large, the model parameters are adjusted, and gradient descent is used to update the model parameters:

[0054]

[0055] Where η is the learning rate. It is the gradient of the loss function with respect to the parameters.

[0056] Training completes nonlinear mapping Subsequently, the prediction error for the control of the spatial dual-arm robot is... The specific formula is as follows:

[0057]

[0058]

[0059] Furthermore, LQR optimal control is designed, and the specific method is as follows:

[0060] By incorporating the prediction error into the state equation, an extended state equation is constructed.

[0061] Design the objective function of the LQR controller;

[0062] Solve the Ri ccat i equation to calculate the extended feedback gain matrix and the optimal control law.

[0063] Furthermore, the extended state equations are constructed using the following method:

[0064] Prediction error Introduced into the state equations, the dynamics of the original system are extended, and the state variables are expanded:

[0065]

[0066] but

[0067]

[0068] The extended equations are integrated into the state description:

[0069]

[0070] in

[0071]

[0072] In the extended system, the controller is designed using LQR optimization to minimize state deviation and control input energy consumption. The objective function is designed as follows:

[0073]

[0074] Where Q is the extended state weight matrix, which includes weights for position, velocity, and prediction error; R is the input weight matrix, which constrains the control energy.

[0075] Furthermore, the Riccati equation is solved to calculate the extended feedback gain matrix and the optimal control law, using the following specific method:

[0076] Solve the continuous Riccati equation, and use the solution P of the Riccati equation to calculate the extended feedback gain matrix K. ext :

[0077]

[0078] Where P is a symmetric positive definite matrix, describing the weights of the extended state;

[0079] Based on P, calculate the extended feedback gain matrix:

[0080]

[0081] The final optimal control law is:

[0082] u(t) = -K ext z ext (t)

[0083] The unfolded form is as follows:

[0084]

[0085] Where K1 is the feedback gain of the controller to the state variable z(t); K2 is the feedback gain of the controller to the prediction error. Feedback gain.

[0086] Due to the adoption of the above technical solutions, the present invention has the following beneficial effects:

[0087] 1. Unlike traditional controllers that rely solely on current state feedback, this invention predicts future deviations and performs control compensation in advance, significantly improving the adaptability of dynamic systems to external changes.

[0088] 2. This invention combines extended state modeling of prediction error to extend static feedback into a control scheme that includes dynamic prediction.

[0089] 3. This invention adds a feedforward correction term based on machine learning prediction to the classic LQR control law, thereby improving the tracking accuracy of the controller.

[0090] 4. This invention systematically improves control performance from dynamic modeling and error prediction to controller design, and is suitable for complex orbital mission scenarios.

[0091] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained from the following description. Attached Figure Description

[0092] The accompanying drawings of this invention are described below.

[0093] Figure 1 This is a schematic diagram of a space dual-arm robot.

[0094] Figure 2 This is a block diagram illustrating the control principle of a space dual-arm robot.

[0095] Figure 3 This is a schematic diagram of the overall process. Detailed Implementation

[0096] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0097] A space robot is a special type of robot capable of performing various tasks in the space environment. It typically consists of a base spacecraft and two six-degree-of-freedom robotic arms. The structure of a space dual-arm robot is as follows: Figure 1As shown, the satellite base carries two robotic arms, each with only one end effector. Considering that the robotic arm base is always in a free-floating state during the capture of non-cooperative targets, the space multi-arm robot system is in an underactuated state. According to the Lagrangian method, a dynamic model of the system can be established.

[0098] A control method for a space dual-arm robot based on machine learning and LQR control, such as Figure 2 and Figure 3 As shown, the specific steps are as follows:

[0099] S1. Construct a dynamic model of a space dual-arm robot in the space environment.

[0100] In step S1, the dynamic model uses the Lagrange equations:

[0101]

[0102] Where L = KP is the Lagrange function, K is the kinetic energy, P is the potential energy, and τ is the generalized force.

