Composite anti-interference and anti-skid motion control method for four-footed inspection robot
By establishing a single rigid body dynamic model of a quadruped robot and designing a disturbance observer and a model predictive controller, the problems of rapid disturbance estimation and anti-slip control of quadruped inspection robots in complex environments were solved, achieving higher control accuracy and stability and enhancing anti-disturbance capability.
Patent Information
- Application Number
- CN202511698535.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-19
- Publication Date
- 2026-02-13
AI Technical Summary
Existing control methods for quadruped inspection robots struggle to effectively handle rapid disturbance estimation, multi-disturbance coupling, and anti-slip control in complex dynamic environments, leading to performance degradation and instability.
A composite anti-disturbance and anti-slip motion control method is adopted. By establishing a single rigid body dynamic model of the quadruped robot, an interference observer and a model predictive controller are designed to estimate and compensate for interference, optimize the control input, limit the force at the foot end to the friction cone range, and design an auxiliary controller to achieve system stability.
It effectively improves the control accuracy and stability of quadruped inspection robots in complex environments, reduces the impact of external interference, avoids slippage at the feet, and enhances the robot's anti-interference ability under complex working conditions.
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Figure CN121523385A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of robot control technology, and in particular relates to a composite anti-disturbance and anti-slip motion control method for a quadruped inspection robot. Background Technology
[0002] Compared to traditional wheeled or tracked robots, quadruped inspection robots demonstrate enormous application potential in complex and varied environments such as railways, tunnels, construction sites, and mines. The core advantage of quadruped robots lies in their breakthrough in biomimetic locomotion. Mimicking animal movement, their feet have discrete foot points, allowing them to actively choose where to land. Whether in extreme environments like construction sites with rubble and debris, steep slopes, railway tracks with ballast and sleepers, or even staircases and ditches, they can walk, step, and trot smoothly, reaching areas difficult or dangerous for manual inspection, achieving comprehensive coverage. Furthermore, the quadrupedal structure provides dynamic balance and superior stability. Combined with advanced control algorithms and sensor systems, they can adjust their posture and gait in real time, effectively adapting to highly dynamic environments.
[0003] However, quadruped inspection robots face numerous challenges in practical operation: First, their dynamic model possesses high degrees of freedom and strong coupling; second, the complexity of inspection conditions also presents significant challenges to robot control, including variations in ground material, unpredictable terrain geometry, and load uncertainties, all of which can easily lead to performance degradation and instability; furthermore, improper foot force actuation can cause system response instability and performance deterioration. Therefore, researchers have conducted studies on composite anti-disturbance and anti-slip control technologies for quadruped inspection robots, aiming to improve the robot's autonomy and reliability in complex environments, maintain stability in dynamic and uncertain environments, expand its application range, replace humans in performing dangerous tasks, and promote the development of intelligent equipment.
[0004] Traditional control methods (such as model-based linear control or simple PID control) often perform poorly in complex dynamic environments, mainly because they struggle to accurately represent the real dynamic model or effectively compensate for model uncertainties. In recent years, with advancements in anti-disturbance control theory, methods such as sliding mode control, adaptive control, disturbance observers, model predictive control, and reinforcement learning-based intelligent control have been widely introduced into the control of quadrupedal inspection robots, significantly improving the system's robustness and adaptability.
[0005] Based on the above analysis, existing methods still have limitations in terms of rapid disturbance estimation, multi-disturbance coupling processing, and real-time performance. Further in-depth research is urgently needed on more efficient and stable composite disturbance rejection control strategies. Furthermore, quadrupedal inspection robots are prone to slippage on slopes and uneven surfaces, where the normal force at the foot tip decreases and the tangential force exceeds the maximum static friction. Research on anti-slip control for quadrupedal robots is urgently needed. Research on disturbance rejection and anti-slip motion control for quadrupedal inspection robots not only compensates for the shortcomings of existing technologies but is also a crucial link in promoting the intelligent development of robots and expanding their application boundaries, possessing profound research value and practical significance.
