Model predictive control-based robot impedance control method, system, and control device

Abstract

This invention provides a robot variable impedance control method, system, and control device based on model predictive control. An iterative vector is constructed based on the current state vector and control vector. An optimization model, based on a nonlinear objective function and the iterative vector, iterates the iterative vector under multiple constraints until preset requirements are met. These constraints include upper and lower bound constraints on impedance and stiffness parameters, rate of change constraints, and passivity constraints. The control vector is extracted from the iterative vector, and the impedance and stiffness matrices are obtained based on the extracted control vector. The impedance and stiffness matrices are input into the impedance controller to predict the torque required for robot control. This scheme can predict the subsequent behavior of the system in each control cycle and optimize the control input under constraints. It not only provides a systematic optimization strategy for parameter adjustment but also considers multiple performance indicators and hardware constraints, improving the robustness of the control.

Description

Technical Field

[0001] This invention relates to the field of robot control technology, and more specifically, to a robot variable impedance control method, system, and control device based on model predictive control. Background Technology

[0002] Impedance control is a classic method for compliant robot control. Its core lies in establishing a fixed mass-damping-stiffness model for the interaction between the robot's end effector and the external environment. Through this model, the system can achieve a dynamic mapping between force and displacement during contact, thereby effectively controlling changes in contact force while satisfying position tracking requirements. Due to its simple structure and ease of implementation, constant impedance control is widely used in force-contact tasks such as grinding, assembly, and rehabilitation, and can improve the stability and safety of robot interactions with the environment or humans to a certain extent.

[0003] However, constant impedance control, because its impedance parameters remain constant during control, cannot dynamically adjust compliance according to changes in the external environment, resulting in insufficient adaptability, especially in tasks with significant uncertainty or variable contact conditions. In robot interactions with the environment or humans, the control system not only needs accurate position tracking but also must exhibit good compliance and adaptability. Traditional impedance control, by introducing a mass-damped-spring model, effectively regulates the dynamic behavior of the robot's end effector, but its fixed parameter settings are difficult to adapt to complex and changing interaction environments. Therefore, variable impedance control (VIC) has emerged, enabling a dynamic trade-off between rigidity and compliance by adjusting impedance parameters in real time. However, the selection of variable impedance parameters often relies on experience and lacks a systematic adjustment mechanism, making it difficult to simultaneously meet the requirements of interaction safety and task performance.

[0004] In existing technologies, trajectory tracking is mostly based on a given reference impedance parameter, requiring a pre-defined reference value for the impedance parameter. Furthermore, parameter setting is highly dependent on human experience, lacking unified adjustment criteria, and often necessitates a trade-off between safety and performance, limiting its widespread application in complex environments. Moreover, the stability issues caused by varying impedance are not considered during the control process. Summary of the Invention

[0005] The purpose of this invention is to provide a robot variable impedance control method, system, and control device based on model predictive control, which can balance multi-objective performance indicators and hardware constraints to improve the robustness of control.

[0006] In a first aspect, the present invention provides a robot variable impedance control method based on model predictive control, the method comprising:

[0007] The current state vector and control vector are obtained during the robot control process, and an iteration vector is constructed based on the state vector and control vector;

[0008] The optimization model is based on the constructed nonlinear objective function and the iteration vector. The iteration vector is iterated under multiple constraints until the preset requirements are met. The multiple constraints include upper and lower bound constraints of impedance parameters and stiffness parameters, rate of change constraints, and passivity constraints.

[0009] Extract the control vector from the iterative vector, and obtain the impedance parameter vector and stiffness parameter vector based on the extracted control vector;

[0010] The impedance matrix and stiffness matrix are obtained by expanding the impedance parameter vector and stiffness parameter vector.

[0011] The impedance matrix and stiffness matrix are input into the impedance controller to predict the torque for controlling the robot.

[0012] In an optional implementation, the step of obtaining the current state vector and control vector during robot control includes:

[0013] Acquire the current position error, impedance parameters, stiffness parameters, and external forces during robot control;

[0014] A state vector is constructed based on the position error, impedance parameter, stiffness parameter, and external force.

[0015] A control vector is constructed based on the impedance and stiffness parameters.

[0016] In an optional implementation, the nonlinear objective function is constructed in the following manner:

[0017] Based on the Cartesian pose of the robot's end effector at the initial planning moment, the Cartesian inertial matrix is ​​obtained;

[0018] Construct a continuous-time state equation based on the control vector and the Cartesian inertia matrix;

[0019] Discretize the continuous-time state equation to obtain the discrete-time state equation;

[0020] Under the discrete-time state equation and multiple constraints, a nonlinear objective function constructed from the stage cost function and the terminal cost function is obtained based on the state vector and the control vector.

