A data-driven rolling horizon dynamics prediction method

Abstract

The present invention discloses a data-driven rolling time-domain dynamics prediction method, which first initializes the working state of the robot arm, and then generates the speed information of the end of the robot arm based on the data-driven rolling time-domain model prediction; next, according to the collected position information and the predicted speed information, a non-singular terminal sliding surface is designed to perform a human-computer interaction process; finally, according to the position information updated by the system, the model prediction is continued to generate speed information to complete the algorithm closed loop. The method of the present invention can better take into account both dynamic performance and steady-state performance, and ensure that the trajectory tracking error of the robot arm converges within a limited time.

Description

Technical Field

[0001] The invention belongs to the technical field of robots, and in particular relates to a rolling time-domain dynamics prediction method. Background Art

[0002] The dynamic model prediction method studied in the present invention is based on a human-machine collaborative robot system. The system uses human experience in scene recognition and the evaluation of high-dynamic induction factors as the top-level link of control decision-making, reducing the probability of problems in the process of handling complex or emergency events due to insufficient robot intelligence. The trajectory tracking control of the end of the robot arm in this system is the main research object. However, whether the system accurately collects the robot's own position and speed information directly affects the performance of the control algorithm. However, most of the current speed sensors have problems such as high cost, susceptibility to external interference, and easy damage, so that the collected speed information cannot be directly used in the control system. A series of data filtering and data accuracy identification work is required, which greatly increases the design cost of the control algorithm.

[0003] In addition, the human-machine collaborative robot system has the characteristics of complex dynamic coupling, inherent nonlinearity and model parameter uncertainty, which makes some model-based observer design methods unable to be applied to the system. Summary of the invention

[0004] In order to overcome the shortcomings of the prior art, the present invention provides a data-driven rolling time-domain dynamics prediction method, which first initializes the working state of the robot arm, and then generates the speed information of the end of the robot arm based on the data-driven rolling time-domain model prediction; next, according to the collected position information and the predicted speed information, a non-singular terminal sliding surface is designed to perform a human-computer interaction process; finally, according to the position information updated by the system, the model prediction is continued to generate speed information to complete the algorithm closed loop. The method of the present invention can better take into account both dynamic performance and steady-state performance, and ensure that the trajectory tracking error of the robot arm converges within a limited time.

[0005] The technical solution adopted by the present invention to solve the technical problem includes the following steps:

[0006] Step 1: Initialize the working state of the robotic arm;

[0007] The robot performs a given motion, and the position sensor and speed sensor collect a sequence of position and speed data of the robot;

[0008] Step 2: Generate the velocity information of the end of the robot arm based on the data-driven rolling time domain model prediction;

[0009] Step 2-1: The 3-DOF robot arm dynamics model of the human-machine interaction process in the robot joint space is organized into the following form through the Lagrangian method:

[0010]

[0011] in, is the angular acceleration vector at the end of the robotic arm, is the angular velocity vector of the end of the robot arm, is the angle vector at the end of the robot arm; is the inertia matrix of the end of the robotic arm, is the centripetal force / Coriolis force matrix at the end of the robot arm, The gravity vector at the end of the robot arm; represents the control law generated by the controller to complete the trajectory tracking task;

[0012] Step 2-2: Using the Euler discretization method, the dynamic model of the robot arm (1) is discretized to obtain the following mathematical description:

[0013] △q(t+1)=△q(t)+δM(q(t)) -1 [τ c (t)-C(△q(t),q(t))△q(t)-G(t)] (2)

[0014] Where M(q(t)) -1 is the inverse matrix of the inertia matrix M(q(t)) at the end of the manipulator at time t, δ is the sampling time of the system, τ c (t) is the sampling value of the control law generated by the controller at time t to ensure that the system can stably track the desired trajectory; △q(t+1) is the sampling value at time t+1 The sampling value described by the difference of the sequence, △q(t) is the sampling value at time t The sampling value described by the difference of the sequence is expressed in the following mathematical form:

[0015]

[0016]

[0017] In the above formula, q(t+2) is the sampling value of the q sequence of the joint angle of the end of the robot arm at time t+2, q(t+1) is the sampling value of the q sequence of the joint angle of the end of the robot arm at time t+1, and q(t) is the sampling value of the q sequence of the joint angle of the end of the robot arm at time t;