[0006] Therefore, this invention proposes a composite anti-disturbance and anti-slip motion control method for quadruped inspection robots affected by multi-source uncertain disturbances in complex working environments. This method effectively reduces the impact of external disturbances on the motion of quadruped inspection robots, improves the motion control accuracy of quadruped inspection robots, and effectively constrains the physical constraints of the system, ensuring the motion stability of the robot. Summary of the Invention
[0007] The purpose of this invention is to provide a composite anti-disturbance and anti-slip motion control method for a quadruped inspection robot, so as to solve the problems that the existing control methods proposed in the background art still have limitations in multiple anti-disturbance control aspects such as rapid disturbance estimation and multi-disturbance coupling processing, as well as insufficient anti-slip control.
[0008] To achieve the above objectives, the present invention employs the following technical solution: This invention proposes a composite anti-disturbance and anti-slip motion control method for a quadruped inspection robot, comprising the following steps: S1. Establish a single rigid body dynamic model of a quadruped robot under the influence of uncertain disturbances and the constraint of Coulomb friction cone, and based on the single rigid body dynamic model of the quadruped robot, establish a tracking error system model of the equivalent motion of the quadruped robot. S2. Design an interference observer based on the tracking error system model to actively estimate and compensate for interference caused by uncertainties in the external environment and the system. S3. Solve the design optimization control problem to obtain the model predictive controller. Based on the error between the actual state and the nominal state affected by the disturbance, design the auxiliary controller. Based on the disturbance observer, the model predictive controller and the auxiliary controller as the composite control input of the tracking error system model, design a composite disturbance rejection model predictive control method. S4. Verify the recursive feasibility of the composite disturbance rejection model predictive control method and the stability of the closed-loop system.
[0009] Preferably, the establishment of the single rigid body dynamic model of the quadruped robot under the influence of uncertain disturbances and the constraint of the Coulomb friction cone is as follows: The disturbed dynamic equations of the quadruped robot are as follows:
[0010]
[0011]
[0012]
[0013] in, This represents the acceleration of the center of mass of the quadruped robot. m Indicates the mass of a quadruped robot. g Represents gravitational acceleration. Indicates the first The reaction force at the foot of one leg; Let be the angular velocity of the robot's center of mass in the world coordinate system. This represents the distance vector from the point of ground reaction force to the center of mass; This is the roll angle. The pitch angle, Yaw angle Indicates circling Z Rotation of axis in the positive direction angle, R This represents the rotation matrix from the body coordinate system to the world coordinate system; I Let be the inertial tensor in the world coordinate system during the movement of the quadruped robot. Let be the inertial tensor in the body coordinate system of the quadruped robot; , This refers to the disturbance term caused by uncertainties in the external environment and the internal workings of the quadruped robot. Euler angles of a quadruped robot Centroid coordinates p ,speed and angular velocity As a quadruped robot system state, and considering gravitational acceleration. g By incorporating the coefficient matrix, the state variables of the quadruped robot system can be obtained. The ground reaction force is defined as the control input, i.e. The state-space equations of the quadruped robot system are obtained as follows:
[0014]
[0015] in, and These represent the state and control inputs of the quadruped robot system. It is a disturbance term, and satisfies ,in, Given constants; matrix ; Constraints based on the friction cone at the foot of a quadruped robot Minimum force Setting the value to 0 and controlling the force applied to the foot within the range of the friction cone, we obtain:
[0016]
[0017] in, Indicates the first The reaction force at the foot of each leg.
[0018] Preferably, the establishment of the tracking error system model for the equivalent motion of the quadruped robot is as follows: Based on the difference between the actual state and the reference state of the quadruped robot system ， The tracking error is defined as:
[0019] Among them, the reference state is The reference trajectory of the quadruped robot under strong interference is set as a stable body height and horizontal non-rotation. The tracking error system model and equivalent constraints are obtained:
[0020]
[0021] The expression for the nominal tracking error system model is:
[0022] Among them, there exists a matrix , making the matrix It is Hurwitz; d This is a disturbance term.
[0023] Preferably, the design of the interference observer is as follows: Composite control input is defined as:
[0024] in, and These are interference compensation and pipe-based model predictive control inputs, respectively. Design a disturbance observer to estimate the mismatch disturbance:
[0025]
[0026] in, For observer gain, As an auxiliary variable, For interference estimation, and ; Define the interference estimation error as ,get ; The interference observer is designed as follows:
[0027] Substituting into the tracking error system model, we obtain the closed-loop system:
[0028] in, This indicates that the model predicts the control input based on the pipe.