[0021] In an optional implementation, the stage cost function is constructed in the following manner:

[0022] A reference stiffness function that varies with position error is constructed, and the stiffness adjustment rate is obtained based on the reference stiffness function;

[0023] The impedance coefficient is constructed based on the stiffness adjustment rate;

[0024] The state reference term is obtained based on the stiffness adjustment rate, impedance coefficient, and external force.

[0025] Based on the state reference term, control vector, and state vector, a stage cost function is constructed for the control vector and state vector.

[0026] In an optional implementation, the passive constraints among the plurality of constraints are constructed in the following manner:

[0027] The total energy of the system is calculated based on the position error, the differential of the position error, the inertia matrix, and the stiffness matrix.

[0028] Differentiating the total energy of the system yields the change in total energy.

[0029] Based on the differential of the position error and the external force, the external force input power is obtained;

[0030] A passive constraint is constructed by combining the total energy change and the external force input power, so that the total energy change is less than the external force input power.

[0031] In an optional implementation, the step of using an optimization model based on a constructed nonlinear objective function and the iteration vector, and iterating the iteration vector under multiple set constraints until a preset requirement is met, includes:

[0032] The iteration vector is subjected to quadratic programming using an optimization model to obtain the variable increment corresponding to the iteration vector;

[0033] Construct the constraint and optimization sub-function for the variable increment;

[0034] The optimization sub-function is iterated under the constraint of the variable increment until the absolute value of the variable increment is less than a preset threshold, at which point the preset requirement is determined to be met.

[0035] In an optional implementation, the step of constructing the constraint and optimization sub-function of the variable increment includes:

[0036] Calculate the first-order gradient and second-order derivative Hassen matrix of the constructed nonlinear objective function with respect to the iterative vector;

[0037] Differentiate the state vector and control vector in the iteration vector respectively, and differentiate the constraint function constructed by the set multiple constraint conditions to obtain the iteration coefficients;

[0038] Based on the iteration coefficients, first-order derivative gradients, and second-order derivative Hassen matrices, constraints and optimization sub-functions regarding variable increments are obtained.

[0039] In an optional implementation, the step of obtaining the impedance parameter vector and stiffness parameter vector based on the extracted control vector includes:

[0040] The elements of the extracted control vectors are integrated to obtain the impedance parameter vector and the stiffness parameter vector.

[0041] Secondly, the present invention provides a robot variable impedance control system based on model predictive control, the system comprising:

[0042] The acquisition module is used to acquire the current state vector and control vector during the robot control process, and to construct an iteration vector based on the state vector and control vector.

[0043] The iteration module is used to use the optimization model based on the constructed nonlinear objective function and the iteration vector to perform iteration of the iteration vector under the constraints of multiple set constraints until the preset requirements are met. The multiple constraints include upper and lower bound constraints of impedance parameters and stiffness parameters, rate of change constraints, and passivity constraints.

[0044] The extraction module is used to extract the control vector from the iterative vector, and obtain the impedance parameter vector and stiffness parameter vector based on the extracted control vector;

[0045] An extension module is used to extend the impedance parameter vector and stiffness parameter vector to obtain the impedance matrix and stiffness matrix;

[0046] The predictive control module is used to input the impedance matrix and stiffness matrix into the impedance controller to predict the torque for executing robot control.

[0047] Thirdly, the present invention provides a control device, including one or more storage media and one or more processors communicating with the storage media, wherein the one or more storage media store machine-executable instructions executable by the processor, and when the control device is running, the processor executes the machine-executable instructions to perform the method described in any of the foregoing embodiments.

[0048] This invention provides a robot variable impedance control method, system, and control device based on model predictive control. It constructs an iterative vector based on the acquired current state vector and control vector. Using an optimization model based on a nonlinear objective function and the iterative vector, it iterates the iterative vector under multiple constraints until preset requirements are met. These constraints include upper and lower bound constraints on impedance and stiffness parameters, rate of change constraints, and passivity constraints. The control vector is extracted from the iterative vector, and the impedance and stiffness parameter vectors are obtained based on the extracted control vectors. The impedance and stiffness matrix are then expanded from the impedance and stiffness parameter vectors to obtain the impedance matrix and stiffness matrix. These impedance and stiffness matrices are input into the impedance controller to predict the torque required for robot control.