[0018] Step 2-3: For the discretized joint space robot dynamics model (2), select the generalized state variable x(t) = (q(t) T ,△q(t)T ) T , where q(t) T is the row vector of vector q(t), △q(t) T is the row vector of vector △q(t), and then formula (2) can be rewritten as a standard nonlinear discrete time state space equation:

[0019]

[0020] The system output is expressed as h(x(t))=q(t); since the model parameters are unknown, f(x(t)) is a nonlinear unknown function, and its mathematical description is as follows:

[0021]

[0022] Step 2-4: Use the linearization method to find the state equilibrium point of the linearized system. The above nonlinear discrete time state space equation (5) is linearized to the following form:

[0023]

[0024] in, and represents the unknown linearization residual, and the linearization deviation of the state equation is expressed as The linearized deviation of the output equation is expressed as And since the system model is unknown, the above ω(t) and ν(t) are both unknown parameters and need to be predicted using a data-driven model prediction method;

[0025] Step 2-5: Define a historical data sequence for data driving as {x [-T,0] ,y [-T,-1]}, which satisfies:

[0026]

[0027] Where x(-T) T is the row vector of the sampled values ​​of the x sequence at time -T, y(-T) T is the row vector of the sampled values ​​of the y sequence at time -T; at time t>0, the length of the rolling time domain window is defined as M t =min{t,M}, where t is the current time of the system, M is the designed maximum rolling time domain prediction length, which needs to satisfy T>2(M+1); the optimization problem is created through formula (8):

[0028]

[0029] The following constraints need to be met:

[0030]

[0031] In the optimization problem (8), ρ is a constant and satisfies ρ∈(0,1], represents the state prediction sequence based on data-driven at time t, is a true value sequence In tM t The prior value at time t, α(t) is the parameter vector of the optimization problem at time t, Indicates tM corresponding to time t t The predicted value at the moment; Represents a depth of M t , the element sequence is y [-T,-1] The Hankel matrix of is described mathematically as follows:

[0032]

[0033] in, y(tM t +δ) T ,…,y(t-1) T ) T represents the historical data sequence collected at time t, Indicates that at time t based on the historical data sequence (x(-T) T ,x(-T+δ) T ,…,x(0) T ) T Predicted values ​​generated using data-driven model prediction methods;

[0034] Step 3: Based on the collected position information and predicted speed information, a non-singular terminal sliding surface is designed to carry out the human-computer interaction process;

[0035] Step 3-1: In a collaborative robot system, the relationship between the operator's force and the desired trajectory of the robot end effector is described in the joint space as follows:

[0036]

[0037] where q d , as well as are the joint angle, angular velocity, and angular acceleration of the desired trajectory of the robot end effector, respectively; represents the operator force used to generate the desired trajectory; as well as Represent the mass matrix, damping matrix and elastic matrix of the desired impedance structure respectively;

[0038] Step 3-2: When designing the controller, the predicted speed information is used instead of the speed information collected by the sensor for control; in the joint space, the dynamic model of the human-machine collaborative robot system based on continuous time is expressed as:

[0039]

[0040] in, is the angular acceleration vector at the end of the robotic arm, is the angular velocity vector of the end of the robot arm, is the angle vector at the end of the robot arm; is the inertia matrix of the end of the robotic arm, is the centripetal force / Coriolis force matrix at the end of the robot arm, The gravity vector at the end of the robot arm; represents the control law generated by the controller to complete the trajectory tracking task;

[0041] Step 3-3: Use the non-singular terminal sliding mode control method to control the robot arm. The non-singular terminal sliding mode surface is expressed as:

[0042]

[0043] in, Represents the angle tracking error, satisfying e=q m -q d , Represents the angular velocity tracking error, satisfying β, a and b are sliding surface parameters, satisfying β>0, 1<a / b<2 and a and b are both positive odd numbers; according to the dynamic model of the end effector of the robot arm (12) and the non-singular terminal sliding surface (13), the following control rate is designed to ensure that the end effector of the robot arm can stably track the desired trajectory:

[0044]

[0045] Among them, D>0, η>0 is used to ensure the stability of the system, sat(s) represents the saturation function of the non-singular terminal sliding surface s, which satisfies the following form:

[0046]

[0047] Where ζ>0 is the boundary layer, which is used to reduce the chattering phenomenon in sliding mode control;

[0048] Step 4: Return to step 2 based on the position information updated by the system to continue model prediction to generate speed information and complete the algorithm closed loop.

