Active compliant control method of robot based on model predictive control

Abstract

This invention discloses a robot active compliant control method based on model predictive control, which includes the following steps: obtaining a physical model of the robot and constructing a dynamic model of the robot; sampling the robot's historical path points on the surface of the manipulated object, and classifying and processing the historical path points; adjusting the position and posture of future path points relative to the manipulated object surface by fitting the trajectory of the historical path points; and utilizing the robot's kinematic and dynamic models, adopting a model predictive control method, minimizing the objective function and setting constraints to achieve precise motion and force control of the robot. This method has high robustness and anti-interference capabilities, and can adapt to different working scenarios and environmental conditions, improving the accuracy and reliability of operations.

Description

Technical Field

[0001] The present invention belongs to the field of robot motion control, and in particular relates to a robot active compliance control method based on model predictive control. Background Art

[0002] The surfaces of objects that robots operate on in actual operations are often not smooth, nor are they perfectly flat or curved. This is a common situation in many practical applications, such as the surfaces of complex workpieces, such as car bodies or airplane wings. The surfaces of objects being operated on may have edges and corners, which are usually where two or more curved surfaces intersect, and where the geometric features suddenly change. The presence of edges and corners makes the shape of the surface more complex, posing a challenge to the robot's operation and perception. The surface of the object being operated on may have raised particles or depressions, making the surface uneven. This situation is common on the surfaces of many materials or workpieces, such as the texture of wood surfaces and the unevenness of metal surfaces.

[0003] For such complex surfaces of operating objects, robots need to face the following challenges: robots need to be equipped with expensive sensors to obtain geometric information of the surface of the operating object, such as laser scanners, cameras and tactile sensors to obtain the shape, texture and changes of the surface. They also need to perform perception and data processing to accurately identify and model the features and shape of the surface of the operating object. Due to the complexity of the surface, robots may need to adopt more flexible motion strategies to adapt to surface changes and unevenness. For example, adjust the posture and motion trajectory of the robot's end effector according to the characteristics of the surface. The robot also needs to have adaptability and adjustment capabilities to cope with changes and imperfections in the surface of the operating object. This may involve the use of complex adaptive control algorithms, deformation sensors or flexible end effectors to achieve adaptation and adjustment to the surface unevenness. Summary of the Invention

[0004] The purpose of the present invention is to provide a robot active compliance control system based on model predictive control, which is used to solve the technical problem in existing solutions that robots cannot adaptively operate objects with complex surfaces.

[0005] The purpose of the present invention can be achieved through the following technical solutions:

[0006] A robot active compliance control method based on model predictive control is characterized by comprising:

[0007] Modeling: Obtain the physical model of the robot and build the robot's dynamic model;

[0008] Data processing: Based on the surface information of the robot's operating object, a series of historical path points are sampled within the contact range between the robot end and the operating object surface, the normal vectors of the historical path points are calculated, and they are classified into smooth points and non-smooth points;

[0009] Path optimization: Fit the trajectory of historical path points and adjust the path of the robot end according to the final fitted trajectory;

[0010] Implementation of control: Model predictive control is introduced. Based on the robot's dynamic model, the control input of the model predictive control is calculated by minimizing the objective function of the model predictive control and setting constraints. The constraints of the model predictive control include:

[0011] x i ∈X,i=0,……,N-1,x i is the system state at time i, X is the system state constraint set;

[0012] u i ∈U,i=0,……,N-1,u i is the system input at time i, and U is the system input constraint set;

[0013]

[0014]

[0015] Among them, F max is the maximum contact force applied by the robot end, A is the adjustment amount, S is the distance from the robot end to the operation object, S0 is the distance threshold, F b is the upper limit of contact force, F s The lower limit of contact force.

[0016] Preferably, the robot dynamics model introduces an uncertainty compensation term.

[0017] Preferably, in the control step, the contact force application is optimized by dynamically adjusting the contact force limit to adapt to different operating scenarios and working conditions.

[0018] Preferably, the contact force limit includes an upper limit and a lower limit of the contact force, and is dynamically adjusted based on the distance and motion state between the robot end and the operation object.

[0019] Preferably, the uncertainty compensation term is estimated based on experimental data, observer or machine learning method.

[0020] Preferably, in the data processing step, the historical waypoints are processed by constructing a local neighborhood covariance matrix of the historical waypoints and calculating eigenvalues and eigenvectors.