[0049] In this scheme, a model prediction method is adopted, which can predict the subsequent behavior of the system in each control cycle and optimize the control input under constraints. This not only provides a systematic optimization strategy for parameter adjustment, but also takes into account multiple performance indicators and hardware constraints, thereby improving the robustness of control. Attached Figure Description

[0050] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments of the present invention will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0051] Figure 1 A flowchart of a robot variable impedance control method based on model predictive control provided in an embodiment of the present invention;

[0052] Figure 2 This is a schematic diagram of a polishing simulation scene constructed in simulation software in an embodiment of the present invention;

[0053] Figure 3 This is a schematic diagram of the curve of normal contact force changing with time in an embodiment of the present invention;

[0054] Figure 4 This is a schematic diagram of the displacement curve under low impedance test in an embodiment of the present invention;

[0055] Figure 5 This is a schematic diagram of the displacement curve under high impedance test in an embodiment of the present invention;

[0056] Figure 6 This is a schematic diagram of the displacement curve under the variable impedance test in an embodiment of the present invention;

[0057] Figure 7A functional block diagram of a robot variable impedance control system based on model predictive control provided in an embodiment of the present invention;

[0058] Figure 8 This is a structural block diagram of a control device provided in an embodiment of the present invention. Detailed Implementation

[0059] The technical solutions of the present invention will now be described with reference to the accompanying drawings in the embodiments of the present invention.

[0060] Please see Figure 1 This invention provides a model predictive control-based robot variable impedance control method. This control method can be executed by a model predictive control-based robot variable impedance control system, which can be implemented in software and / or hardware and configured in a control device, such as a computer device, server, or, for example, a server in a backend control platform. The detailed steps of this model predictive control-based robot variable impedance control method are described below.

[0061] S11, obtain the current state vector and control vector during the robot control process, and construct an iteration vector based on the state vector and control vector.

[0062] S12, using the optimization model based on the constructed nonlinear objective function and the iteration vector, the iteration vector is iterated under multiple set constraints until the preset requirements are met.

[0063] The multiple constraints include upper and lower bound constraints on impedance parameters and stiffness parameters, rate of change constraints, and passive constraints.

[0064] S13, extract the control vector from the iterative vector, and obtain the impedance parameter vector and stiffness parameter vector based on the extracted control vector.

[0065] S14, the impedance matrix and stiffness matrix are obtained by expanding the impedance parameter vector and stiffness parameter vector.

[0066] S15, input the impedance matrix and stiffness matrix into the impedance controller to predict the torque for executing robot control.

[0067] The technical solution provided in this embodiment is implemented within the framework of Cartesian impedance control. The formula for calculating the Cartesian impedance control rate is as follows:

[0068]

[0069] in, To input the control torque of the robotic arm, For gravity, For joint angle, It is a Jacobian matrix. It is the inertial matrix in Cartesian space. It is a Coriolis matrix in Cartesian space. For the impedance matrix, Here is the stiffness matrix. For pose deviation, The desired trajectory.

[0070] Based on the above control law calculation formula, the following dynamic relationship is established:

[0071]

[0072] in It is a six-dimensional vector consisting of the forces and torques acting on the end effector of the robotic arm.

[0073] Rearranging the above dynamic equations to represent the acceleration term yields the following expression:

[0074]

[0075] To facilitate subsequent modeling and optimization of the impedance parameters as system state variables, given the impedance matrix... and stiffness matrix It has been designed as a diagonal matrix, so the impedance parameter vector formed by its diagonal elements can be used. and stiffness parameter vector Let's represent the two matrices above as follows:

[0076]

[0077] in:

[0078]

[0079] Based on this, the system state variables are uniformly constructed into state vectors. The control vector is represented as The steps described above for obtaining the current state vector and control vector during robot control can be implemented in the following ways:

[0080] The current position error, impedance parameters, stiffness parameters, and external forces are obtained during robot control; a state vector is constructed based on the position error, impedance parameters, stiffness parameters, and external forces; and a control vector is constructed based on the impedance parameters and stiffness parameters.

[0081] Specifically, based on position error, impedance parameter, stiffness parameter, and external force, the following state vector is constructed. :

[0082]

[0083] Furthermore, the control vector shown below is constructed based on the impedance and stiffness parameters. :

[0084]

[0085] In this embodiment, the state vector and control vector are concatenated together to form an iteration vector, which can be represented as follows: .