[0029] Preferably, the design of the composite disturbance rejection model predictive control method is as follows: S301. Design an optimization control problem, and obtain the optimal control input sequence by solving the optimization control problem to obtain the model predictive controller; S302. Design an auxiliary controller; the auxiliary controller is a state feedback controller, which is designed based on the actual state affected by disturbance and the nominal state error; based on the combination of the model predictive controller and the auxiliary controller, a tube-based model predictive controller is obtained. The tube-based model predictive controller and the disturbance compensation are used as the composite control input of the tracking error system model, thus obtaining a composite disturbance rejection model predictive control method. S303, Calculate robust tightening constraints.
[0030] Furthermore, the design optimization control problem is as follows: Define the prediction time domain and trigger time series are ,in The quadruped robot system at the trigger moment The local optimization problem is expressed as:
[0031]
[0032]
[0033]
[0034] in, and They represent The time-labeled nominal tracking error system model has feasible input trajectories and corresponding predicted state trajectories, superscript... Optimal case; For terminal state constraints, where It is a positive number; Cost function Represented as:
[0035] in, It is a positive definite weight matrix; pass The optimal control input sequence is designed as follows:
[0036] in, It serves as the control input for model prediction.
[0037] Furthermore, the design of the auxiliary controller is as follows: The state feedback controller is designed based on the actual state affected by disturbances and the nominal state error:
[0038] in, For feedback gain, satisfying It is Hurwitz; The pipe-based model predictive controller is obtained by combining the standard model predictive controller and the auxiliary controller:
[0039] By substituting the pipe-based model predictive controller and disturbance compensation inputs into the tracking error system model and the nominal tracking error system model, a composite closed-loop system is obtained:
[0040] in, and These are the inputs for disturbance compensation and model predictive control, respectively.
[0041] Furthermore, the calculation of robust tightening constraints is specifically as follows: Since the difference between the actual state of the quadruped robot system under disturbance and its nominal state without disturbance satisfies the inequality... Robust tightening constraints are obtained using Minkowski set subtraction:
[0042]
[0043] in, , .
[0044] Preferably, the recursion feasibility is as follows: The online solution process for optimizing control problems involves selecting a reasonable prediction time domain. State weight matrix , control input weight matrix Terminal weight matrix and auxiliary controller feedback gain The recursive feasibility of the composite disturbance rejection model predictive control method was verified.
[0045] Preferably, the stability analysis of the closed-loop system is as follows: By selecting appropriate parameters To ensure that the nominal closed-loop system exhibits asymptotic stability under control input, there exists a class of... function accomplish:
[0046] in, Defined as , It is a type function; In control input The tracking error closed-loop system under the action is input-state stable, verifying the stability of the closed-loop system.
[0047] Compared with the prior art, the beneficial effects of the present invention are: (1) The method in this invention effectively optimizes the overall motion performance of the quadruped inspection robot. By mitigating the adverse effects of multi-source uncertain interference on the robot's motion control, this invention improves the robot's control accuracy and limits the force applied to the feet within a feasible anti-slip range, effectively maintaining the robot's posture stability.
[0048] (2) The method in this invention effectively improves the ability of the quadruped inspection robot to resist external disturbances under complex working conditions. This invention designs an interference observer to actively estimate and compensate for interference caused by uncertainties in the external environment and the system; and designs an auxiliary controller based on the error between the actual state and the nominal state affected by the interference to compensate for the impact of multi-source disturbances of uncertainties in the external environment and the system at different times, thereby achieving anti-interference.
