Robot control methods and systems considering mismatched disturbances and actuator failures

Abstract

This invention belongs to the field of robot control technology and discloses a robot control method and system considering mismatched disturbances and actuator faults, including the following steps: (1) constructing a robot kinematic error model considering mismatched disturbances and actuator faults; (2) designing a fractional-order decoupled sliding surface related to the error; (3) designing a chatter-free superspiral sliding surface reaching law and constructing a gain adaptive barrier function; (4) designing an actuator fault estimator; (5) designing a controller based on the chatter-free superspiral sliding surface reaching law and the actuator fault estimator, and using the controller to perform trajectory tracking control on the robot. This invention enables fast, jitter-free adaptive tracking control of a mobile robot when boundary information of the disturbance derivative is lacking.

Description

Technical Field

[0001] This invention belongs to the field of robot control technology, and more specifically, relates to a robot control method and system that takes into account mismatch disturbances and actuator failures. Background Technology

[0002] In industrial environments, trajectory tracking is one of the most critical issues in the autonomous navigation of mobile robots and a key focus of the robotics industry. Industrial environments typically face mismatched disturbances such as external load variations and model uncertainties, which usually cannot be directly compensated for by control variables. Furthermore, uneven and slippery industrial surfaces can impact actuators, increasing the risk of malfunction or failure. These factors negatively impact the robot's motion and control performance, necessitating appropriate measures to address these problems. Sliding mode control, due to its insensitivity to disturbances, is widely used in mobile robotics. It achieves rapid control of the system state by introducing a sliding surface to counteract the effects of external disturbances and system uncertainties. The balance between its switching gain and the chattering caused by disturbances remains a key research topic. In the field of sliding mode motion control for mobile robots, the aforementioned disturbances and faults are usually treated as concentrated disturbances, such as by designing a disturbance compensator or disturbance observer to compensate for system uncertainties. However, this integrated disturbance handling method is not precise enough and cannot accurately estimate time-varying uncertainties in actual industrial scenarios. Another approach is to enhance the robustness of the system by adaptively adjusting the corresponding control gain. This method requires a bounded disturbance or an upper limit of the derivative, and it is necessary to consider the relationship between chattering caused by the gain and the convergence speed.

[0003] Therefore, based on the above analysis, although sliding mode control has demonstrated its effectiveness in disturbance handling, there are still aspects that urgently need improvement when applying sliding mode control to robot motion control, especially for the diverse disturbances encountered by mobile robots under harsh working conditions:

[0004] 1) In traditional sliding mode control, existing methods treat the system uncertainties of mobile robots, including parameter perturbations, external disturbances, and actuator output errors, as integrated disturbances without distinguishing between matched and unmatched disturbances. This is obviously not suitable for accurate compensation of uncertainties under actual working conditions.

[0005] 2) In the absence of boundary information on the derivative of the unmatched disturbance, how to balance the relationship between switching gain and disturbance change in sliding mode control in order to achieve fast convergence while reducing chattering;

[0006] Therefore, in the face of harsh industrial environments for mobile robots, there is an urgent need for a compensation scheme for control input errors under unknown and uncertain boundaries, which can compensate for external mismatch disturbances and actuator failures, thereby enabling mobile robots to achieve robust and stable tracking control. Summary of the Invention

[0007] In view of the above-mentioned defects or improvement needs of the prior art, the present invention provides a robot control method and system that takes into account mismatch disturbances and actuator failures. Its purpose is to achieve fast and jitter-free adaptive tracking control of mobile robots when boundary information of disturbance derivatives is lacking.

[0008] To achieve the above objectives, according to one aspect of the present invention, a robot control method considering mismatched disturbances and actuator failures is provided, the control method comprising the following steps:

[0009] (1) Construct a robot kinematic error model that considers mismatched disturbances and actuator failures. The mathematical expression of the robot kinematic error model is as follows:

[0010]

[0011] In the formula, Let u be the pose error in the vehicle coordinate system, and φ be the control variable. This refers to the error bias caused to the controller by actuator failure. This is a non-matching perturbation;

[0012] in,

[0013]

[0014] In the formula, (x,y,θ) represents the pose space of the mobile robot, including its position (x,y) and orientation θ. r ,y r ,θ r (v) represents the reference state pose space, v represents the axial velocity, and ω represents the rotational speed of the robot body. r ,ω r (x) is the reference input signal; e ,y e ,θ e The position space error is in the vehicle coordinate system.