[0086] In this embodiment, high-precision control is achieved using nonlinear model predictive control (NMPC). This control method considers multiple constraints and transforms the NMPC problem into a nonlinear rule (NLP) problem in the finite time domain. Common solutions for NLP problems include algorithms such as the Lagrange multiplier method, trust region method, and penalty function method to obtain the optimal solution. However, the relevant theories and algorithms still need improvement in practical applications. SQP based on the Newton-Lagrange method is currently one of the optimal algorithms for solving nonlinear programming problems. In this embodiment, for the case where the optimization model contains a nonlinear objective function and complex constraints, a sequential quadratic programming method is used. This method approximates the optimal solution of the original nonlinear programming problem by solving an approximate second-order programming subproblem in each iteration.

[0087] In the above steps, which utilize an optimization model based on a constructed nonlinear objective function and an iteration vector, and perform iteration of the iteration vector under multiple set constraints, the nonlinear objective function is constructed in the following way:

[0088] Based on the Cartesian pose of the robot's end effector at the initial planning moment, the Cartesian inertia matrix is ​​obtained; a continuous-time state equation is constructed based on the control vector and the Cartesian inertia matrix; the continuous-time state equation is discretized to obtain a discrete-time state equation; under the discrete-time state equation and multiple constraints, a nonlinear objective function constructed from the stage cost function and the terminal cost function is obtained based on the state vector and the control vector.

[0089] In this embodiment, to simplify the computational complexity of model predictive control, it is assumed that the Cartesian inertia matrix is ​​constant throughout the entire prediction time domain. External forces Keeping constant, they are approximated to their values ​​at the start of the planning process. The corresponding value. The specific representation is as follows:

[0090]

[0091] in, For the initial planning time The robot's end effector is in Cartesian pose.

[0092] Based on the control vector and the Cartesian inertia matrix, the following continuous-time state equation is constructed:

[0093]

[0094] For ease of analysis, it is abbreviated as:

[0095]

[0096] Fixed sampling step size Discretizing the continuous-time state equation yields the discrete-time state equation of the system:

[0097]

[0098] Based on the Model Predictive Control (MPC) framework, it has The nonlinear objective function for step prediction capability is constructed as follows:

[0099]

[0100] in, To optimize the variable sequence, For the stage cost function, This is the terminal cost function.

[0101] The design of the objective function needs to consider the complex interactive environment that the system often faces during actual task execution, including external disturbances, contact uncertainties, and deviations between the desired and actual trajectories. Therefore, it needs to simultaneously reflect compliance and control precision. Specifically, stiffness and impedance should be adjusted in real time according to the task status, especially the magnitude of external resistance and the degree of positional deviation.

[0102] The design of the objective function should not only consider the system stability and the minimization of trajectory tracking error, but also incorporate the adjustment behavior of impedance parameters into the optimization framework, so that the controller can have higher robustness and response sensitivity while meeting dynamic performance requirements.

[0103] For stiffness adjustment requirements, an ideal adjustment mechanism should have the following characteristics: when the deviation is small, the stiffness should not over-respond to maintain the system's compliance and safety, and avoid rigid reactions to small disturbances; while when the deviation gradually increases, the stiffness should be appropriately enhanced to improve the system's disturbance rejection capability and avoid error accumulation and task failure.

[0104] This design ensures a dynamic trade-off between compliance and precision. Under normal conditions, the system prioritizes compliant interaction, while in scenarios where the deviation from the target is large or the contact is rigid, the goal is to enhance control precision and system stability.

[0105] In impedance control, the dynamic characteristics of environmental interaction forces can be characterized by motion deviation.

[0106] The nonlinear objective function constructed above includes a terminal cost function and a stage cost function. The terminal cost function can be constructed using currently common methods, while the stage cost function can be constructed in the following way:

[0107] A reference stiffness function that varies with position error is constructed, and a stiffness adjustment rate is obtained based on the reference stiffness function; an impedance coefficient is constructed based on the stiffness adjustment rate; a state reference term is obtained based on the stiffness adjustment rate, the impedance coefficient, and the external force; and a stage cost function is constructed based on the state reference term, the control vector, and the state vector, relating to the control vector and the state vector.

[0108] In this embodiment, to achieve autonomous adjustment of stiffness parameters, it is necessary to construct a system that adapts to position errors. Variational reference stiffness function It satisfies the following characteristics:

[0109] Strictly increasing property: This ensures increased stiffness and improved disturbance rejection capability when deviation increases.

[0110] Properties of convex functions: This ensures that the stiffness increases faster as the error increases, thus adapting to sudden disturbances.

[0111] The stiffness adjustment factor is constructed using the natural exponential function:

[0112]

[0113] in, As the reference stiffness coefficient, This is the stiffness growth rate coefficient.

[0114] While adjusting the stiffness, it is also necessary to maintain good damping characteristics, and further design the impedance coefficient to prevent oscillation. .