[0021] Preferably, weight coefficients are introduced in the construction process of the local neighborhood covariance matrix.

[0022] The present invention also provides a robot active compliance control system based on model predictive control, which is characterized by comprising:

[0023] A modeling module is used to obtain the physical model of the robot and build the dynamic model of the robot;

[0024] a data processing module for sampling a series of historical path points within the contact range between the robot end and the surface of the operation object based on the surface information of the robot's operation object, calculating the normal vectors of the historical path points, and classifying them into smooth points and non-smooth points;

[0025] The path optimization module is used to fit the trajectory of historical path points and adjust the path of the robot end according to the final fitting trajectory;

[0026] The controller module introduces model predictive control and calculates the control input of the model predictive control by minimizing the objective function of the model predictive control and setting constraints based on the robot's dynamic model. The constraints of the model predictive control include:

[0027] x i ∈X,i=0,……,N-1,x i is the system state at time i, X is the system state constraint set;

[0028] u i ∈U,i=0,……,N-1,u i is the system input at time i, and U is the system input constraint set;

[0029]

[0030]

[0031] Among them, F max is the maximum contact force applied by the robot end, A is the adjustment amount, S is the distance from the robot end to the operation object, S0 is the distance threshold, F b is the upper limit of contact force, F s The lower limit of contact force.

[0032] The present invention also provides a storage medium comprising at least one processor; and a memory communicatively connected to the at least one processor;

[0033] The memory stores a computer program that can be executed by at least one processor, and the computer program is executed by at least one processor so that the at least one processor can execute the aforementioned robot active compliant control method based on model predictive control.

[0034] Compared with the existing solutions, the present invention achieves the following beneficial effects:

[0035] The present invention can significantly improve the robustness and anti-interference ability of the robot dynamic model by introducing uncertainty compensation terms into the dynamic model. By calculating the normal vectors of historical path points, classifying smooth points and non-smooth points, and adaptively selecting the neighborhood size, the accuracy, robustness and immediacy of the normal vector estimation of the path points are improved. The classified smooth points are used to fit the overall trend, and the non-smooth points capture local changes, thereby ensuring the accuracy of path planning. The density of the path points is adjusted by up and down sampling to ensure the appropriate distribution of the path points, thereby optimizing the path planning of the robot on complex surfaces. The accuracy and efficiency of the fitting trajectory are improved by randomly extracting path points for preliminary fitting, and then through dual screening of the normal vector angle and spatial distance. The preliminary screening quickly eliminates fitting results that do not conform to the actual surface, and further distance screening ensures that the fitting trajectory not only matches well in the normal vector, but also conforms to the actual surface characteristics in terms of spatial distance, thereby improving the fitting accuracy.

[0036] Model predictive control technology, combined with a robot dynamics model, can more accurately predict the robot's end-point's trajectory and force trends, allowing for real-time adjustments to control inputs. Model predictive control calculates the optimal control input by optimizing the objective function within set constraints, enabling the robot's end-point to precisely follow the desired path while simultaneously adjusting the contact force to ensure rapid response and safe operation in dynamic environments. By setting upper and lower limits for the contact force and dynamically adjusting the contact force limits, the appropriate force is applied under varying distances and environmental conditions, thereby improving operational safety and efficiency. Dynamic contact force limits based on distance and motion state enable the robot to flexibly respond to diverse operational scenarios, maintaining appropriate contact force and enhancing operational accuracy and reliability. This precise control allows the robot to dynamically adjust force application based on the distance to the object being manipulated and environmental conditions, improving operational safety and efficiency and ensuring optimal operation in various scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The present invention will be further described below with reference to the accompanying drawings.

[0038] Figure 1 This is a flow chart of the robot active compliant control method based on model predictive control of the present invention.

[0039] Figure 2 Schematic diagram of the maximum contact force constraint for model predictive control. DETAILED DESCRIPTION

[0040] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0041] Example 1: Figure 1 As shown, this embodiment is a robot active compliance control method based on model predictive control, which includes the following steps:

[0042] 1. Modeling:

[0043] 1.1 Obtaining the Robot's Physical Model: Obtain a rigid-body dynamics model of the robot by modeling its geometry, mass, inertia, and other physical parameters. Specifically, establish the robot's geometric model, including parameters such as joint lengths and link lengths; determine the robot's mass distribution, including the mass of each link and joint; and estimate the robot's inertial parameters, such as the moment of inertia and center of mass.