[0015] (2) Design of a fractional-order decoupled sliding surface related to error;

[0016] (3) Design a chatter-free superspiral sliding membrane approach law and construct a gain-adaptive barrier function;

[0017] (4) Design an actuator fault estimator. The expression for the actuator fault estimator is:

[0018]

[0019] In the formula, σ1 is a constant greater than 0; g T (q e ) is g(q e The transpose of )

[0020] (5) A controller is designed based on the flutter-free super-helical sliding membrane approach law and the actuator fault estimator, and the controller is used to perform trajectory tracking control on the robot.

[0021] Furthermore, error bias Assuming constant bias, For bounded unmatched perturbations,

[0022] Furthermore, the expression corresponding to the fractional-order decoupled sliding surface is:

[0023]

[0024] For sliding surface, σ1,σ2,α,γ are positive numbers, and α<1,γ<1, The first-α fractional differential in the Riemann-Liouville form is expressed as: Γ(α) is a Gamma function. e is the natural index, and t0 and t are the lower and upper limits, respectively.

[0025] Furthermore, differentiating the expression corresponding to the fractional-order decoupled sliding surface yields:

[0026]

[0027] Therefore, the equation for calculating the control law is expressed as follows:

[0028]

[0029] in, An estimator for actuator fault bias.

[0030] Furthermore, the expression for the flutter-free superspiral sluice film reaching law is:

[0031]

[0032] In the formula, ||s|| is the Euclidean norm of s, and ||s|| = (s T s)1 / 2 The adaptive gain κ(s) is:

[0033]

[0034] in, The value is positive, and t0 is the gain switching time, indicating when ||s|| is satisfied for the first time. At that moment.

[0035] Furthermore, when far from the sliding surface, a time-linearly related gain is used, while when close to the sliding surface, a variable gain based on the barrier function is switched.

[0036] Furthermore, the expression for the controller is:

[0037]

[0038] Actuator failures can be mitigated using the proposed estimator.

[0039] Furthermore, the variable gain sliding mode controller of the barrier function can resolve unknown disturbances for any And for all t≥0, the inequality Established.

[0040] Furthermore, time-varying gain is used to ensure the reachability of small neighborhoods of the sliding surface, and then gain based on the barrier function is used to ensure the maintenance of this neighborhood during sliding motion.

[0041] The present invention also provides a robot control system that takes into account mismatch disturbances and actuator failures. The control system includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it performs the robot control method that takes into account mismatch disturbances and actuator failures as described above.

[0042] In summary, compared with the prior art, the robot control method and system considering mismatched disturbances and actuator failures provided by the present invention have the following advantages:

[0043] 1. This invention establishes a kinematic tracking error model that includes unmatched disturbances and actuator faults. By constructing a fractional-order differential sliding surface related to the error, the system uncertainty of the mobile robot is distinguished into matched disturbances and unmatched disturbances, such as parameter perturbations and external disturbances. The actuator output error is a matched disturbance, thus achieving accurate compensation for uncertainty.

[0044] 2. Since actuator failures are prone to occur in real-world systems, this invention designs a fault estimator for mobile robot applications. This fault estimator is integrated with the controller to form an overall controller that takes into account mismatch disturbances and actuator failures.

[0045] 3. This invention designs a two-phase variable gain sliding diaphragm approaching law. The approaching law has no overgain, which significantly reduces chatter reaching the sliding diaphragm surface, thereby reducing jitter and improving tracking accuracy. The designed chatter-free variable gain sliding diaphragm approaching law, as well as the linear adaptive gain far from the sliding diaphragm surface and the variable gain of the barrier function when approaching the sliding diaphragm surface, ensure that the error approaches zero within a finite time. The design of the new barrier function ensures that the gain increases as the disturbance increases, thereby ensuring that the output value belongs to the required range and improving the robustness of control. Attached Figure Description

[0046] Figure 1 This is a schematic diagram of the motion model of the mobile robot involved in the embodiments of the present invention;

[0047] Figure 2 This is a schematic diagram of the variable gain sliding diaphragm control system according to an embodiment of the present invention;

[0048] Figure 3 This is a schematic diagram illustrating the approach process of the sliding membrane variable gain barrier function involved in an embodiment of the present invention. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0050] This invention provides a robot control method and system that considers mismatched disturbances and actuator failures. The variable gain process of the control method, under mismatched disturbances, possesses sufficient gain variation capability to adapt to rapid changes in the disturbance, thereby achieving rapid disturbance suppression. Furthermore, this process avoids over-gain, reducing adverse effects such as chatter. Simultaneously, this invention achieves rapid convergence, enabling robust, jitter-free tracking control even in the absence of boundary information regarding the derivative of the mismatched disturbance.