[0115] Combining stiffness regulation, impedance coefficient, and external force, the following state reference term is constructed:

[0116]

[0117] in, This represents the pose error in six dimensions.

[0118] , This means that the function is applied to each element of the vector, and the output is a vector of the corresponding dimension.

[0119] Based on this, a stage cost function is constructed using the state reference term, control vector, and state vector:

[0120]

[0121] In the formula, It is the weight matrix of the state vector, used to measure the cost of the system deviating from the desired state. This is the weight matrix that controls the input, suppressing the input magnitude to prevent drastic state changes. Desired state The design assumes that the differential of the pose deviation is zero, meaning that the components no longer change when the system approaches a steady state. Furthermore, the expected values ​​of damping and stiffness are set as dynamic adjustment targets for damping and stiffness during the mission.

[0122] To ensure the safety and stability of the system during parameter adjustment, the design of constraints mainly revolves around the following two aspects:

[0123] Upper and lower bound constraints on stiffness, damping, and their rates of change: By setting upper and lower limits for stiffness and damping, problems such as insufficient control performance due to excessively small values, or rigid collisions and excessive system excitation due to excessively large values, are avoided. This constraint ensures that parameter adjustments are within physically feasible and system stability ranges, thereby improving the robustness and reliability of control.

[0124] System passivity constraints ensure stability: To prevent impedance parameter changes from causing non-conservative or unstable energy behavior in the system, a passivity-based constraint mechanism is introduced. Specifically, by constructing a passivity function and ensuring that the impedance system satisfies the conditions of non-increase in energy (passive) or strict passivity at any time, the direction and rate of parameter adjustment are restricted, thereby ensuring that the system always remains within an energy-stable and controllable domain. This constraint not only effectively suppresses the amplification effect of external disturbances but also enhances the stability and safety during interaction with the environment.

[0125] Specifically, the constraint design for variable impedance control is as follows:

[0126] The control constraints are designed as follows:

[0127]

[0128] In variable impedance control, stiffness and damping parameters need to be dynamically adjusted according to task requirements, environmental characteristics, or system errors. However, if the adjustment rate is too fast, it may cause abrupt changes in the system's dynamic response, leading to control instability or even excitation of system resonance. Therefore, in addition to imposing upper and lower bounds on the stiffness and damping themselves, it is also necessary to constrain their rate of change to ensure the smoothness of the adjustment process and system stability.

[0129] By simply replacing it with vector form, the design of the rate-of-change constraint in variable impedance control can be obtained:

[0130]

[0131] The aforementioned passive constraints can be constructed in the following ways:

[0132] The total system energy is calculated based on the position error, its derivative, the inertia matrix, and the stiffness matrix. The total energy is then differentiated to obtain the total energy change. The external force input power is obtained based on the derivative of the position error and the external force. Passive constraints are constructed by combining the total energy change and the external force input power to ensure that the total energy change is less than the external force input power.

[0133] First, by considering the stability during free motion, we can obtain the dynamic equations for free motion, i.e., when there is no external force contact:

[0134]

[0135] To analyze the stability of the system, the following Lyapunov function is constructed. , W This can represent the total energy of the system:

[0136]

[0137] The first term represents the change in the system's kinetic energy, and the second term represents the change in potential energy. Note the inertia matrix. and stiffness matrix Both are symmetric matrices, therefore for Differentiation yields the total energy change:

[0138]

[0139] Substituting the kinetic equations into the total energy change equations, we get:

[0140]

[0141] The above equation shows that the change in system energy is subject to the rate of change of the inertia matrix, the damping dissipation term, and the change in stiffness.

[0142] To ensure the stability of the system without external disturbances, the following conditions are set:

[0143]

[0144] This means that the rate of change of the damping and stiffness matrix needs to be designed to counteract the instability caused by changes in inertia.

[0145] When the system is subjected to external forces At that time, the calculation of the total energy change is updated as follows:

[0146]

[0147] To ensure the stability of the system under no external disturbance, the passive constraint shown below can be further obtained:

[0148]

[0149] Right now:

[0150]

[0151] The above equation shows that the total energy change of the system is less than the external input power. Therefore, the system does not generate energy on its own, but can only consume or store external input energy, thus satisfying the definition of passivity.

[0152] Combining the above constraints, the overall inequality constraints for variable impedance control are as follows: It can be constructed as follows:

[0153]

[0154] Considering the above constraints, the non-objective function under these constraints is constructed as follows:

[0155]

[0156] Let the first The state vector and input vector obtained in the second iteration are respectively , , , }, { , , , }, concatenate the two vectors into an iterative vector, denoted as . .

