Robot active compliance control method based on model predictive control

Abstract

The invention discloses a robot active compliance control method based on model predictive control. The robot active compliance control method comprises the following steps that a physical model of a robot is obtained, and a kinetic model of the robot is constructed; historical path points of the robot on the surface of the operation object are sampled, and the historical path points are classified and processed; through track fitting of the historical path points, the positions and poses of the future path points relative to the surface of the operation object are adjusted; according to the method, kinematics and dynamics models of the robot are utilized, a model predictive control method is adopted, and precise motion and force control of the robot are achieved by minimizing an objective function and setting constraint conditions. The method has high robustness and anti-interference capability, can adapt to different working scenes and environmental conditions, and improves the accuracy and reliability of operation.

Description

Technical Field

[0001] The 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 surfaces, nor are they perfectly flat or curved surfaces. This is common in many practical applications, such as the surfaces of complex workpieces, such as the body of a car or the wing of an airplane. The surfaces of objects that can be operated may have edges and corners, which are usually where two or more surfaces intersect and where geometric features suddenly change. The presence of edge points and corners makes the shape of the surface more complex, posing a challenge to the operation and perception of robots. The surface of an object that can be operated may have raised particles or depressions, making the surface not flat. This is common on the surfaces of many materials or workpieces, such as the texture of a wood surface, the bumps on a metal surface, etc.

[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 shapes 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, which may involve the use of complex adaptive control algorithms, deformation sensors or flexible end effectors to achieve adaptation and adjustment to the surface convexity and concavity. 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 that the robot in the existing solution cannot adaptively operate an operating object with a complex surface.

[0005] The purpose of the present invention can be achieved through the following technical solutions: The active compliance control method of a robot based on model predictive control is characterized by comprising: Modeling: Obtain the physical model of the robot and build the dynamic model of the robot; 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 surface of the operating object, the normal vectors of the historical path points are calculated, and they are classified into smooth points and non-smooth points; Path optimization: perform trajectory fitting on historical path points and adjust the path of the robot end according to the final fitting trajectory; Implement control: Introduce model predictive control. Based on the robot's dynamic model, minimize the objective function of model predictive control and set constraints to calculate the control input of model predictive control. The constraints of model predictive control include: x i ∈X,i=0,……,N-1,x i is the system state at time i, 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;

[0006]

[0007] 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, and F b is the upper limit of contact force, F s The contact force is the lower limit.

[0008] Preferably, the robot dynamics model introduces uncertainty compensation terms.

[0009] Preferably, in the implementation control step, the contact force limit is dynamically adjusted to adapt to different operating scenarios and working conditions and optimize the application of the contact force.

[0010] 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 from the robot end to the operation object.

[0011] Preferably, the uncertainty compensation term is estimated based on experimental data, observer or machine learning method.

[0012] 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.

[0013] Preferably, weight coefficients are introduced in the construction process of the local neighborhood covariance matrix.

[0014] The present invention also provides a robot active compliance control system based on model predictive control, which is characterized by comprising: A modeling module, which is used to obtain the physical model of the robot and build a dynamic model of the robot; A data processing module, which is used to sample a series of historical path points within the contact range between the robot end and the surface of the operation object according to the surface information of the operation object of the robot, calculate the normal vectors of the historical path points, and classify 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, based on the robot's dynamic model, minimizes the objective function of model predictive control, and sets constraints to calculate the control input of model predictive control; the constraints of model predictive control include: x i ∈X,i=0,……,N-1,x i is the system state at time i, 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;

[0015]

[0016] 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, and F b is the upper limit of contact force, F s The contact force is the lower limit.

[0017] The present invention also provides a storage medium, comprising at least one processor; and a memory in communication with the at least one processor; 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.