[0044] 1.2 Constructing the robot's dynamic model: Using the Lagrangian dynamics method, the robot's motion equations are derived, including the relationship between joint angles, joint angular velocities, and joint torques. Considering the incompleteness of the model and the presence of external interference, uncertainty compensation terms can be introduced to optimize the robot's dynamic model. The compensation terms can be estimated based on experimental data, observers, or machine learning methods. The optimized robot dynamic model is as follows:

[0045]

[0046] Where τ is the joint torque, q d is the desired joint position, is the desired joint velocity, is the expected joint acceleration, M is the mass matrix, which describes the mass distribution of the robot joints, C is the Coriolis force matrix, which describes the centrifugal force and Coriolis force generated by the joint motion, and G is the gravity matrix, which describes the gravity effect caused by the robot mass. is the adaptive term, is the reference acceleration of the adaptive term, e is the joint position error, K p , K d are proportional gain and differential gain respectively. By introducing uncertainty compensation terms in the modeling step, the robustness and anti-interference ability of the model can be improved.

[0047] 2. Data processing:

[0048] 2.1 Sampling: Sample a series of historical path points within the contact range between the robot end and the surface of the operation object.

[0049] 2.2 Historical path point processing: Calculate the normal vectors of historical path points and classify them into smooth points and non-smooth points. Specifically, construct the local neighborhood covariance matrix of the historical path points and calculate the eigenvalues and eigenvectors of the covariance matrix. The eigenvector corresponding to the minimum eigenvalue is the normal vector of the historical path point. If the product of the minimum eigenvalue ratio of the historical path point and the standard deviation of the normal vector angle is greater than the feature threshold, the path point is a non-smooth point, otherwise it is a smooth point. Based on the classified path points, downsample the smooth points and / or upsample the non-smooth points to ensure a moderate density of path points.

[0050] Construct the local neighborhood covariance matrix of the historical path point. The following will take a historical path point as an example to explain it in detail. i As the center, R is the radius of the sphere encompassing all historical path points, constructing the historical path point p i The local neighborhood point set of . A fixed neighborhood size can be selected, or it is more optimal to dynamically and adaptively set the neighborhood based on the distance. Specifically, R∈[R min ,R max ], R min is the minimum neighborhood radius, R max is the maximum neighborhood radius. The determination of R includes:

[0051] Get the robot's historical path point p i The velocity v of the robot end at the time, and the historical path point p i With centered on the path, traverse the neighboring historical path points in a spherical manner from the center outward according to the radius from small to large, until the robot passes through the two closest historical path points with the velocities of the robot end being v-∆v and v+∆v respectively.

[0052] According to the distance between the two closest historical path points and [R min ,R max ], determine R, specifically: if the distance between the two closest historical path points is greater than R max , then R=R max , in the process of constructing the covariance matrix, the weights of the points in the local neighborhood point set are the same; if the distance between the two closest historical path points ∈ [R min ,R max ], then R is the distance between the two closest historical path points. In the process of constructing the covariance matrix, the weights of the points in the local neighborhood point set are the same; if the distance between the two closest historical path points is less than R min , then R=Rmin , and introduce weight coefficients in the process of covariance matrix construction, such as for historical path point p i The j-th point p in the local neighborhood point set j The weight coefficient is , where k,c∈R.

[0053] For historical path points in a fixed neighborhood, in the local neighborhood covariance matrix process, the weights of each point in the local neighborhood point set can be the same, and weight coefficients can be introduced as needed. The specific settings of the weight coefficients can be as shown above.

[0054] The eigenvalue represents the variance of the covariance matrix in the direction of each eigenvector, while the eigenvector represents the principal direction of the covariance matrix, i.e., the normal vector of that point. For each path point, the eigenvector corresponding to the minimum eigenvalue is selected as its neighborhood normal vector. The adaptive neighborhood size selection method ensures that more appropriate neighborhood points are included when calculating the path point normal vector, ensuring a smaller neighborhood in smooth areas and a larger neighborhood in complex areas (such as edges and corners). This improves the accuracy, robustness, and timeliness of the normal vector estimation. A weighting coefficient is introduced to ensure that points closer to the center point in the neighborhood contribute more to the normal vector estimation, while points farther away contribute less, improving the accuracy of the normal vector estimation, especially when processing complex surfaces. Historical path points are classified into smooth and non-smooth points. Smooth points are used to fit overall trends, while non-smooth points are used to capture local sharp changes, such as edges and corners. This results in a fitting trajectory that better matches the actual surface, improving fitting accuracy and efficiency. The minimum eigenvalue ratio is the ratio of the minimum eigenvalue of the covariance matrix to all eigenvalues, and the standard deviation of the normal vector angle is the historical path point p i The standard deviation of the normal vector angle of each point in its local neighborhood point set is used, and the product of the minimum eigenvalue ratio and the standard deviation of the normal vector angle is used as the judgment indicator. This can comprehensively reflect the geometric characteristics of the local surface of the path point, such as the smoothness of the local surface and the stability of the normal vector change, and improve the classification accuracy, robustness and stability.