[0103] For a space dual-arm robot, a generalized velocity variable is defined. in To describe the linear velocity of the base motion With angular velocity Generalized variables. and These are the angular velocities of the joints of the two robotic arms. The kinetic and potential energies at the generalized coordinate x are:

[0104]

[0105] In a microgravity environment, G(x) can be neglected. Substituting L=KP into the Lagrange equation and introducing joint force / external force terms, we obtain the dynamic equations of the dual-arm robot:

[0106]

[0107] In the formula: M is the inertia matrix of the space dual-arm robot; C is the nonlinear term; To control the control force and torque of the robotic arm; J e For the Jacobian matrix of the end effector of a dual-arm robot, it maps the velocity in the joint space to the velocity in the maneuvering space; This represents the contact force and torque acting on the ends of both arms, and assuming f e It can be accurately measured by a force sensor installed at the end of the robotic arm.

[0108] The inertia matrix M(x) is in the form of:

[0109]

[0110] M 12 (x1,x2) and M 21 (x1, x2) represents the coupling inertial characteristics between the two robotic arms; M b For the inertia of the floating base; M b,i M i,b Let M1(x1) represent the coupling inertia between the base and the robotic arm; M2(x2) are the inertia matrices of robotic arm 1 and robotic arm 2, respectively, specifically expressed as:

[0111]

[0112] Among them, J i (x j The Jacobian matrix of the j-th link; j The inertia tensor of the j-th link; The Jacobian matrix of the centroid of the j-th link; m j The mass of the j-th link.

[0113] Terminal Jacobian matrix J e Related joint velocity and end-effector velocity Including linear velocity and angular velocity, the expression is:

[0114]

[0115] The terminal Jacobian matrix J e It is a block matrix, in the form of:

[0116]

[0117] J e1 (x1) and J e2 (x2) is the end Jacobian matrix of robotic arm 1 and robotic arm 2:

[0118]

[0119] J v (x i ) and J ω (x i ) represents the Jacobian matrix of the linear and angular velocities at the end.

[0120] Based on the dynamic equations of the space dual-arm robot, the system's state equations can be expressed as:

[0121]

[0122] in,

[0123] It is a state matrix;

[0124] It is the control input matrix;

[0125] It is the external force input matrix.

[0126] S2. Observe the trajectory of the dual-arm robot in space and construct the following error.

[0127] For a dual-arm space robot, the actual state x of the system is obtained by measurements from various sensors. If the actual state is expressed using generalized coordinates... The description, and the expected state is The error is then expressed as:

[0128] e(t) = x(t) - x d (t)

[0129] For a tracking control task, the expected error e(t) converges to zero, or varies within an acceptable range:

[0130] ∥e(t)∥≤∈

[0131] Where ∈ represents the error tolerance of the spatial dual-arm robot system.

[0132] S3. By combining the following error with a deep learning model, the prediction error for the control of the spatial dual-arm robot is obtained.

[0133] In real-world systems, external disturbances and uncertainties exist that may be unpredictable, making real-time computation difficult with traditional optimization methods. Machine learning can predict the system's following error. It can utilize offline training data to learn models, enabling rapid online predictions and adapting to unmodeled uncertainties.

[0134] In step S3, a deep learning model is constructed, and the specific method is as follows:

[0135] S31. Training data construction:

[0136] Collect system state, end-effector input force, and following error data for a dual-arm robot system, covering as many task conditions and workspaces as possible. Based on the system state and end-effector input force, predict the system's following error, defining a training dataset D:

[0137]

[0138] in:

[0139] System state variables;

[0140] f ei: Input force at the end of the robotic arm;

[0141] Systematic errors;

[0142] N: The total number of data points.

[0143] S32, Machine Learning Models:

[0144] Train a nonlinear mapping using the collected data

[0145]

[0146] Where θ are the model parameters, and the objective is to minimize the difference between the model's prediction error and the actual error, which is optimized by minimizing the loss function:

[0147]

[0148] To facilitate the subsequent design of LQR controllers by conveniently incorporating the error as a feedback variable, the following will be introduced: For continuous-time dynamics, the relationship between the rate of change of error can be regressed from the sequence prediction results. This can be described using a dynamic equation:

[0149]

[0150] Where f err It is a mapping relationship extracted from the training data.