[0018] Compared with the existing solutions, the present invention achieves the following beneficial effects: The present invention can significantly improve the robustness and anti-interference ability of the robot dynamics model by introducing uncertainty compensation terms into the dynamics model. The accuracy, robustness and immediacy of the normal vector estimation of the path point are improved by calculating the normal vector of the historical path points, classifying the smooth points and the non-smooth points, and adaptively selecting the neighborhood size. The classified smooth points are used to fit the overall trend, and the non-smooth points capture the local changes, thereby ensuring the accuracy of the path planning. The density of the path points is adjusted by up and down sampling to ensure the moderate distribution of the path points, thereby optimizing the path planning of the robot on complex surfaces. The path points are randomly selected for preliminary fitting, and then the normal vector angle and spatial distance are double-screened to improve the accuracy and efficiency of the fitting trajectory. The preliminary screening quickly eliminates the fitting results that do not conform to the actual surface, and the 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 the spatial distance, thereby improving the fitting accuracy.

[0019] Through model predictive control technology, combined with the robot dynamics model, the motion trajectory and force change trend of the robot end can be predicted more accurately, and the control input can be adjusted in real time. Under the set constraints, model predictive control calculates the optimal control input by optimizing the objective function, so that the robot end moves accurately along the expected path, and adjusts the contact force at the same time to ensure the robot's rapid response and safe operation in a dynamic environment. The upper and lower limits of the contact force are set, and the contact force limit is dynamically adjusted to ensure that the appropriate force is applied under different distances and environmental conditions, thereby improving the safety and efficiency of the operation. The dynamic contact force limit based on distance and motion state enables the robot to respond flexibly in different work scenarios and maintain the appropriate contact force, thereby improving the accuracy and reliability of the operation. This precise control allows the robot to dynamically adjust the force application according to the distance and environmental conditions of the operation object, improve the safety and efficiency of the operation, and ensure the best working state in different scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The present invention will be further described below in conjunction with the accompanying drawings.

[0021] Figure 1 The present invention is a flow chart of the robot active compliance control method based on model predictive control.

[0022] Figure 2 Schematic diagram of the maximum contact force constraint for model predictive control. DETAILED DESCRIPTION

[0023] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. 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 creative work are within the scope of protection of the present invention.

[0024] 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: 1. Modeling: 1.1 Obtain the physical model of the robot: Obtain the rigid body dynamics model of the robot by modeling the robot's geometry, mass, inertia and other physical parameters. Specifically, establish the robot's geometric model, including parameters such as joint length and connecting rod length; determine the robot's mass distribution, including the mass of each connecting rod, the mass of the joint, etc.; estimate the robot's inertial parameters, such as moment of inertia, center of mass position, etc.

[0025] 1.2 Construct the dynamic model of the robot: Use the Lagrangian dynamics method to derive the robot's motion equations, which include the relationship between joint angles, joint angular velocities, and joint torques. Considering the incompleteness of the model and the existence 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 or observers or machine learning-based methods. The optimized robot dynamic model is as follows:

[0026] Where τ is the joint torque, q d is the desired joint position, is the expected joint velocity, is the expected joint acceleration, M is the mass matrix, describing the mass distribution of the robot joints, C is the Coriolis force matrix, describing the centrifugal force and Coriolis force generated by joint motion, G is the gravity matrix, describing the gravity effect caused by the robot mass, is an 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.

[0027] 2. Data processing: 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.

[0028] 2.2 Historical path point processing: Calculate the normal vectors of historical path points and classify historical path points into smooth points and non-smooth points. Specifically: construct the local neighborhood covariance matrix of 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 characteristic threshold, the path point is a non-smooth point, otherwise it is a smooth point; according to the classified path points, downsample the smooth points and / or upsample the non-smooth points to ensure a moderate density of path points.