[0055] 3. Path optimization: The specific steps are as follows: (1) Divide the smooth points into several regions to form several sets, and divide the non-smooth points into several regions to form several sets. Select a small number of path points from each smooth point set and more path points from the non-smooth point set to perform preliminary trajectory fitting; (2) Randomly extract a part of the smooth points and calculate the angle between their neighborhood normal vector and the trajectory normal vector of the corresponding projection point on the preliminary fitting trajectory; (3) Set the angle threshold and filter value. If the number of smooth points with an angle less than the angle threshold is greater than the filter value, proceed to the next step, otherwise return to step (1); (4) Randomly extract several smooth points and non-smooth points, calculate the distance from each extracted point to the current fitting trajectory, set the distance threshold and filter value. If the number of path points with a distance less than the distance threshold is greater than the filter value, determine the current fitting trajectory as the final fitting trajectory; otherwise return to step (1). Use the final fitting trajectory to correct the robot's future path and adjust the position and posture information of the path points relative to the surface of the object being operated.

[0056] By randomly selecting some path points for preliminary fitting, the amount of calculation can be effectively reduced. The preliminary screening of the normal vector angles of smooth points with higher precision can quickly eliminate fitting results that do not conform to the actual surface characteristics. Further distance screening ensures that the fitting trajectory not only matches well in normal vectors, but also conforms to the actual surface characteristics in spatial distance, thereby improving fitting accuracy.

[0057] 4. Implement control: Control the robot along the optimized future motion path of the robot end while controlling the force at the end. By introducing model predictive control, based on the robot's kinematic model, the control input u of the model predictive control is calculated by minimizing the objective function of the model predictive control and setting constraints. The specific robot dynamics model is:

[0058]

[0059] Where τ is the joint torque, F is the contact force, J is the Jacobian matrix, and q d is the desired joint position, is the desired joint velocity, is the expected joint acceleration, M is the mass matrix, which describes the mass distribution of the robot joints, C is the Coriolis force matrix, which describes the centrifugal force and Coriolis force generated by the joint motion, and G is the gravity matrix, which describes the gravity effect caused by the robot mass. is the adaptive term, is the reference acceleration of the adaptive term, e is the joint position error, K p , K d are the proportional gain and the differential gain respectively.

[0060] like Figure 2As shown in Figure 2, the constraints of model predictive control include:

[0061] x i+1 =f(x i ,u i ), x i is the system state at time i;

[0062] x i ∈X, i=0,……,N-1, N is the control time domain, X is the system state constraint set;

[0063] u i ∈U, i=0,……,N-1, U is the system input constraint set.

[0064]

[0065]

[0066] Among them, F max is the maximum contact force applied by the robot end, A is the adjustment amount, S is the distance from the robot end to the operation object, S0 is the distance threshold, F b F is the upper limit of contact force. s is the lower limit of contact force. The objective function of model control is J(x,u).

[0067] In the control step, the robot's kinematic and dynamic models are utilized, and model predictive control is employed to predict future states and behaviors, thereby adjusting the control input in real time. This allows for more accurate predictions of the robot's end-of-line motion trajectory and force trends, allowing the robot to more accurately follow the desired path while responding quickly in dynamic environments. This not only considers the optimized motion of the robot's end-of-line path, but also adjusts the end-of-line contact force in real time. By precisely controlling the contact force, the robot can ensure safety and precision when contacting the task object. For example, in assembly operations, the controller can adjust the contact force to avoid damaging parts or maintain appropriate friction to stabilize the workpiece. Dynamic contact force limits based on distance and motion state are introduced to adapt to different operating scenarios and working conditions. By dynamically adjusting the contact force limits, the application of contact force can be optimized under different distances and environmental conditions, thereby maximizing the safety and efficiency of the operation. For example, in collaborative robots, this capability can ensure a safe distance and contact force between the robot and the human operator.