[0151] S33. Error Feedback and Model Adaptation:

[0152] When the actual error e(t) and the prediction error If the deviation is large, the model parameters are adjusted, and gradient descent is used to update the model parameters:

[0153]

[0154] Where η is the learning rate. It is the gradient of the loss function with respect to the parameters.

[0155] S34. Model training stopping condition:

[0156] When the model's loss function value L(θ) no longer decreases significantly after several consecutive iterations during training, the model training is considered to have converged. At this point, training can be stopped.

[0157]

[0158] S4. Based on the prediction error, design LQR optimal control to control the space dual-arm robot.

[0159] In step S, the LQR optimal controller is designed, and the specific steps are as follows:

[0160] S41. Constructing the extended state equations

[0161] Errors in machine learning predictions Introduced into the state equations, the dynamics of the original system are extended, and the state variables are expanded:

[0162]

[0163] but

[0164]

[0165] The extended equations are integrated into the state description:

[0166]

[0167] in

[0168]

[0169] S42. Definition of Cost Function

[0170] In the extended system, the controller is designed using LQR optimization to minimize state deviation and control input energy consumption. The objective function is:

[0171]

[0172] Where Q is the extended state weight matrix, which includes weights for position, velocity, and prediction error; R is the input weight matrix, which constrains the control energy.

[0173] S43. Solving the Riccati equation

[0174] To design the LQR control law, it is necessary to first solve the continuous Riccati equation, and then use the solution P of the Riccati equation to calculate the extended feedback gain matrix K. ext :

[0175]

[0176] Where P is a symmetric positive definite matrix, describing the weights of the extended state.

[0177] S44, Feedback Gain Matrix

[0178] Based on P, calculate the extended feedback gain matrix:

[0179]

[0180] S45, Calculation of Control Law

[0181] The final optimal control law is:

[0182] u(t) = -K ext z ext (t)

[0183] The unfolded form is as follows:

[0184]

[0185] Where K1 is the feedback gain of the controller to the state variable z(t); K2 is the feedback gain of the controller to the prediction error. Feedback gain.

[0186] The traditional LQR feedback law, K1z(t), governs the dynamic adjustment of the current state, ensuring the convergence and stability of the system. This is achieved through feedback of the prediction error. This enables feedforward correction of future deviations, further improving control accuracy.