[0029] Construct the local neighborhood covariance matrix of the historical path point. The following will take a historical path point as an example for specific explanation. i As the center, R is the radius of the sphere that encompasses all historical path points, constructing the historical path point p i The local neighborhood point set of R∈[R min ,R max ], R min is the minimum neighborhood radius, R max is the maximum neighborhood radius. The determination of R includes: Get the robot's historical path points p i The velocity v of the robot end at the time, and the historical path point p i With centered at 9, the robot traverses 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 whose velocities at the robot end are v-∆v and v+∆v respectively; 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 each point 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 mentioned above. In the process of constructing the covariance matrix, the weights of each point in the local neighborhood point set are the same; if the distance between the two closest historical path points mentioned above is less than R min , then R = R min , and introduce weight coefficients in the process of covariance matrix construction, such as for the historical path point p i The jth point p in the local neighborhood point set j The weight coefficient is , where k,c∈R.

[0030] 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.

[0031] The eigenvalue represents the variance of the covariance matrix in the direction of each eigenvector, while the eigenvector represents the main direction of the covariance matrix, that is, the normal vector of the point. For each path point, the eigenvector corresponding to the minimum eigenvalue is selected as its neighborhood normal vector. The method of adaptively selecting the neighborhood size allows more suitable neighborhood points to be included when calculating the path point normal vector, ensuring that a smaller neighborhood is selected in smooth areas and a larger neighborhood is selected in complex areas (such as edges and corners), thereby improving the accuracy, robustness and immediacy of normal vector estimation. The introduction of weight coefficients makes the points closer to the center point in the neighborhood contribute more to the normal vector estimation, while the points farther away contribute less, improving the accuracy of normal vector estimation, especially when dealing with complex surfaces. The historical path points are classified into smooth points and non-smooth points. Smooth points are used to fit the overall trend, and non-smooth points are used to capture local sharp changes, such as edges and corners. In this way, a fitting trajectory that is more in line with the actual surface can be obtained, improving the 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 and the product of the minimum eigenvalue ratio and the standard deviation of the normal vector angle are used as the judgment index. 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.

[0032] 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.

[0033] 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 the fitting results that do not conform to the actual surface characteristics. 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.

[0034] 4. Implement control: Control the robot to move along the optimized future motion path of the robot end, and control the force at the robot end. By introducing model predictive control, based on the robot's kinematic model, by minimizing the objective function of model predictive control and setting constraints, the control input u of model predictive control is calculated. The robot dynamics model is specifically:

[0035] Among them, τ is the joint torque, F is the contact force, J is the Jacobian matrix, q d is the desired joint position, is the expected joint velocity, is the expected joint acceleration, M is the mass matrix, describing the mass distribution of the robot joints, C is the Coriolis force matrix, describing the centrifugal force and Coriolis force generated by joint motion, G is the gravity matrix, describing the gravity effect caused by the robot mass, is an 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.

[0036] like Figure 2 As shown in Figure 2, the constraints of model predictive control include: x i+1 =f(x i ,u i ), x i is the system state at time i; x i ∈X, i=0,……,N-1, N is the control time domain, X is the system state constraint set; u i ∈U, i=0,…,N-1, U is the system input constraint set.

[0037]

[0038]

[0039] 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, and F b is the upper limit of contact force, F s is the lower limit of contact force. The objective function of model control is J(x,u).

[0040] In the implementation of the control step, the robot's kinematic and dynamic models are used to adopt model predictive control to predict future states and behaviors, so as to adjust the control input in real time. It can more accurately predict the motion trajectory and force change trend of the robot's end, so that the robot can move more accurately along the desired path and respond quickly in a dynamic environment. Not only the optimized motion of the robot's end path is considered, but also the contact force of the end is adjusted in real time. By accurately controlling the contact force, the robot can ensure safety and accuracy 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 limit, 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.

[0041] The maximum contact force constraint includes force control strategies in different situations, corresponding to different force control strategies when the robot end approaches or moves away from the work object, so that the system can flexibly respond to different working environments and task requirements, and can prevent the robot from applying excessive force, thereby avoiding damage to the operated object or the robot itself. By adjusting the contact force, the interaction between the robot end and the surface can be more accurately controlled, thereby improving the accuracy of tracking unknown surfaces, increasing the robustness of the system, and reducing deviations caused by external disturbances or uncertain factors. This precise control allows the robot to respond flexibly in different working scenarios, ensuring that the appropriate contact force is maintained at different distances, thereby improving the accuracy and reliability of the operation.

