A robot robust safety control method based on control barrier function

Abstract

The application belongs to the technical field of robot control, and particularly relates to a robot robust safety control method based on a control barrier function, which comprises the following steps: step S1: a robot system model containing state variables, control inputs and disturbance terms is established; step S2: a disturbance observer is designed to estimate and compensate the disturbance of the system in real time; step S3: based on the disturbance estimation result, a system safety target is defined, a control barrier function is constructed to convert the safety constraints of the system into inequality conditions that need to be met by the control input, and system safety analysis is carried out to prove the forward invariance of the system safety set; step S4: a safety controller is designed by combining the control barrier function with an expected tracking controller, and system safety analysis is carried out to prove the forward invariance of the system safety set. The application realizes the control target of giving consideration to the safety and tracking performance of the system in an uncertain environment.

Description

Technical Field

[0001] This invention belongs to the field of robot control technology, specifically relating to a robust safety control method for robots based on a control obstacle function. Background Technology

[0002] With the rapid development of robotics technology in various fields such as industrial automation, medical-assisted surgery, warehousing and logistics, intelligent manufacturing, and home services, the operating environment is becoming increasingly complex and the task objectives are becoming more diversified, posing unprecedented challenges to the safety of control systems. In practical applications, robot systems often face a variety of uncertainties, such as external disturbances, uncertain system parameters, model nonlinearity errors, friction, load changes, and dynamic environmental interactions. If these factors are not effectively handled, they can easily lead to system performance degradation or even state out-of-bounds errors, resulting in serious safety hazards and affecting the accuracy of task completion and system stability, especially in scenarios with extremely high safety requirements, such as medical robots and collaborative robots.

[0003] Traditional control methods, such as PID control, robust control, optimal control, or adaptive control, can suppress system uncertainties to a certain extent, but they often struggle to balance control performance with ensuring real-time safety constraints. Furthermore, most of these methods rely on relatively ideal model assumptions, making them ill-suited for real-time response and proactive defense in the face of sudden disturbances or rapidly changing environments. Therefore, this application proposes a robust safety control method for robots based on a control obstacle function. Summary of the Invention

[0004] The purpose of this invention is to provide a robust safety control method for robots based on a control obstacle function, which can overcome the problems of insufficient safety control capability and weak robustness of robots in the existing technology under disturbed environments, so as to achieve the control objective of balancing safety and tracking performance of the system in uncertain environments.

[0005] The specific technical solution adopted by this invention is as follows:

[0006] A robust safety control method for robots based on a control obstacle function includes the following steps:

[0007] Step S1: Establish a robot system model that includes state variables, control inputs, and disturbance terms;

[0008] Step S2: Design a disturbance observer to estimate and compensate for system disturbances in real time;

[0009] Step S3: Based on the disturbance estimation results, define the system safety objective, construct the control barrier function to transform the system's safety constraints into inequality conditions that the control inputs must satisfy, and perform system safety analysis to prove the forward invariance of the system's safety level;

[0010] Step S4: Design a safety controller by combining the control barrier function with the desired tracking controller; and perform system safety analysis to prove the forward invariance of the system safety set.

[0011] The technical effects achieved by this invention are as follows:

[0012] In this invention, the method prioritizes safety as the core objective of control design. It introduces a disturbance observer to perform online estimation and dynamic compensation for unknown disturbances in the system, effectively improving the system's robustness in uncertain environments. Through precise modeling and real-time compensation of disturbances, the system can more accurately respond to environmental changes and dynamic disturbances, reducing the risk of the system deviating from its safe operating range. Furthermore, by utilizing a control barrier function, the originally difficult-to-handle safety constraint problem is transformed into inequality constraints that can be directly implemented in the controller, ensuring that the system state always remains within the preset safe region, thereby guaranteeing the safety of system operation. In addition, under the premise of satisfying safety constraints, this method can still achieve precise control of the tracking target, improving the flexibility and practicality of the control strategy. This method comprehensively considers the coordination between task execution and safety constraints, possessing good robustness, safety, and tracking performance. It is suitable for robot systems with disturbances and has high engineering application value and promotion potential.

[0013] The control method proposed in this invention combines robustness and flexibility, ensuring the safe operation of the robot in complex environments with uncertain disturbances while maintaining good control performance. It is suitable for robot systems with actual disturbance conditions. Attached Figure Description

[0014] Figure 1 A schematic diagram of the robot's safe state trajectory;

[0015] Figure 2 Schematic diagram of robot control input;

[0016] Figure 3 External interference and interference estimation diagram;

[0017] Figure 4 A schematic diagram comparing the safe state trajectory of robots using the method in this application with existing worst-case-based methods;

[0018] Figure 5 The control input diagram of the method in this application is compared with that of existing robots based on worst-case methods. Detailed Implementation

[0019] To make the objectives and advantages of this invention clearer, the invention will be specifically described below with reference to embodiments. It should be understood that the following text is merely used to describe one or more specific embodiments of the invention and does not strictly limit the scope of protection specifically claimed by the invention.