[0049] The beneficial effects of the present invention are as follows:

[0050] The method of the present invention is not affected by the system model. It only needs a relatively stable position and speed information of the system to predict relatively accurate speed information according to the subsequent position change of the system. In the whole human-machine interaction process, the robot speed information predicted by the method of the present invention is adopted, and the control system can better take into account the dynamic performance and steady-state performance at the same time, and ensure that the trajectory tracking error of the robot arm converges within a limited time. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 This is the angular velocity prediction in the X-axis direction of the embodiment of the present invention.

[0052] Figure 2 This is the angular velocity prediction in the Y-axis direction of the embodiment of the present invention.

[0053] Figure 3 This is the angular velocity prediction in the Z-axis direction of the embodiment of the present invention.

[0054] Figure 4 The figure shows the trajectory tracking of the end effector of the robot arm in the X-axis direction according to the embodiment of the present invention.

[0055] Figure 5 The figure shows the trajectory tracking of the end effector of the robot arm in the Y-axis direction according to the embodiment of the present invention.

[0056] Figure 6 The figure shows the trajectory tracking of the end effector of the robot arm in the Z-axis direction according to the embodiment of the present invention. DETAILED DESCRIPTION

[0057] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0058] In view of the above problems, the present invention designs a data-driven rolling time-domain dynamics prediction method for predicting the complex dynamics model of the robot during the interaction process, which includes the following parts:

[0059] 1. Data-driven rolling horizon dynamics prediction method

[0060] The 3-DOF robot arm dynamics model of the human-machine interaction process in the joint space can be organized into the following form by the Lagrangian method:

[0061]

[0062] in, is the angular acceleration vector at the end of the robotic arm, is the angular velocity vector of the end of the robot arm, is the angle vector at the end of the robot arm; is the inertia matrix of the end of the robotic arm, is the centripetal force / Coriolis force matrix at the end of the robot arm, The gravity vector at the end of the robot arm; Represents the control law generated by the controller to complete the trajectory tracking task.

[0063] Using the Euler discretization method, the dynamic model (1) of the robot arm is discretized to obtain the following mathematical description:

[0064] △q(t+1)=△q(t)+δM(q(t)) -1 [τ c (t)-C(△q(t),q(t))△q(t)-G(t)] (2)

[0065] Where M(q(t)) -1 is the inverse matrix of the inertia matrix M(q(t)) at the end of the manipulator at time t, δ is the sampling time of the system, τ c (t) is the sampling value of the control law generated by the controller at time t to ensure that the system can stably track the desired trajectory. △q(t+1) is the sampling value of the control law generated by the controller at time t to ensure that the system can stably track the desired trajectory. The sampling value described by the difference of the sequence, △q(t) is the sampling value at time t The sampling value described by the difference of the sequence can be expressed mathematically as follows:

[0066]

[0067]

[0068] In the above formula, q(t+2) is the sampling value of the q sequence of the joint angle at the end of the robot arm at time t+2, q(t+1) is the sampling value of the q sequence of the joint angle at the end of the robot arm at time t+1, and q(t) is the sampling value of the q sequence of the joint angle at the end of the robot arm at time t. In this system, the sampling values ​​of the q sequence of the joint angle at the end of the robot arm are relatively smooth.

[0069] For the discretized joint space robot dynamics model (2), select the generalized state variable x(t) = (q(t) T ,△q(t) T ) T , where q(t) T is the row vector of vector q(t), △q(t) T is the row vector of vector △q(t), and then formula (2) can be rewritten as a standard nonlinear discrete time state space equation:

[0070]

[0071] The system output can be expressed as h(x(t))=q(t). Since the model parameters are unknown, f(x(t)) is a nonlinear unknown function, and its mathematical description is as follows:

[0072]

[0073] Using the linearization method, at the state equilibrium point of the linearized system Linearizing the above nonlinear discrete time state space equation (5) gives the following form:

[0074]

[0075] in, and Represents the unknown linearization residual, and the linearization deviation of the state equation can be expressed as The linearization deviation of the output equation can be expressed as And since the system model is unknown, the above ω(t) and ν(t) are both unknown parameters and need to be predicted using a data-driven model prediction method.