[0157] Based on this, the optimization model, using the constructed nonlinear objective function and iteration vector, iterates the iteration vector under multiple constraints until the preset requirements are met. This can be achieved in the following way:

[0158] The iteration vector is subjected to quadratic programming using an optimization model to obtain the variable increment corresponding to the iteration vector; constraints and optimization sub-functions for the variable increments are constructed; the optimization sub-functions are iterated under the constraints of the variable increments until the absolute value of the variable increments is less than a preset threshold, at which point the preset requirements are determined to be met.

[0159] In this embodiment, for optimization models containing nonlinear objective functions and complex constraints, a sequential quadratic programming method is used for solution. This method approximates the optimal solution of the original nonlinear programming problem by solving an approximate second-order programming subproblem in each iteration. Specifically, the steps of constructing the constraints of variable increments and the optimization subfunction can be implemented in the following way:

[0160] Calculate the first-order derivative gradient and the second-order derivative Hassen matrix of the constructed nonlinear objective function with respect to the iteration vector; differentiate the state vector and control vector in the iteration vector respectively, and differentiate the constraint function constructed by the set multiple constraints to obtain the iteration coefficients; based on the iteration coefficients, the first-order derivative gradient and the second-order derivative Hassen matrix, obtain the constraint and optimization sub-function with respect to the variable increment.

[0161] In this embodiment, at the current point Calculate the nonlinear objective function first derivative gradient and the second derivative Hessian matrix :

[0162]

[0163] The iterative coefficients are obtained by differentiating the dynamic matrix from the state and action. , ,satisfy:

[0164]

[0165] Similarly, for constraint functions Differentiation yields the iteration coefficients , ,satisfy:

[0166]

[0167] Convert the above calculation formula into about Format:

[0168]

[0169] The above constraints apply at the current iteration point. Constructing based on variable increment The optimization sub-function is as follows:

[0170]

[0171] By solving the optimization problem under the above optimization sub-function, the variable increment for the current iteration step can be obtained. Furthermore, by utilizing the step size of the line search strategy... Adjustments are made to achieve the update iteration of the iteration vector as a variable:

[0172]

[0173] When the absolute value of the variable increment The iteration terminates when the value is less than a preset threshold, and the control vector in the iteration vector at this point is extracted. , as the current input.

[0174] Based on the above, impedance parameter vectors and stiffness parameter vectors are obtained from the extracted control vectors. Specifically, the elements in the extracted control vectors are integrated to obtain the impedance parameter vectors and stiffness parameter vectors.

[0175] The impedance parameter vector and stiffness parameter vector are the diagonal elements of the impedance matrix and stiffness matrix, respectively. By expanding the impedance parameter vector and stiffness parameter vector by adding zero elements, the impedance matrix can be obtained. and stiffness matrix .

[0176] The obtained impedance matrix and stiffness matrix are input into the impedance controller, which predicts the torque required to control the robot, thereby controlling the robot's pose at the next moment.

[0177] Please refer to the following: Figure 2 This is a schematic diagram of a grinding simulation scenario built using the robotic tools tool in MATLAB. In this simulation scenario, under the control scheme provided in this embodiment, the change in the robot's normal contact force over time is as follows: Figure 3 As shown, by Figure 3 It can be seen that the robot maintains stable contact in the normal direction.

[0178] In addition, low-impedance, high-impedance, and variable-impedance tests were performed, and the displacement curves in the x-direction for the three sets of tests are shown below. Figure 4 , Figure 5 and Figure 6As shown in the graphs of the three sets of tests, the solid lines represent the actual trajectory curves, and the dashed lines represent the desired trajectory curves. It can be seen from the graphs that in the low-stiffness, damped control test, it is difficult to track the desired trajectory, resulting in a large tracking error. Under high stiffness, it can maintain a high level of tracking, and by varying the impedance, it can achieve a similar effect to high stiffness, exhibiting good tracking performance.

[0179] Based on the same inventive concept, please refer to Figure 7 This invention also provides a functional module diagram of a robot variable impedance control system based on model predictive control. This embodiment divides the robot variable impedance control system based on model predictive control into functional modules according to the above method embodiments. For example, each function can be divided into its own functional modules, or two or more functions can be integrated into one processing module. The integrated module can be implemented in hardware or as a software functional module. It should be noted that the module division in this invention embodiment is illustrative and only represents one logical functional division; other division methods may be used in actual implementation.