[0020] like Figures 1-5 As shown, a robust safety control method for robots based on a control obstacle function includes the following steps:

[0021] Step S1: Establish a robot system model that includes state variables, control inputs, and disturbance terms;

[0022] In step S1, the single-link robot is modeled as follows:

[0023]

[0024] Equation (1) describes the dynamic characteristics of a single-link system; θ represents the joint angle. They represent angular velocity and angular acceleration, respectively; I = ml 2 Let m be the moment of inertia, l be the rod mass, b be the coefficient of viscous friction, g be the acceleration due to gravity, mglsinθ represent the nonlinear gravity term, τ∈R be the joint torque, and d∈R be the moment of inertia. n For disturbance terms;

[0025] To facilitate controller design and analysis, a state-space variable x1 = θ is introduced. Then equation (1) is written as

[0026]

[0027] Step S2: Design a disturbance observer to estimate and compensate for system disturbances in real time;

[0028] In step S2, the interference observer is designed as follows:

[0029]

[0030] Where p is the internal state function. For interference estimation, c is the adjustment parameter;

[0031] Define the interference error function as follows:

[0032]

[0033] Since the actual disturbance is bounded, we define |d|≤μ; taking the time derivative of the error function, we get...

[0034]

[0035] Define the Lyapunov function as:

[0036]

[0037] Combining Young's inequality, for V ed Taking the time derivative, we can obtain

[0038]

[0039] in, ω is a positive constant and satisfies 0 < ω < 2c;

[0040] For all All This holds true. According to equation (7) and the comparison lemma, we can obtain...

[0041]

[0042] As can be seen from equation (8), the disturbance estimation error e d Bounded.

[0043] Step S3: Based on the disturbance estimation results, define the system safety objective, construct the control barrier function to transform the system's safety constraints into inequality conditions that the control inputs must satisfy, and perform system safety analysis to prove the forward invariance of the system safety set;

[0044] In step S3, the system security objective function is defined as h1 and its security set is as follows:

[0045] C1={x1∈R|h1≥0} (9)

[0046] The control barrier function h is then constructed as follows:

[0047]

[0048] Among them, s1 is a virtual controller, and Differentiating the control barrier function yields:

[0049]

[0050] Therefore, the system's safety constraints are transformed into the inequalities that the control inputs must satisfy:

[0051]

[0052] Where γ is a positive constant,

[0053] Security Analysis:

[0054] Define the function as h s =h-βVed , for h s The time derivative is:

[0055]

[0056] The given controller is:

[0057]

[0058] Substituting equation (14) into equation (13) and rearranging, we get:

[0059]

[0060] Note the following in equation (15) Scaling up to

[0061]

[0062] Substituting equation (16) into equation (15), we have

[0063]

[0064] inequalities Substituting into equation (17), we can obtain

[0065]

[0066] According to the comparison lemma and equation (18), for all initial values ​​x1(0)∈C, x2(0)∈C, we have

[0067]

[0068] Therefore, set C is forward invariant with respect to the system, that is...

[0069]

[0070] Therefore, the system always operates safely.

[0071] Step S4: Design a safety controller by combining the control barrier function with the desired tracking controller; and perform system safety analysis to prove the forward invariance of the system safety set.

[0072] In step S4, according to equation (12), the quadratic programming problem can be written as:

[0073]

[0074] in, ξ1=-(x2-s1), k d It is the desired controller.

[0075] Define a = ξ0 + γh, b = ||ξ1||, and the Lagrange factor λ obtained by solving equation (13) is:

[0076]

[0077] After safety filtering along the ξ1 direction, the safety controller is:

[0078] τ * =k d +λξ1 (23).

[0079] During the experimental verification process of this invention:

[0080] To verify the effectiveness and superiority of the robust safety control method for robots based on control obstacle functions in a single-link robot, this application conducted a simulation experiment on the single-link robot in MATLAB 2024a. The simulation was run on a computer equipped with an NVIDIA RTX 4060 GPU, and the total task duration was 40 seconds. To realistically evaluate the performance of the algorithm in a real environment, the external disturbance was set to d = 0.5sin(t) + cos(0.5t). The dynamic model of the single-link robot is shown in Equation (1), where the various control parameters are configured as I = 2, m = 1, g = 9.8, l = 1, and the initial state is [x1(0), x2(0)]. T =[0.35,0.1] T The security objective is The target being tracked is y d =2sin(t)+cos(0.5t).