[0049] (3) The method in this invention considers the Coulomb friction cone constraint to effectively solve the problem of foot slippage in quadruped inspection robots. In establishing the state space equation of the quadruped robot system, in order to avoid foot slippage when the robot walks, the method of this invention designs the foot force to be within the range of the friction cone, and establishes a corresponding tracking error system model. The reference trajectory of the quadruped robot under strong interference is set as the reference state of body height stability and horizontal non-rotation, thereby realizing the constraint on the feet of the quadruped inspection robot. Attached Figure Description
[0050] Figure 1 This is a flowchart of the composite anti-disturbance and anti-slip motion control method for the quadrupedal inspection robot in this invention; Figure 2 This is a schematic diagram of the composite anti-disturbance and anti-slip motion control method for the quadrupedal inspection robot in this invention. Figure 3 This is a schematic diagram of the Euler angles and position trajectory of the quadruped inspection robot under the composite anti-disturbance and anti-slip motion control method of the present invention; Figure 4 This is a schematic diagram of the angular velocity and linear velocity trajectory of the quadruped inspection robot under the composite anti-disturbance and anti-slip motion control method of the present invention; Figure 5 This is a schematic diagram of the force trajectory at the front foot of the quadruped inspection robot under the composite anti-disturbance and anti-slip motion control method of the present invention; Figure 6 This is a schematic diagram of the force trajectory of the rear foot of a quadruped inspection robot under the composite anti-disturbance and anti-slip motion control method of the present invention. Detailed Implementation
[0051] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0052] Example 1: See Figure 1 A composite anti-disturbance and anti-slip motion control method for a quadruped inspection robot includes the following steps: S1. Establish a single rigid body dynamic model of a quadruped inspection robot affected by uncertain disturbances and constrained by Coulomb friction cones, and establish an equivalent motion tracking error system model based on the quadruped robot dynamic model.
[0053] Specifically, the single-rigid-body dynamic model of the quadrupedal inspection robot, which is affected by uncertain disturbances and constrained by the Coulomb friction cone, is established as follows: Quadruped robots have complex mechanical structures. To simplify the complexity of dynamic analysis and control algorithm design, a single rigid body dynamics model is used to approximate the motion of the quadruped robot. The inertial effects caused by leg movements are ignored, and only the most important center of mass dynamics is considered. The quadruped robot is simplified to a single rigid body dynamics model consisting only of the torso and joint modules. A world coordinate system for global reference. Using the robot's own body coordinate system, and based on the Newton-Euler equations, a dynamic analysis of the quadruped robot is performed to obtain the dynamic relationship between the quadruped robot's center of mass acceleration and the force applied to its feet: (1) in, This indicates the position of the robot's center of mass in the world coordinate system. Indicates the mass of a quadruped robot. Represents gravitational acceleration. Indicates the first The reaction force at the foot of one leg; set up The inertial tensor in the robot's body coordinate system can be expressed as the mass of the quadruped robot. ,length ,width and height Conclusion: (2) When the quadruped robot moves, the inertia tensor in the world coordinate system is: (3) in, This represents the rotation matrix from the body coordinate system to the world coordinate system.
[0054] According to the angular momentum theorem, the vector expression for the moment of inertia of the quadruped robot is obtained as follows: (4) (5) in, Let be the angular velocity of the robot's center of mass in the world coordinate system. This represents the distance vector from the ground reaction point to the center of mass, calculated by subtracting the first value from the center of mass position obtained from the state estimator. The position of one leg For any vector , Indicates satisfaction The antisymmetric matrix; The robot's pose is typically determined using ZYX Euler angles in the body coordinate system. It means that, among them This is the roll angle. The pitch angle, Let yaw be the angle of rotation; from this, the expression for the rotation matrix from the body coordinate system to the world coordinate system is: (6) in, , , , indicating around Rotation of axis in the positive direction angle.
[0055] in, (7) Next, using the rotation matrix, the angular velocity of the robot's center of mass in the world coordinate system is obtained based on the robot's attitude Euler angles: (8) in: (9) Considering only the case where the quadruped robot walks on the ground, and assuming the robot's pitch angle is not 90° (i.e. ), for the mapping matrix Inverse mapping yields the reverse mapping relationship: (10) To ensure stability during movement, the pitch angle of a quadruped robot... and roll angle Approaching zero; simultaneously, the angle between the Z-axis of the body coordinate system and the Z-axis of the world coordinate system is almost zero; simplifying the above expression yields: (11) According to Euler's formula, considering that the angular velocity of the robot during motion is relatively small, it can be ignored. From the item, we can obtain: (12) Considering the multi-source disturbances caused by external environmental and internal system uncertainties affecting the robot, and given that the robot's pitch and roll angles are close to zero, the disturbed dynamic equations for the quadruped robot can be obtained as follows: (13) (14) (15) (16) The Euler angles, center-of-mass coordinates, velocity, and angular velocity of the quadruped robot are taken as the system state, and the gravitational acceleration is written into the coefficient matrix to obtain the system state variables. The ground reaction force is defined as the control input, i.e. The state-space equations of the system can be obtained as follows: (17) (18) in, and These are the system's state and control inputs, respectively. It is a disturbance term, and satisfies ,in, Given constants; matrix Furthermore, the constraint conditions for the friction cones at the foot ends of the quadruped robot are as follows: (19) Since the force exerted by the ground on the feet of the quadruped robot in the vertical direction cannot be negative, the minimum force is... Set to 0; furthermore, to prevent the robot's feet from slipping while walking, the force applied to the feet must be within the range of the friction cone, i.e.: (20) Therefore, we can conclude that: (twenty one) (twenty two) Assuming the quadruped robot's reference trajectory under strong disturbance is one where the robot is height-stable and horizontally non-rotating, i.e., the reference state is... The tracking error is defined as: (twenty three) Therefore, the tracking error system and equivalent constraints are obtained: (twenty four) (25) The expression for the nominal tracking error system is: (26) And there exists a matrix , making the matrix It's by Hurwitz.