[0068] The maximum contact force constraint includes force control strategies for different situations, corresponding to different force control strategies when the robot end approaches or moves away from the work object. This enables the system to flexibly respond to different working environments and task requirements, preventing the robot from applying excessive force, thereby avoiding damage to the object being operated or the robot itself. By adjusting the contact force, the interaction between the robot end and the surface can be more precisely controlled, thereby improving the accuracy of tracking unknown surfaces, increasing the robustness of the system, and reducing deviations caused by external disturbances or uncertainties. This precise control allows the robot to flexibly respond to different work scenarios, ensuring that the appropriate contact force is maintained at different distances, thereby improving the accuracy and reliability of operations.

[0069] Example 2: Figure 2 As shown, this embodiment is a robot active compliance control method based on impedance control, which includes the steps of modeling, data processing, path optimization, and implementation control, wherein the modeling, data processing, and path optimization steps can adopt the same or similar design as Example 1.

[0070] Specifically, in the control step, the robot is controlled to move along the optimized future motion path of the robot end through optimized impedance control, while the force at the robot end is controlled, specifically:

[0071]

[0072] Where ΔF is the difference between the desired contact force and the actual contact force at the end of the robot, m is the quality coefficient of the impedance control, E is the state error of the end of the robot, b is the damping coefficient, k is the stiffness coefficient, T is the control period, F is the desired contact force at the end of the robot, and F r is the actual contact force at the end of the robot, l r is the actual normal vector of the path point, and α is the control coefficient.

[0073] In the optimized impedance control, the damping part and the stiffness part are optimized, which can make the control system more flexible and adapt to the control requirements of the robot end force under different working conditions. At the same time, the force of the robot end can be controlled more accurately, which is especially important for applications that require fine operation and force control, such as medical robots, precision assembly and other fields. It can also enhance the system's ability to suppress external disturbances and improve the system's stability and reliability, especially in complex working environments. This ability is particularly prominent.

[0074] Example 3: This example is a method for active compliance control of a robot, which includes the steps of modeling, data processing, path optimization, and implementation control, wherein the modeling, data processing, and path optimization steps can adopt the same or similar design as that of Example 1.

[0075] Specifically, in the control implementation step, the robot's motion is adjusted to fit the optimized path by integrating a hybrid control method of model predictive control and impedance control.

[0076] The integrated control input u bind =γu m +(1-γ)u z , where γ is the balance coefficient, preferably sin 2 θ, θ is the angle between the contact force and the normal vector of the path point, u m is the input of the model predictive control, which can be equal to the input in Example 1, u z is the impedance-controlled input, which can be equal to the input in Example 2.

[0077] In the control implementation, model predictive control (MPC) is often used to optimize the robot's trajectory tracking, generating optimal control inputs by predicting future states. Impedance control, on the other hand, primarily controls contact forces and the forces at the robot's end-point. Combining these two control strategies, leveraging their respective strengths, can both optimize the robot's motion path and precisely control its forces and torques. The introduction of the parameter γ allows it to dynamically adjust with the robot's motion state, thereby balancing the influence of MPC and impedance control under varying motion paths and operating conditions. For example, when the robot needs to more precisely follow the optimized path (when θ is small), γ is larger, relying more on MPC inputs. However, when responding to large changes in external forces (when θ is large), γ is smaller, relying more on impedance control inputs. By integrating MPC and impedance control, more accurate and smoother robot path tracking can be achieved. MPC optimizes the prediction of future motion states, enabling the robot to more accurately follow the optimized path; simultaneously, impedance control effectively adjusts forces and torques to adapt to changes in the external environment and task requirements. The dynamic adjustment of parameter γ makes the control system more adaptable and flexible. In practice, this means the robot can quickly respond to environmental changes while maintaining stable trajectory tracking and force control performance. By properly distributing control inputs, energy consumption can be effectively optimized, especially in applications with long operating times and high energy conservation requirements. Model predictive control helps reduce unnecessary motion, while impedance control effectively balances energy consumption with task execution requirements.

[0078] Embodiment 4: This embodiment is a robot active compliance control system, which includes a modeling module, a data processing module, a path optimization module and a controller module. Each module is used to implement the relevant steps of any of the above embodiments.