[0076] Assuming that the speed sensor is disturbed by the external environment and cannot operate normally at t = 0, it is necessary to use a data-driven model prediction method to predict the dynamic model of the system and obtain the speed information of the system. Define a historical data sequence for data driving as {x [-T,0] ,y [-T,-1]}, which satisfies:

[0077]

[0078] Where x(-T) T is the row vector of the sampled values ​​of the x sequence at time -T, y(-T) T is the row vector of the sampled values ​​of the y sequence at time -T. At time t>0, the length of the rolling time domain window is defined as M t =min{t,M}, where t is the current time of the system, M is the designed maximum rolling time domain prediction length, and it is necessary to satisfy T>2(M+1). The optimization problem is created by the following formula:

[0079]

[0080] The following constraints need to be met:

[0081]

[0082] In the optimization problem (8), ρ is constant and satisfies ρ∈(0,1], represents the state prediction sequence based on data-driven at time t, is the true value sequence x in tM t The prior value at time t, α(t) is the parameter vector of the optimization problem at time t, Indicates tM corresponding to time t t The predicted value at time. Represents a depth of M t , the element sequence is y [-T,-1] The Hankel matrix of is described mathematically as follows:

[0083]

[0084] in, y(tM t +δ) T ,…,y(t-1) T ) T Represents the historical data sequence collected at time t, which ensures that the data-driven rolling time domain dynamics prediction method can adjust the predicted value accordingly according to the changes in the current state of the system and the predicted dynamics model. Indicates that at time t based on the historical data sequence (x(-T) T ,x(-T+δ) T ,…,x(0) T ) T The prediction value generated by the data-driven model prediction method. By creating an optimization problem (8) and setting corresponding constraints (9), it can be ensured that the prediction error of the prediction method designed by the present invention is bounded.

[0085] 2. Human-computer interaction dynamics model

[0086] In a collaborative robot system, the relationship between the operator’s force and the desired trajectory of the robot’s end effector can be described mathematically in the joint space as follows:

[0087]

[0088] where q d , as well as are the joint angle, angular velocity, and angular acceleration of the desired trajectory of the robot end effector, respectively; represents the operator force used to generate the desired trajectory. In this system, the operator's force needs to be accurately measured by the sensor to generate a relatively smooth desired trajectory; as well as They represent the mass matrix, damping matrix, and elastic matrix of the expected impedance structure respectively. By adjusting these parameters, the operator can obtain the expected operating experience during the human-computer interaction process.

[0089] 3. Design of controller for human-machine collaborative robot system

[0090] In order to verify the data-driven rolling time domain dynamics prediction method proposed in this invention, the predicted speed information will be used instead of the speed information collected by the sensor for control when designing the controller. In the joint space, the dynamics model of the human-machine collaborative robot system based on continuous time can be expressed as:

[0091]

[0092] in, is the angular acceleration vector at the end of the robotic arm, is the angular velocity vector of the end of the robot arm, is the angle vector at the end of the robot arm; is the inertia matrix of the end of the robotic arm, is the centripetal force / Coriolis force matrix at the end of the robot arm, The gravity vector at the end of the robot arm; Represents the control law generated by the controller to complete the trajectory tracking task. In order to further highlight the accuracy of the predicted speed information, this design uses a non-singular terminal sliding mode control method with high requirements on speed information to control the manipulator. The non-singular terminal sliding mode surface can be expressed as:

[0093]

[0094] in, Represents the angle tracking error, satisfying e=q m -q d , Represents the angular velocity tracking error, satisfying β, a and b are sliding surface parameters, satisfying β>0, 1<a / b<2 and a and b are both positive odd numbers. According to the dynamic model of the end effector of the robot arm (12) and the non-singular terminal sliding surface (13), the following control rate can be designed to ensure that the end effector of the robot arm can stably track the desired trajectory:

[0095]

[0096] Among them, D>0, η>0 is used to ensure the stability of the system, sat(s) represents the saturation function of the non-singular terminal sliding surface s, which satisfies the following form:

[0097]

[0098] Where ζ>0 is the boundary layer, which is used to reduce the chattering phenomenon in the sliding mode control. According to the non-singular terminal sliding mode control method designed above, combined with the data-driven rolling time domain dynamics prediction method, it can ensure that the end effector of the robot arm can stably and accurately track the desired trajectory, while taking into account the dynamic performance and steady-state performance of the system. Specific embodiment:

[0100] Step 1: Initialize the working state of the robotic arm.

[0101] The robot performs a given movement, which requires the normal operation of components such as position sensors and velocity sensors to collect a relatively stable sequence of position and velocity data, providing the necessary driving data for the subsequent data-driven rolling time-domain dynamics prediction method.