[0180] For example, when dividing functional modules according to their respective functions, Figure 7 The illustrated model predictive control-based robot impedance control system is merely a schematic diagram. This system may include an acquisition module, an iteration module, an extraction module, an extension module, and a predictive control module. The functions of each module in this model predictive control-based robot impedance control system will be described in detail below.

[0181] The acquisition module is used to acquire the current state vector and control vector during the robot control process, and to construct an iteration vector based on the state vector and control vector.

[0182] The iteration module is used to use the optimization model based on the constructed nonlinear objective function and the iteration vector to perform iteration of the iteration vector under the constraints of multiple set constraints until the preset requirements are met. The multiple constraints include upper and lower bound constraints of impedance parameters and stiffness parameters, rate of change constraints, and passivity constraints.

[0183] The extraction module is used to extract the control vector from the iterative vector, and obtain the impedance parameter vector and stiffness parameter vector based on the extracted control vector;

[0184] An extension module is used to extend the impedance parameter vector and stiffness parameter vector to obtain the impedance matrix and stiffness matrix;

[0185] The predictive control module is used to input the impedance matrix and stiffness matrix into the impedance controller to predict the torque for executing robot control.

[0186] The robot variable impedance control system based on model predictive control provided in this embodiment can be used to execute the robot variable impedance control method based on model predictive control under any of the above embodiments. For details not covered in this embodiment, please refer to the corresponding descriptions in the above embodiments. This embodiment will not elaborate further here.

[0187] Please see Figure 8 This is a structural block diagram of a control device provided in an embodiment of the present invention. The control device can be a computer device, server, or similar component within a control platform. The control device includes a memory, a processor, and a communication module. The memory, processor, and communication module are electrically connected directly or indirectly to each other to achieve data transmission or interaction. For example, these components can be electrically connected to each other through one or more communication buses or signal lines.

[0188] The memory is used to store computer programs or data. Memory can be, but is not limited to, Random Access Memory (RAM), Read Only Memory (ROM), Programmable Read-Only Memory (PROM), Erasable Programmable Read-Only Memory (EPROM), Electrically Erasable Programmable Read-Only Memory (EEPROM), etc.

[0189] The processor is used to read / write data or programs stored in the memory and execute the robot variable impedance control method based on model predictive control provided in any embodiment of the present invention.

[0190] The communication module is used to establish communication connections between the control device and other communication terminals via the network, and to send and receive data via the network.

[0191] It should be understood that, Figure 8 The structure shown is only a schematic diagram of the control device; the control device may also include components such as... Figure 8 The more or fewer components shown, or having the same Figure 8 The different configurations shown.

[0192] Furthermore, embodiments of the present invention also provide a computer-readable storage medium storing machine-executable instructions, which, when executed, implement the robot variable impedance control method based on model predictive control provided in the above embodiments.

[0193] Specifically, the computer-readable storage medium can be a general-purpose storage medium, such as a removable disk or hard disk. When the computer program on the computer-readable storage medium is executed, it can perform the aforementioned model predictive control-based robot variable impedance control method. The processes involved in the execution of the executable instructions on the computer-readable storage medium can be referred to the relevant descriptions in the above method embodiments, and will not be detailed here.

[0194] In the embodiments provided by this invention, it should be understood that the disclosed apparatus and method can be implemented in other ways. The apparatus embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. Furthermore, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Additionally, the displayed or discussed mutual couplings, direct couplings, or communication connections may be through some communication interfaces; indirect couplings or communication connections between devices or units may be electrical, mechanical, or other forms.

[0195] Furthermore, the units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0196] Furthermore, the functional modules in the various embodiments of the present invention can be integrated together to form an independent part, or each module can exist independently, or two or more modules can be integrated to form an independent part.

[0197] It should be noted that if the functionality is implemented as a software module and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0198] The above description is merely an embodiment of the present invention and is not intended to limit the scope of protection of the present invention. For those skilled in the art, the present invention can have various modifications and variations. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A robot variable impedance control method based on model predictive control, characterized in that, The method includes: The current state vector and control vector are obtained during the robot control process, and an iteration vector is constructed based on the state vector and control vector; The optimization model is based on the constructed nonlinear objective function and the iteration vector. The iteration vector is iterated under multiple constraints until the preset requirements are met. The multiple constraints include upper and lower bound constraints of impedance parameters and stiffness parameters, rate of change constraints, and passivity constraints. Extract the control vector from the iterative vector, and obtain the impedance parameter vector and stiffness parameter vector based on the extracted control vector; The impedance matrix and stiffness matrix are obtained by expanding the impedance parameter vector and stiffness parameter vector. The impedance matrix and stiffness matrix are input into the impedance controller to predict the torque for controlling the robot.