[0051] Please see Figure 1 , Figure 2 and Figure 3 The control method mainly includes the following steps:

[0052] S1, Construct a robot kinematic error model considering mismatched disturbances and actuator failures. The mathematical expression of the robot kinematic error model is as follows:

[0053]

[0054] In the formula, Let u be the pose error in the vehicle coordinate system, and φ be the control variable. This refers to the error bias caused to the controller by actuator failure. This is a non-matching perturbation;

[0055] in,

[0056]

[0057] In the formula, (x,y,θ) represents the pose space of the mobile robot, including its position (x,y) and orientation θ. r ,y r ,θ r (v) represents the reference state pose space, v represents the axial velocity, and ω represents the rotational speed of the robot body. r ,ω r (x) is the reference input signal; e ,y e ,θ e ) represents the pose space error in the vehicle coordinate system.

[0058] In this embodiment, such as Figure 1 As shown, the mobile robot is a four-wheel, all-steering, independently driven mobile robot capable of operating in different modes. Continuous input u represents:

[0059]

[0060] Where, θ f This is the front steering angle, with counter-clockwise angles defined as positive and clockwise angles as negative; L = L f +L r The axial length r of the robot is represented by the front wheel rotation angle θ. f and rear wheel steering angle θ r The determining coefficient is expressed as r = tan(θ) r ) / tan(θ f ).

[0061] r is represented as:

[0062]

[0063] Error bias Assuming constant bias, It is a bounded unmatched perturbation, but the upper bound is unknown.

[0064] S2, designing a fractional-order decoupled sliding surface related to error.

[0065] The expression corresponding to the fractional-order decoupled sliding surface is:

[0066]

[0067] For sliding surface, σ1,σ2,α,γ are positive numbers, and α<1,γ<1, The first-α fractional differential in the Riemann-Liouville form is expressed as: Γ(α) is a Gamma function. e is the natural index, and t0 and t are the lower and upper limits, respectively.

[0068] Differentiate the above equation:

[0069]

[0070] Therefore, the equation for calculating the control law is expressed as follows:

[0071]

[0072] in, An estimator for actuator fault bias.

[0073] S3, design a chatter-free superspiral sliding membrane approach law and construct a gain-adaptive barrier function.

[0074] The expression for the flutter-free superspiral sluice membrane reaching law is:

[0075]

[0076] In the formula, ||s|| is the Euclidean norm of s, and ||s|| = (s T s) 1 / 2 The adaptive gain κ(s) is:

[0077]

[0078] in, The value is positive, and t0 is the gain switching time, indicating when ||s|| is satisfied for the first time. At that moment.

[0079] A time-linearly dependent gain is used when far from the sliding surface, switching to a variable gain based on the barrier function as the surface approaches. This variable gain sliding mode controller based on the barrier function can handle unknown disturbances and is suitable for any... And for all t≥0, the inequality The proposed two-phase gain mechanism, used to assist the non-decoupled sliding mode reachability law, is established to resist uncertain disturbances. Time-varying gain ensures the reachability of a small neighborhood on the sliding surface, and then a barrier function-based gain is employed to maintain this neighborhood during sliding mode motion. The barrier function gain strategy avoids gain overestimation while providing sufficient adaptability to drastic changes in disturbances.

[0080] S4, Design an actuator fault estimator. The expression for the actuator fault estimator is:

[0081]

[0082] In the formula, σ1 is a constant greater than 0; g T (q e ) is g(q e The transpose of ).

[0083] S5. A controller is designed based on the flutter-free super-helical sliding membrane approach law and the actuator fault estimator. The controller is used to perform trajectory tracking control on the robot.

[0084] The expression for the controller is:

[0085]

[0086] Actuator failures can be mitigated using the proposed estimator.