[0102] Step 2: Generate the velocity information of the end of the robotic arm based on the data-driven rolling time domain model prediction.

[0103] The 3-DOF robot arm dynamics model of the human-machine interaction process in the joint space can be organized into the following form by the Lagrangian method:

[0104]

[0105] in, is the angular acceleration vector at the end of the robotic arm, is the angular velocity vector of the end of the robot arm, is the angle vector at the end of the robot arm; is the inertia matrix of the end of the robotic arm, is the centripetal force / Coriolis force matrix at the end of the robot arm, The gravity vector at the end of the robot arm; Represents the control law generated by the controller to complete the trajectory tracking task.

[0106] Using the Euler discretization method, the dynamic model (1) of the robot arm is discretized to obtain the following mathematical description:

[0107] △q(t+1)=△q(t)+δM(q(t)) -1 [τ c (t)-C(△ q (t),q( t ))△ q ( t )-G( t )] (17)

[0108] Where M(q(t)) -1 is the inverse matrix of the inertia matrix M(q(t)) at the end of the manipulator at time t, δ is the sampling time of the system, τ c(t) is the sampling value of the control law generated by the controller at time t to ensure that the system can stably track the desired trajectory. △q(t+1) is the sampling value of the control law generated by the controller at time t to ensure that the system can stably track the desired trajectory. The sampling value described by the difference of the sequence, △q(t) is the sampling value at time t The sampling value described by the difference of the sequence can be expressed mathematically as follows:

[0109]

[0110]

[0111] In the above formula, q(t+2) is the sampling value of the q sequence of the joint angle at the end of the robot arm at time t+2, q(t+1) is the sampling value of the q sequence of the joint angle at the end of the robot arm at time t+1, and q(t) is the sampling value of the q sequence of the joint angle at the end of the robot arm at time t. In this system, the sampling values ​​of the q sequence of the joint angle at the end of the robot arm are relatively smooth.

[0112] For the discretized joint space robot dynamics model (2), select the generalized state variable x(t) = (q(t) T ,△q(t) T ) T , where q(t) T is the row vector of vector q(t), △q( t ) T is the row vector of vector △q(t), and then formula (2) can be rewritten as a standard nonlinear discrete time state space equation:

[0113]

[0114] The system output can be expressed as h(x(t))=q(t). Since the model parameters are unknown, f(x(t)) is a nonlinear unknown function, and its mathematical description is as follows:

[0115]

[0116] Using the linearization method, at the state equilibrium point of the linearized system Linearizing the above nonlinear discrete time state space equation (5) gives the following form:

[0117]

[0118] in, and Represents the unknown linearization residual, and the linearization deviation of the state equation can be expressed as The linearization deviation of the output equation can be expressed as And since the system model is unknown, the above ω(t) and ν(t) are both unknown parameters and need to be predicted using a data-driven model prediction method.

[0119] assumed t = 0, the speed sensor is disturbed by the external environment and cannot operate normally. It is necessary to use a data-driven model prediction method to predict the dynamic model of the system and obtain the speed information of the system. Define a historical data sequence for data driving as {x [-T,0] ,y [-T,-1]}, which satisfies:

[0120]

[0121] in x (-T) T is the row vector of the sampled values ​​of the x sequence at time -T, y(-T) T is the row vector of the sampled values ​​of the y sequence at time -T. At time t>0, the length of the rolling time domain window is defined as M t =min{t,M}, where t is the current time of the system, M is the designed maximum rolling time domain prediction length, and it is necessary to satisfy T>2(M+1). The optimization problem is created by the following formula:

[0122]

[0123] The following constraints need to be met:

[0124]

[0125] In the optimization problem (8), ρ is constant and satisfies ρ∈(0,1], represents the state prediction sequence based on data-driven at time t, is the true value sequence x in tM t The prior value at time t, α(t) is the parameter vector of the optimization problem at time t, Indicates tM corresponding to time t t The predicted value at time. Represents a depth of M t , the element sequence is y [-T,-1] The Hankel matrix of is described mathematically as follows:

[0126]

[0127] in, y(tM t +δ) T ,…,y(t-1) T ) TRepresents the historical data sequence collected at time t, which ensures that the data-driven rolling time domain dynamics prediction method can adjust the predicted value accordingly according to the changes in the current state of the system and the predicted dynamics model. Indicates that at time t based on the historical data sequence (x(-T) T ,x(-T+δ) T ,…,x(0) T ) T The prediction value generated by the data-driven model prediction method. By creating an optimization problem (8) and setting corresponding constraints (9), it can be ensured that the prediction error of the prediction method designed by the present invention is bounded.