[0042] 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.

[0043] Specifically, in the implementation control step, the robot is controlled to move along the optimized future motion path of the robot end through optimized impedance control, and the force of the robot end is controlled at the same time, specifically:

[0044] Where ΔF is the difference between the expected contact force and the actual contact force at the end of the robot, m is the quality coefficient of 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 expected 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.

[0045] 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's end force under different working conditions. At the same time, the force at the robot's 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.

[0046] Embodiment 3: This embodiment 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 may adopt the same or similar design as that of Embodiment 1.

[0047] Specifically, in the implementation control 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.

[0048] 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 may be equal to the input in Example 2.

[0049] In the implementation of the control step, model predictive control is usually used to optimize the robot's trajectory tracking and generate the optimal control input by predicting the future state. Impedance control is mainly used to control the contact force and the force at the end of the robot. Combining these two control strategies and taking advantage of their respective advantages can not only optimize the robot's motion path, but also accurately control the robot's force and torque. The introduction of parameter γ allows γ to be dynamically adjusted with the robot's motion state, thereby balancing the influence of model predictive control and impedance control under different motion paths and working conditions. For example, when the robot needs to follow the optimized path more accurately (θ is small), γ is larger and relies more on model predictive control input; while when it needs to respond to large changes in external forces (θ is large), γ is smaller and relies more on impedance control input. By integrating model predictive control and impedance control, more accurate and smooth robot motion path tracking can be achieved. Model predictive control can optimize the prediction of future motion states, allowing the robot to follow the optimized path more accurately; at the same time, impedance control can effectively adjust the force and torque 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 practical operation, this means that the robot can respond quickly to environmental changes while maintaining stable trajectory tracking and force control performance. Through reasonable distribution of control inputs, energy consumption can be effectively optimized, especially in application scenarios with long-term operation and high energy saving requirements. Model predictive control helps to reduce unnecessary movements, while impedance control can effectively control the balance between energy consumption and task execution requirements.

[0050] 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.

[0051] It is obvious to those skilled in the art that the present invention is not limited to the details of the above exemplary embodiments, and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the present invention.

[0052] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. 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 solution of the present invention can be modified or replaced by equivalents without departing from the spirit and scope of the technical solution of the present invention.

Claims

1. A robot active compliance control method based on model predictive control, characterized in that: include: Modeling: Obtain the physical model of the robot and build the dynamic model of the robot; Data processing: Sample a series of historical path points within the contact range between the robot end and the surface of the operation object, calculate the normal vectors of the historical path points, and classify them into smooth points and non-smooth points; Path optimization: perform trajectory fitting on historical path points and adjust the path of the robot end according to the final fitting trajectory; Implement control: introduce model predictive control, based on the robot's dynamic model, by minimizing the objective function of model predictive control and setting constraints to calculate the control input of model predictive control; 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, and F b is the upper limit of contact force, F s The contact force is the lower limit.

2. The robot active compliance control method based on model predictive control according to claim 1 is characterized in that: The robot dynamics 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 expected joint velocity, is the expected joint acceleration, M is the mass matrix, describing the mass distribution of the robot joints, C is the Coriolis force matrix, describing the centrifugal force and Coriolis force generated by joint motion, G is the gravity matrix, describing the gravity effect caused by the robot mass, is an 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.

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 limit is dynamically adjusted to adapt to different operating scenarios and working conditions and optimize the application of contact force.

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 from the robot end to the object being operated.

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: 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, which is used to obtain the physical model of the robot and build a dynamic model of the robot; A data processing module, which is used to sample a series of historical path points within the contact range between the robot end and the surface of the operation object according to the surface information of the operation object of the robot, calculate the normal vectors of the historical path points, and classify 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; A controller module, which 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 dynamic model of the robot; 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, and F b is the upper limit of contact force, F s The contact force limit.

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 executable 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 1-9.

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