[0056] S2. Design an interference observer to actively estimate and compensate for interference caused by uncertainties in the external environment and the system.
[0057] Specifically, the composite control input is defined as: (27) in, and These are interference compensation and pipe-based model predictive control inputs, respectively. Design a disturbance observer to estimate mismatch disturbances: (28) (29) in, For observer gain, As an auxiliary variable, For interference estimation, and The interference estimation error is defined as... Therefore, we can conclude that: (30) Therefore, the interference observer is designed as follows: (31) Substituting the above equation into the tracking error model yields the closed-loop system: (32) S3. Based on the equivalent tracking error system of the quadruped robot, design a composite disturbance rejection model predictive control method, such as... Figure 2 As shown. Specifically, it includes the following steps: S3.1 Optimization control problem design: Define the prediction time domain and trigger time series are ,in The system at the trigger time The local optimization problem can be expressed as: (33) (34) (35) (36) (37) (38) in, and They represent The time signature indicates the feasible input trajectory and the corresponding predicted state trajectory of the nominal system, superscript Optimal case; For terminal state constraints, where It is a positive number; Cost function Represented as:
[0059] in, It is a positive definite weight matrix; By solving optimization problems The optimal control input sequence is designed as follows: (39) S3.2 Design of auxiliary controller: The state feedback controller is designed based on the actual state affected by disturbances and the nominal state error: (40) in, For feedback gain, satisfying It's by Hurwitz; The pipe-based model predictive controller is obtained by combining the standard model predictive controller and the auxiliary controller: (41) By incorporating the pipe-based model predictive controller and disturbance compensation inputs into the tracking error system and the nominal system, a composite closed-loop system is obtained: (42) S3.3 Calculate robust tightening constraints: Since the difference between the actual state of the quadruped robot system under disturbance and its nominal state without disturbance satisfies the inequality... ,in, , Robust tightening constraints can be obtained using Minkowski set subtraction: (43) (44) S4. Verify the recursive feasibility of the control method and the stability of the closed-loop system. This specifically includes the following steps: S4.1 Feasibility analysis of recursion in the optimization problem: The online solution process for optimizing control problems involves selecting a reasonable prediction time domain. State weight matrix , control input weight matrix Terminal weight matrix and auxiliary controller feedback gain This ensures the recursive feasibility of the proposed control strategy. S4.2, Stability analysis of closed-loop system: By selecting appropriate parameters This ensures that the nominal closed-loop system exhibits asymptotic stability under control input, therefore there exists a class of... function Make: (45) Therefore, we get: (46) in, Defined as , It is a type Function; therefore, in control input The closed-loop tracking error system under the action is input-state stable, therefore the actual system controls the input... Input-state stability was also achieved; the stability verification of the closed-loop system was completed.
[0060] Experimental verification: To verify the composite anti-disturbance and anti-slip motion control method for the quadrupedal inspection robot provided in this embodiment, MATLAB was used for simulation experiments, and detailed explanations are provided below: The quadruped inspection robot single rigid body model provided in this embodiment is designed with a composite anti-disturbance and anti-slip motion control method, which can alleviate the adverse effects of multi-source uncertain interference on robot motion control, improve the robot's control accuracy, and limit the force applied to the feet to the anti-slip feasible range, thus better maintaining the robot's posture stability.