[0128] Step 3: Based on the collected position information and predicted speed information, a non-singular terminal sliding surface is designed to carry out the human-computer interaction process.

[0129] In a collaborative robot system, the relationship between the operator’s force and the desired trajectory of the robot’s end effector can be described mathematically in the joint space as follows:

[0130]

[0131] where q d , as well as are the joint angle, angular velocity, and angular acceleration of the desired trajectory of the robot end effector, respectively; represents the operator force used to generate the desired trajectory. In this system, the operator's force needs to be accurately measured by the sensor to generate a relatively smooth desired trajectory; as well as They represent the mass matrix, damping matrix, and elastic matrix of the expected impedance structure respectively. By adjusting these parameters, the operator can obtain the expected operating experience during the human-computer interaction process.

[0132] In order to verify the data-driven rolling time domain dynamics prediction method proposed in this invention, the predicted speed information will be used instead of the speed information collected by the sensor for control when designing the controller. In the joint space, the dynamics model of the human-machine collaborative robot system based on continuous time can be expressed as:

[0133]

[0134] in, is the angular acceleration vector at the end of the robotic arm, is the angular velocity vector of the end of the robot arm, is the angle vector at the end of the robot arm; is the inertia matrix of the end of the robotic arm, is the centripetal force / Coriolis force matrix at the end of the robot arm, The gravity vector at the end of the robot arm; Represents the control law generated by the controller to complete the trajectory tracking task. In order to further highlight the accuracy of the predicted speed information, this design uses a non-singular terminal sliding mode control method with high requirements on speed information to control the manipulator. The non-singular terminal sliding mode surface can be expressed as:

[0135]

[0136] in, Represents the angle tracking error, satisfying e=q m -q d , Represents the angular velocity tracking error, satisfying β, a and b are sliding surface parameters, satisfying β>0, 1<a / b<2 and a and b are both positive odd numbers. According to the dynamic model of the end effector of the robot arm (12) and the non-singular terminal sliding surface (13), the following control rate can be designed to ensure that the end effector of the robot arm can stably track the desired trajectory:

[0137]

[0138] Among them, D>0, η>0 is used to ensure the stability of the system, sat(s) represents the saturation function of the non-singular terminal sliding surface s, which satisfies the following form:

[0139]

[0140] Where ζ>0 is the boundary layer, which is used to reduce the chattering phenomenon in the sliding mode control. According to the non-singular terminal sliding mode control method designed above, combined with the data-driven rolling time domain dynamics prediction method, it can ensure that the end effector of the robot arm can stably and accurately track the desired trajectory, while taking into account the dynamic performance and steady-state performance of the system.

[0141] According to the position information updated by the system, return to step 2 to continue model prediction to generate speed information, completing the algorithm closed loop.