2. The robot variable impedance control method based on model predictive control according to claim 1, characterized in that, The steps for obtaining the current state vector and control vector during robot control include: Acquire the current position error, impedance parameters, stiffness parameters, and external forces during robot control; A state vector is constructed based on the position error, impedance parameter, stiffness parameter, and external force. A control vector is constructed based on the impedance and stiffness parameters.

3. The robot variable impedance control method based on model predictive control according to claim 1, characterized in that, The nonlinear objective function is constructed in the following way: Based on the Cartesian pose of the robot's end effector at the initial planning moment, the Cartesian inertial matrix is ​​obtained; Construct a continuous-time state equation based on the control vector and the Cartesian inertia matrix; Discretize the continuous-time state equation to obtain the discrete-time state equation; Under the discrete-time state equation and multiple constraints, a nonlinear objective function constructed from the stage cost function and the terminal cost function is obtained based on the state vector and the control vector.

4. The robot variable impedance control method based on model predictive control according to claim 3, characterized in that, The stage cost function is constructed in the following way: A reference stiffness function that varies with position error is constructed, and the stiffness adjustment rate is obtained based on the reference stiffness function; The impedance coefficient is constructed based on the stiffness adjustment rate; The state reference term is obtained based on the stiffness adjustment rate, impedance coefficient, and external force. Based on the state reference term, control vector, and state vector, a stage cost function is constructed for the control vector and state vector.

5. The robot variable impedance control method based on model predictive control according to claim 1, characterized in that, The passive constraints among the multiple constraints are constructed in the following way: The total energy of the system is calculated based on the position error, the differential of the position error, the inertia matrix, and the stiffness matrix. Differentiating the total energy of the system yields the change in total energy. Based on the differential of the position error and the external force, the external force input power is obtained; A passive constraint is constructed by combining the total energy change and the external force input power, so that the total energy change is less than the external force input power.

6. The robot variable impedance control method based on model predictive control according to claim 1, characterized in that, The step of using an optimization model based on a constructed nonlinear objective function and the iteration vector, and iterating the iteration vector under multiple set constraints until a preset requirement is met, includes: The iteration vector is subjected to quadratic programming using an optimization model to obtain the variable increment corresponding to the iteration vector; Construct the constraint and optimization sub-function for the variable increment; The optimization sub-function is iterated under the constraint of the variable increment until the absolute value of the variable increment is less than a preset threshold, at which point the preset requirement is determined to be met.

7. The robot variable impedance control method based on model predictive control according to claim 6, characterized in that, The steps for constructing the constraint and optimization sub-function for the variable increment include: Calculate the first-order gradient and second-order derivative Hassen matrix of the constructed nonlinear objective function with respect to the iterative vector; Differentiate the state vector and control vector in the iteration vector respectively, and differentiate the constraint function constructed by the set multiple constraint conditions to obtain the iteration coefficients; Based on the iteration coefficients, first-order derivative gradients, and second-order derivative Hassen matrices, constraints and optimization sub-functions regarding variable increments are obtained.

8. The robot variable impedance control method based on model predictive control according to claim 1, characterized in that, The steps of obtaining the impedance parameter vector and stiffness parameter vector based on the extracted control vector include: The elements of the extracted control vectors are integrated to obtain the impedance parameter vector and the stiffness parameter vector.

9. A robot variable impedance control system based on model predictive control, characterized in that, The system includes: The acquisition module is used to acquire the current state vector and control vector during the robot control process, and to construct an iteration vector based on the state vector and control vector. The iteration module is used to use the optimization model based on the constructed nonlinear objective function and the iteration vector to perform iteration of the iteration vector under the constraints of multiple set constraints until the preset requirements are met. The multiple constraints include upper and lower bound constraints of impedance parameters and stiffness parameters, rate of change constraints, and passivity constraints. The extraction module is used to extract the control vector from the iterative vector, and obtain the impedance parameter vector and stiffness parameter vector based on the extracted control vector; An extension module is used to extend the impedance parameter vector and stiffness parameter vector to obtain the impedance matrix and stiffness matrix. The predictive control module is used to input the impedance matrix and stiffness matrix into the impedance controller to predict the torque for executing robot control.

10. A control device, characterized in that, The device includes one or more storage media and one or more processors communicating with the storage media. The one or more storage media store machine-executable instructions that can be executed by the processor. When the control device is running, the processor executes the machine-executable instructions to perform the method according to any one of claims 1-8.

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