[0187] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A control method for a space dual-arm robot based on machine learning and LQR control, characterized in that, The specific method is as follows: Construct a dynamic model of a space dual-arm robot in the space environment; Observe the trajectory of a dual-arm robot in space and construct the following error; By combining the error with a deep learning model, the prediction error for the control of a spatial dual-arm robot can be obtained. Based on the prediction error, LQR optimal control is designed to control the space dual-arm robot; The dynamic model of the space dual-arm robot in the space environment includes base inertia terms, coupling terms between the robotic arms, joint dynamic terms, and end-effector force terms. The specific formulas of the dynamic model are constructed as follows: The Lagrange equation is: Where L=KP is the Lagrange function, K is the kinetic energy, P is the potential energy, and τ is the generalized force; For a space dual-arm robot, a generalized velocity variable is defined. in, To describe the linear velocity of the base motion With angular velocity Generalized variables; and These are the angular velocities of the joints of the two robotic arms, respectively. Then the kinetic and potential energy of the generalized coordinate x are: In a microgravity environment, G(x) can be neglected; substituting L=KP into the Lagrange equation and introducing joint force / external force terms, we obtain the dynamic equations of the dual-arm robot: In the formula: M is the inertia matrix of the space dual-arm robot; C is the nonlinear term; To control the force and torque of the robotic arm; J e For the Jacobian matrix of the end effector of a dual-arm robot, it maps the velocity in the joint space to the velocity in the maneuvering space; This represents the contact force and torque acting on the ends of both arms, and f e Accurately measured by a force sensor installed at the end of the robotic arm; The inertia matrix M(x) is in the form of: M 12 (x1,x2) and M 21 (x1, x2) represents the coupling inertial characteristics between the two robotic arms; M b For the inertia of the floating base; M b,i 、M i,b Let M1(x1) represent the coupling inertia between the base and the robotic arm; M2(x2) are the inertia matrices of the first and second robotic arms, respectively, specifically expressed as follows: Among them, J i (x j The Jacobian matrix of the j-th link; j The inertia tensor of the j-th link; The Jacobian matrix of the centroid of the j-th link; m j The mass of the j-th link; Terminal Jacobian matrix J e Related joint velocity and end-effector velocity The expression is: The terminal Jacobian matrix J e It is a block matrix, in the form of: J e1 (x1) and J e2 (x2) is the end Jacobian matrix of the first and second robotic arms: J v (x i ) and J ω (x i ) represents the Jacobian matrix of the linear and angular velocities at the terminal. Based on the dynamic equations of the space dual-arm robot, the system's state equations can be expressed as: in, It is a state matrix; It is the control input matrix; It is the external force input matrix; The following method is used to construct the following tracking error: The actual state x of the space dual-arm robot is obtained by measurements from various sensors; The actual state is expressed in generalized coordinates. The desired state is The formula for following error is: e(t)=x(t)-x d (t) If the expected following error is within the target range, then ||e(t)||≤∈ Where ∈ represents the error tolerance of the spatial dual-arm robot; The specific method for obtaining the prediction error of the control of a spatial dual-arm robot is as follows: Collect data on the state of the dual-arm space robot system, the input force at the end of the robotic arm, and the following error to construct a training dataset D: in, f is a system state variable; ei Input force to the end effector of the robotic arm; The tracking error is represented by N; N is the total number of data points. Train a nonlinear mapping using training dataset D make: Where θ are model parameters, the objective is to minimize the difference between the prediction error and the actual error; During training, the loss function is optimized by minimizing it, and the loss function is constructed as follows: During training, when the actual error e i With prediction error If the deviation is large, the model parameters are adjusted, and gradient descent is used to update the model parameters: Where η is the learning rate. It is the gradient of the loss function with respect to the parameters; Training completes nonlinear mapping Subsequently, the prediction error for the control of the spatial dual-arm robot is... The specific formula is as follows:

2. The spatial dual-arm robot control method based on machine learning and LQR control as described in claim 1, characterized in that, The specific method for designing LQR optimal control is as follows: By incorporating the prediction error into the state equation, an extended state equation is constructed. Design the objective function of the LQR controller; Solve the Riccati equations to calculate the extended feedback gain matrix and the optimal control law.

3. The spatial dual-arm robot control method based on machine learning and LQR control as described in claim 2, characterized in that, The extended state equations are constructed as follows: Prediction error Introduced into the state equations, the dynamics of the original system are extended, and the state variables are expanded: but The extended equations are integrated into the state description: in In the extended system, the controller is designed using LQR optimization to minimize state deviation and control input energy consumption. The objective function is designed as follows: Where Q is the extended state weight matrix, which includes weights for position, velocity, and prediction error; R is the input weight matrix, which constrains the control energy.

4. The spatial dual-arm robot control method based on machine learning and LQR control as described in claim 3, characterized in that, Solving the Riccati equations and calculating the extended feedback gain matrix and optimal control law follows the specific method below: Solve the continuous Riccati equation, and use the solution P of the Riccati equation to calculate the extended feedback gain matrix K. ext : Where P is a symmetric positive definite matrix, describing the weights of the extended state; Based on P, calculate the extended feedback gain matrix: The final optimal control law is: u(t)=-K ext z ext (t) The unfolded form is as follows: Where K1 is the feedback gain of the controller to the state variable z(t); K2 is the feedback gain of the controller to the prediction error. Feedback gain.

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