[0061] The quadruped robot system parameters are set as follows. In the simulation, the robot's body is simplified to a rectangle, the leg mass is ignored, the robot's center of mass is at the geometric center of gravity, and the mass is [value missing]. Its length, width and height are respectively , ,as well as The acceleration due to gravity is The coefficient of friction is Set the minimum force at the foot. Maximum force at the foot Inertial tensor in body coordinate system Assume the initial state of the quadrupedal inspection robot. At the initial moment, the force exerted vertically upward on the feet of all four legs is... In addition, a perturbation acceleration is applied to the quadruped robot. and disturbance angular acceleration The control objective is to stabilize the posture of a quadruped robot that is subject to multiple disturbances.
[0062] The parameter design of the composite disturbance rejection model predictive controller for the quadrupedal inspection robot is as follows: State weight matrix Input weight matrix It is a diagonal matrix with all diagonal elements equal to 0.05; the interference observer is used for active interference compensation, and its gain is... Terminal domain constants Sampling time is Predicting the time domain Total simulation duration .
[0063] Based on the above parameters, the control method proposed in this invention was simulated and verified. The corresponding simulation results are as follows: Figures 3-6 As shown. Among them, Figure 3 and Figure 4 The state trajectory of the quadruped robot under the proposed composite disturbance rejection model predictive control strategy is shown, proving that the proposed control method can guarantee the stability of the quadruped robot's posture. Figure 5 and Figure 6 The diagram illustrates the force trajectories of the four legs of the quadruped robot in the XYZ axis directions under the proposed control method, and is constrained within the anti-slip force constraint.
[0064] The above description is only for the purpose of helping to understand the method and core essence of the present invention, but the scope of protection of the present invention is not limited thereto. For those skilled in the art, any equivalent substitutions or modifications made to the technical solution and inventive concept disclosed in the present invention within the scope of the technology disclosed in the present invention should be covered within the scope of protection of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.
Claims
1. A composite anti-disturbance and anti-slip motion control method for a quadruped inspection robot, characterized in that, Includes the following steps: S1. Establish a single rigid body dynamic model of a quadruped robot under the influence of uncertain disturbances and the constraint of Coulomb friction cone, and based on the single rigid body dynamic model of the quadruped robot, establish a tracking error system model of the equivalent motion of the quadruped robot. S2. Design an interference observer based on the tracking error system model to actively estimate and compensate for interference caused by uncertainties in the external environment and the system. S3. Solve the design optimization control problem to obtain the model predictive controller. Based on the error between the actual state and the nominal state affected by the disturbance, design the auxiliary controller. Based on the disturbance observer, the model predictive controller and the auxiliary controller as the composite control input of the tracking error system model, design a composite disturbance rejection model predictive control method. S4. Verify the recursive feasibility of the composite disturbance rejection model predictive control method and the stability of the closed-loop system.
2. The composite anti-disturbance and anti-slip motion control method for a quadrupedal inspection robot according to claim 1, characterized in that, The establishment of a single rigid body dynamic model for a quadruped robot subject to uncertain disturbances and Coulomb friction cone constraints is detailed below: The disturbed dynamic equations of the quadruped robot are as follows: in, This represents the acceleration of the center of mass of the quadruped robot. m Indicates the mass of a quadruped robot. g Represents gravitational acceleration. Indicates the first The reaction force at the foot of one leg; Let be the angular velocity of the robot's center of mass in the world coordinate system. This represents the distance vector from the point of ground reaction force to the center of mass; This is the roll angle. The pitch angle, Yaw angle Indicates circling Z Rotation of axis in the positive direction angle, R This represents the rotation matrix from the body coordinate system to the world coordinate system; I Let be the inertial tensor in the world coordinate system during the movement of the quadruped robot. Let be the inertial tensor in the body coordinate system of the quadruped robot; , This refers to the disturbance term caused by uncertainties in the external environment and the internal workings of the quadruped robot. Euler angles of a quadruped robot Centroid coordinates p ,speed and angular velocity As a quadruped robot system state, and considering gravitational acceleration. g By incorporating the coefficient matrix, the state variables of the quadruped robot system can be obtained. The ground reaction force is defined as the control input, i.e. The state-space equations of the quadruped robot system are obtained as follows: in, and These represent the state and control inputs of the quadruped robot system. It is a disturbance term, and satisfies ,in, Given constants; matrix ; Constraints based on the friction cone at the foot of a quadruped robot Minimum force Setting the value to 0 and controlling the force applied to the foot within the range of the friction cone, we obtain: in, Indicates the first The reaction force at the foot of each leg.