[0081] The main objective of this simulation is to ensure that the robot's state x1 always remains within the safe zone. When the tracked target is outside the safe zone, the system state operates along the safe boundary; when the tracked target is within the safe zone, the system state can stably track the target. The simulation results are presented below. Figures 1-3 . Figure 1 This demonstrates the robot's safe tracking performance. Figure 2 The control input u is displayed. Figure 3 The actual disturbance d was compared with the estimated disturbance d. The results show that the trajectory of the single-link robot remained strictly within its respective safety range throughout the simulation, verifying the effectiveness and practicality of the proposed control strategy.

[0082] To highlight the advancement and superiority of the proposed method, it is compared with the latest research results—the worst-case-based safety control method. The dynamic model of the single-link robot is shown in Equation (1), with the other control parameters and safety objectives remaining unchanged, and the initial state being [x1(0), x2(0)]. T=[0.05,0.05] T The target being tracked is y d =0.5sin(t)+sin(0.5t), and the external disturbance is set to d=0.1sin(t)+0.1cos(0.5t). Simulation results are shown in Figures 4-5 . Figure 4 The paper shows the safe state trajectory of the robot using the method of this application and existing worst-case-based methods. Figure 5 The method of this application is shown compared with the control input u of a robot based on the worst-case method in the prior art.

[0083] Simulation results show that both control methods effectively maintain the system state within their respective preset safety regions throughout the simulation, meeting basic safety requirements. However, comparison reveals that, compared to traditional control strategies based on worst-case assumptions, the proposed method exhibits superior trajectory tracking performance within the safety region, with smoother control input, indicating a more ideal controller effect. This not only verifies that the proposed method achieves higher control accuracy and efficiency while ensuring system safety but also further demonstrates its feasibility and practical value in real-world applications.

[0084] The above description is merely a preferred embodiment of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention. Structures, devices, and operating methods not specifically described or explained in this invention are implemented according to conventional methods in the art unless otherwise specified or limited.

Claims

1. A robust safety control method for robots based on a control obstacle function, characterized in that: Includes the following steps: Step S1: Establish a robot system model that includes state variables, control inputs, and disturbance terms; In step S1, the single-link robot is modeled as follows: ； Equation (1) describes the dynamic characteristics of a single-link system. Indicates joint angle, These represent angular velocity and angular acceleration, respectively. Let be the moment of inertia, where For the mass of the rod, The length of the rod; The coefficient of viscous friction is... It is the acceleration due to gravity. Represented as a nonlinear gravity term, For joint torque, For disturbance terms; Introducing state-space variables Then equation (1) can be written as ； Step S2: Design a disturbance observer to estimate and compensate for system disturbances in real time; In step S2, the interference observer is designed as follows: ； in, It is an internal state function. For interference estimation, To adjust the parameters; Define the interference error function as follows: ； Since actual disturbances are bounded, the definition is... ; The meaning refers to the boundary of the interference, which is a known constant; by taking the time derivative of the error function, we obtain... ； Define the Lyapunov function as: ； Combining Young's inequality, for Taking the time derivative, we can obtain ； in, It is a positive constant and satisfies ; For all They all This holds true. According to equation (7) and the comparison lemma, we can obtain... ； As can be seen from equation (8), the interference estimation error Bounded; Step S3: Based on the disturbance estimation results, define the system safety objective, construct the control barrier function to transform the system's safety constraints into inequality conditions that the control inputs must satisfy, and perform system safety analysis to prove the forward invariance of the system safety set; In step S3, the system security objective function is defined as follows: Its security set is: ； Then control barrier function Constructed as ； in, Virtual controller, and ; It means, right The meaning of partial derivative, It is a positive constant. This refers to the security objective function mentioned above. For the design parameters; taking the derivative of the control barrier function, we get: ； Therefore, the system's safety constraints are transformed into the inequalities that the control inputs must satisfy: ； in, For positive integers, Step S4: Design a safety controller by combining the control barrier function with the desired tracking controller; and perform system safety analysis to prove the forward invariance of the system safety set; In step S4, according to equation (12), the quadratic programming problem can be written as: ； in, , , It is the expected controller; definition , The Lagrange factor obtained by solving equation (13) for ； lamda is the Lagrange factor, A and B represent the equations above, delta is the smoothing factor, log(·) is the logarithmic function and exp(·) is the exponential function; along After directional safety filtering, the safety controller is: 。 2. The robust safety control method for robots based on a control obstacle function according to claim 1, characterized in that: Security Analysis: Define the function as ,right The time derivative is: ； The given controller is: ； Substituting equation (14) into equation (13) and rearranging, we get: ； Note the following in equation (15) Scaling up to ； Substituting equation (16) into equation (15), we have ； inequalities Substituting into equation (17), we can obtain ； According to the comparison lemma and equation (18), for all initial values They all ； Therefore, set C is forward invariant with respect to the system, that is... ； Therefore, the system always operates safely.

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