[0087] This invention also employs a Lyapunov function to verify the stability of the controller. The Lyapunov function is:

[0088]

[0089] in

[0090] Differentiating the Lyapunov function and substituting the controller, we get:

[0091]

[0092] Since the actuator fault is a constant bias, i.e. Substituting this into the estimator, we get:

[0093]

[0094] Because of ||s|| 2 =sT s, and the aforementioned Lyapunov function is:

[0095]

[0096] When 0≤t<t0, κ(s)=αt, and the Lyapunov function becomes:

[0097]

[0098] If Since αt||s|| 1 / 2 is increasing for t≥0, suppose that when , the Lyapunov function is decreasing at this time; when t=t0, it indicates that the sliding variable has entered the region, which proves the reachability of

[0099] When t≥t0,

[0100]

[0101] Let

[0102]

[0103]

[0104] Since Ψ1(||s||) and Ψ2(||s||) are increasing, Ψ(||s||) is decreasing, and therefore, there exists a value between the interval such that Ψ(||s||)=0. When , is less than 0, and the error variable will force to decrease to This proves the convergence of the variables for t>0 and ensures the maintenance of the sliding variable ||s||

[0105] The present invention also provides a robot control system considering unmatched disturbances and actuator faults, the control system comprising a memory and a processor, the memory storing a computer program, and the processor executing the computer program to perform the above-described robot control method considering unmatched disturbances and actuator faults.

[0106] ​Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements 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 control method considering mismatched disturbances and actuator failures, characterized in that, The control method includes the following steps: (1) Construct a robot kinematic error model that considers mismatched disturbances and actuator failures. The mathematical expression of the robot kinematic error model is as follows: In the formula, Let u be the pose error in the vehicle coordinate system, and φ be the control variable. This refers to the error bias caused to the controller by actuator failure. This is a non-matching perturbation; in, In the formula, (x,y,θ) represents the pose space of the mobile robot, including its position (x,y) and orientation θ. r ,y r ,θ r (v) represents the reference state pose space, v represents the axial velocity, and ω represents the rotational speed of the robot body. r ,ω r (x) is the reference input signal; e ,y e ,θ e The position space error is in the vehicle coordinate system. (2) Design a fractional-order decoupled sliding surface related to error; (3) Design a chatter-free super-spiral sliding mode reaching law and construct a gain adaptive barrier function; (4) Design an actuator fault estimator. The expression for the actuator fault estimator is: In the formula, σ1 is a constant greater than 0; g T (q e ) is g(q e The transpose of ) (5) A controller is designed based on the flutter-free super-helical sliding mode approach law and the actuator fault estimator, and the controller is used to perform trajectory tracking control on the robot.

2. The robot control method considering mismatched disturbances and actuator failures as described in claim 1, characterized in that: Error bias Assuming a constant bias, For bounded unmatched perturbations, 3. The robot control method considering mismatched disturbances and actuator failures as described in claim 1, characterized in that: The expression corresponding to the fractional-order decoupled sliding surface is: For sliding surface, σ1,σ2,α,γ are positive numbers, and α<1,γ<1, The first-α fractional differential in the Riemann-Liouville form is expressed as: Γ(α) is a Gamma function. e is the natural index, and t0 and t are the lower and upper limits, respectively.

4. The robot control method considering mismatched disturbances and actuator failures as described in claim 1, characterized in that: Differentiating the expression corresponding to the fractional-order decoupled sliding surface yields: Therefore, the equation for calculating the control law is expressed as follows: in, An estimator for actuator fault bias.

5. The robot control method considering mismatched disturbances and actuator failures as described in claim 3, characterized in that: The expression for the flutter-free superspiral sliding mode reaching law is: In the formula, ||s|| is the Euclidean norm of s, and ||s|| = (s T s) 1 / 2 The adaptive gain κ(s) is: in, The value is positive, and t0 is the gain switching time, indicating when ||s|| is satisfied for the first time. At that moment.

6. The robot control method considering mismatched disturbances and actuator failures as described in claim 5, characterized in that: When far from the sliding surface, a time-linearly related gain is used, while when close to the sliding surface, a variable gain based on the barrier function is switched.

7. The robot control method considering mismatched disturbances and actuator failures as described in claim 5, characterized in that: The expression for the controller is: Actuator failures can be mitigated using the proposed estimator.

8. The robot control method considering mismatched disturbances and actuator failures as described in claim 5, characterized in that: A variable-gain sliding mode controller for the barrier function can resolve unknown disturbances for any And for all t≥0, the inequality Established.

9. The robot control method considering mismatched disturbances and actuator failures as described in claim 5, characterized in that: The reachability of a small neighborhood of the sliding surface is guaranteed by using time-varying gain, and then the gain based on the barrier function is used to ensure the maintenance of this neighborhood during the sliding motion.

10. A robot control system that considers mismatch disturbances and actuator failures, characterized in that: The control system includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it performs the robot control method according to any one of claims 1-9, which takes into account mismatch disturbances and actuator failures.

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