[0079] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the present invention.

[0080] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention.

Claims

1. A robot active compliant control method based on model predictive control, characterized in that: include: Modeling: Obtain the physical model of the robot and build the robot's dynamic model; Data processing: Sample a series of historical path points within the contact range between the robot end and the surface of the object being operated, calculate the normal vectors of the historical path points, and classify them into smooth points and non-smooth points; Path optimization: Fit the trajectory of historical path points and adjust the path of the robot end according to the final fitted trajectory; Implementing control: Introducing model predictive control. Based on the robot's dynamic model, the control input of the model predictive control is calculated by minimizing the objective function of the model predictive control and setting constraints. The constraints of model predictive control include: x i ∈X,i=0,……,N-1,x i is the system state at time i, N is the control time domain, and X is the system state constraint set; u i ∈U,i=0,……,N-1,u i is the system input at time i, and U is the system input constraint set; ； ； Where F is the contact force applied by the robot end, F max is the maximum contact force applied by the robot end, A is the adjustment amount, S is the distance from the robot end to the operation object, S0 is the distance threshold, F b F is the upper limit of contact force. s The lower limit of contact force.

2. The robot active compliance control method based on model predictive control according to claim 1 is characterized in that: The robot dynamic model is: , where τ is the joint torque, F is the contact force, J is the Jacobian matrix, and q d is the desired joint position, is the desired joint velocity, is the expected joint acceleration, M is the mass matrix, which describes the mass distribution of the robot joints, C is the Coriolis force matrix, which describes the centrifugal force and Coriolis force generated by the joint motion, and G is the gravity matrix, which describes the gravity effect caused by the robot mass. is the adaptive term, is the reference acceleration of the adaptive term, e is the joint position error, K p , K d are the proportional gain and the differential gain respectively.

3. The robot active compliance control method based on model predictive control according to claim 1, characterized in that: Uncertainty compensation terms are introduced into the robot dynamics model.

4. The robot active compliance control method based on model predictive control according to claim 1, characterized in that: In the implementation control step, the contact force application is optimized by dynamically adjusting the contact force limit to adapt to different operating scenarios and working conditions.

5. The robot active compliance control method based on model predictive control according to claim 4 is characterized in that: The contact force limit includes the upper and lower limits of the contact force, and is dynamically adjusted based on the distance and motion state between the robot end and the operation object.

6. The robot active compliance control method based on model predictive control according to claim 1, characterized in that: The uncertainty compensation term is estimated based on experimental data, observers or machine learning methods.

7. The robot active compliance control method based on model predictive control according to claim 1, characterized in that: In the data processing step, the historical path points are processed by constructing the local neighborhood covariance matrix of the historical path points and calculating the eigenvalues and eigenvectors.

8. The robot active compliance control method based on model predictive control according to claim 7, characterized in that: The weight coefficients are introduced in the construction process of the local neighborhood covariance matrix.

9. A robot active compliance control system based on model predictive control, characterized in that: include: A modeling module is used to obtain the physical model of the robot and build the dynamic model of the robot; a data processing module for sampling a series of historical path points within the contact range between the robot end and the surface of the operation object based on the surface information of the robot's operation object, calculating the normal vectors of the historical path points, and classifying them into smooth points and non-smooth points; The path optimization module is used to fit the trajectory of historical path points and adjust the path of the robot end according to the final fitting trajectory; The controller module introduces model predictive control, calculates the control input of the model predictive control by minimizing the objective function of the model predictive control and setting constraints based on the robot's dynamic model; The constraints of model predictive control include: x i ∈X,i=0,……,N-1,x i is the system state at time i, N is the control time domain, and X is the system state constraint set; u i ∈U,i=0,……,N-1,u i is the system input at time i, and U is the system input constraint set; ； ； Where F is the contact force applied by the robot end, F max is the maximum contact force applied by the robot end, A is the adjustment amount, S is the distance from the robot end to the operation object, S0 is the distance threshold, F b F is the upper limit of contact force. s The lower limit of contact force.

10. A storage medium comprising at least one processor; and a memory communicatively connected to the at least one processor; in, The memory stores a computer program that can be executed by at least one processor, and the computer program is executed by at least one processor so that the at least one processor can execute the robot active compliant control method based on model predictive control as described in any one of claims 1-8.

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