Claims

1. A data-driven rolling time domain dynamics prediction method, characterized in that: The following steps are involved: Step 1: Initialize the working state of the robotic arm; The robot performs a given motion, and the position sensor and speed sensor collect a sequence of position and speed data of the robot; Step 2: Generate the velocity information of the end of the robot arm based on the data-driven rolling time domain model prediction; Step 2-1: The 3-DOF robot arm dynamics model of the human-machine interaction process in the robot joint space is organized into the following form through the Lagrangian method: in, is the angular acceleration vector at the end of the robotic arm, is the angular velocity vector of the end of the robot arm, is the angle vector at the end of the robot arm; is the inertia matrix of the end of the robotic arm, is the centripetal force / Coriolis force matrix at the end of the robot arm, The gravity vector at the end of the robot arm; represents the control law generated by the controller to complete the trajectory tracking task; Step 2-2: Using the Euler discretization method, the dynamic model of the robot (1) is discretized to obtain the following mathematical description: △q(t+1)=△q(t)+δM(q(t)) -1 [τ c (t)-C(△q(t),q(t))△q(t)-G(t)] (2) Among them, M(q(t)) -1 is the inverse matrix of the inertia matrix M(q(t)) at the end of the manipulator at time t, δ is the sampling time of the system, τ c (t) is the sampling value of the control law generated by the controller at time t to ensure that the system can stably track the desired trajectory; △q(t+1) is the sampling value at time t+1 The sampling value described by the difference of the sequence, △q(t) is the sampling value at time t The sampling value described by the difference of the sequence is expressed in the following mathematical form: In the above formula, q(t+2) is the sampling value of the q sequence of the joint angle of the end of the robot arm at time t+2, q(t+1) is the sampling value of the q sequence of the joint angle of the end of the robot arm at time t+1, and q(t) is the sampling value of the q sequence of the joint angle of the end of the robot arm at time t; Step 2-3: For the discretized joint space robot dynamics model (2), select the generalized state variable x(t) = (q(t) T ,△q(t) T ) T , where q(t) T is the row vector of vector q(t), △q(t) T is the row vector of vector △q(t), and then formula (2) can be rewritten as a standard nonlinear discrete time state space equation: The system output is expressed as h(x(t))=q(t); since the model parameters are unknown, f(x(t)) is a nonlinear unknown function, and its mathematical description is as follows: Step 2-4: Use the linearization method to find the state equilibrium point of the linearized system. The above nonlinear discrete time state space equation (5) is linearized to the following form: in, and represents the unknown linearization residual, and the linearization deviation of the state equation is expressed as The linearized deviation of the output equation is expressed as And since the system model is unknown, the above ω(t) and ν(t) are both unknown parameters and need to be predicted using a data-driven model prediction method; Step 2-5: Define a historical data sequence for data driving as {x [-T,0] ,y [-T,-1] }, which satisfies: Where x(-T) T is the row vector of the sampled values ​​of the x sequence at time -T, y(-T) T is the row vector of the sampled values ​​of the y sequence at time -T; at time t>0, the length of the rolling time domain window is defined as M t =min{t,M}, where t is the current time of the system, M is the designed maximum rolling time domain prediction length, which needs to satisfy T>2(M+1); the optimization problem is created through formula (8): The following constraints need to be met: In the optimization problem (8), ρ is a constant and satisfies ρ∈(0,1], represents the state prediction sequence based on data-driven at time t, is the true value sequence x in tM t The prior value at time t, α(t) is the parameter vector of the optimization problem at time t, Indicates tM corresponding to time t t The predicted value at the moment; Represents a depth of M t , the element sequence is y [-T,-1] The Hankel matrix of is described mathematically as follows: in, represents the historical data sequence collected at time t, Indicates that at time t based on the historical data sequence (x(-T) T ,x(-T+δ) T ,…,x(0) T ) T Predicted values ​​generated using data-driven model prediction methods; Step 3: Based on the collected position information and predicted speed information, a non-singular terminal sliding surface is designed to carry out the human-computer interaction process; Step 3-1: In a collaborative robot system, the relationship between the operator's force and the desired trajectory of the robot end effector is described in the joint space as follows: where q d , as well as are the joint angle, angular velocity, and angular acceleration of the desired trajectory of the robot end effector, respectively; represents the operator force used to generate the desired trajectory; as well as Represent the mass matrix, damping matrix and elastic matrix of the desired impedance structure respectively; Step 3-2: When designing the controller, the predicted speed information is used instead of the speed information collected by the sensor for control; in the joint space, the dynamic model of the human-machine collaborative robot system based on continuous time is expressed as: in, is the angular acceleration vector at the end of the robotic arm, is the angular velocity vector of the end of the robot arm, is the angle vector at the end of the robot arm; is the inertia matrix of the end of the robotic arm, is the centripetal force / Coriolis force matrix at the end of the robot arm, The gravity vector at the end of the robot arm; represents the control law generated by the controller to complete the trajectory tracking task; Step 3-3: Use the non-singular terminal sliding mode control method to control the robot arm. The non-singular terminal sliding mode surface is expressed as: in, Represents the angle tracking error, satisfying e=q m -q d , Represents the angular velocity tracking error, satisfying β, a and b are sliding surface parameters, satisfying β>0, 1<a / b<2 and a and b are both positive odd numbers; according to the dynamic model of the end effector of the robot arm (12) and the non-singular terminal sliding surface (13), the following control rate is designed to ensure that the end effector of the robot arm can stably track the desired trajectory: Among them, D>0, η>0 is used to ensure the stability of the system, sat(s) represents the saturation function of the non-singular terminal sliding surface s, which satisfies the following form: Where ζ>0 is the boundary layer, which is used to reduce the chattering phenomenon in sliding mode control; Step 4: Return to step 2 based on the position information updated by the system to continue model prediction and generate speed information.

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