3. The composite anti-disturbance and anti-slip motion control method for a quadrupedal inspection robot according to claim 2, characterized in that, The specific steps for establishing the tracking error system model for the equivalent motion of the quadruped robot are as follows: Based on the difference between the actual state and the reference state of the quadruped robot system ， The tracking error is defined as: Among them, the reference state is The reference trajectory of the quadruped robot under strong interference is set as a stable body height and horizontal non-rotation. The tracking error system model and equivalent constraints are obtained: The expression for the nominal tracking error system model is: Among them, there exists a matrix , making the matrix It is Hurwitz; d This is a disturbance term.
4. The composite anti-disturbance and anti-slip motion control method for a quadrupedal inspection robot according to claim 3, characterized in that, The design of the interference observer is as follows: Composite control input is defined as: in, and These are interference compensation and pipe-based model predictive control inputs, respectively. Design a disturbance observer to estimate the mismatch disturbance: in, For observer gain, As an auxiliary variable, For interference estimation, and ; Define the interference estimation error as ,get ; The interference observer is designed as follows: Substituting into the tracking error system model, we obtain the closed-loop system: in, This indicates that the model predicts the control input based on the pipe.
5. The composite anti-disturbance and anti-slip motion control method for a quadrupedal inspection robot according to any one of claims 1-4, characterized in that, The design of the composite disturbance rejection model predictive control method is as follows: S301. Design an optimization control problem, and obtain the optimal control input sequence by solving the optimization control problem to obtain the model predictive controller; S302, Design an auxiliary controller; The auxiliary controller is a state feedback controller, which is designed based on the actual state affected by disturbance and the nominal state error. The combination of the model predictive controller and the auxiliary controller yields a tube-based model predictive controller. The tube-based model predictive controller and the disturbance compensation serve as the composite control input of the tracking error system model, resulting in a composite disturbance rejection model predictive control method. S303, Calculate robust tightening constraints.
6. The composite anti-disturbance and anti-slip motion control method for a quadrupedal inspection robot according to claim 5, characterized in that, The design optimization and control problem is as follows: Define the prediction time domain and trigger time series are ,in The quadruped robot system at the trigger moment The local optimization problem is expressed as: in, and They represent The time-labeled nominal tracking error system model has feasible input trajectories and corresponding predicted state trajectories, superscript... Optimal case; For terminal state constraints, where It is a positive number; Cost function Represented as: in, It is a positive definite weight matrix; pass The optimal control input sequence is designed as follows: in, It serves as the control input for model prediction.
7. The composite anti-disturbance and anti-slip motion control method for a quadrupedal inspection robot according to claim 6, characterized in that, The design of the auxiliary controller is as follows: The state feedback controller is designed based on the actual state affected by disturbances and the nominal state error: in, For feedback gain, satisfying It is Hurwitz; The pipe-based model predictive controller is obtained by combining the standard model predictive controller and the auxiliary controller: By substituting the pipe-based model predictive controller and disturbance compensation inputs into the tracking error system model and the nominal tracking error system model, a composite closed-loop system is obtained: in, and These are the inputs for disturbance compensation and model predictive control, respectively.
8. The composite anti-disturbance and anti-slip motion control method for a quadrupedal inspection robot according to claim 7, characterized in that, The calculation of robust tightening constraints is as follows: Since the difference between the actual state of the quadruped robot system under disturbance and its nominal state without disturbance satisfies the inequality... Robust tightening constraints are obtained using Minkowski set subtraction: in, , .
9. The composite anti-disturbance and anti-slip motion control method for a quadruped inspection robot according to claim 6, characterized in that, The feasibility of the recursion is as follows: The online solution process for optimizing control problems involves selecting a reasonable prediction time domain. State weight matrix , control input weight matrix Terminal weight matrix and auxiliary controller feedback gain The recursive feasibility of the composite disturbance rejection model predictive control method was verified.
10. The composite anti-disturbance and anti-slip motion control method for a quadrupedal inspection robot according to claim 7, characterized in that, The stability analysis of the closed-loop system is as follows: By selecting appropriate parameters To ensure that the nominal closed-loop system exhibits asymptotic stability under control input, there exists a class of... function accomplish: in, Defined as , It is a type function; In control input The tracking error closed-loop system under the action is input-state stable, verifying the stability of the closed-loop system.