Robot robust safety control method based on control barrier function

Abstract

The invention 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 of: S1, establishing a robot system model containing a state variable, control input and a disturbance term; S2, designing a disturbance observer, and estimating and compensating disturbance of a system in real time; s3, based on an interference estimation result, defining a system security target, constructing a control barrier function to convert security constraints of the system into inequality conditions which need to be met by control input, performing system security analysis, and proving forward invariance of a system security set; s4, designing a safety controller by controlling a barrier function in combination with an expected tracking controller; and carrying out system security analysis to prove the forward invariance of the system security set. According to the method, the control target of considering the safety and the tracking performance of the system in an uncertain environment is achieved.

Description

TECHNICAL FIELD

[0001] 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. BACKGROUND

[0002] With the rapid development of robot technology in industrial automation, medical auxiliary surgery, warehouse logistics, intelligent manufacturing and home service and other fields, the operation environment of robots is increasingly complex, and the task targets are increasingly diversified, which poses unprecedented challenges to the safety of control systems. In actual application, a robot system often faces various uncertain factors such as external disturbance, system parameter uncertainty, model nonlinear error, friction, load change and dynamic environment interaction. If these factors are not effectively processed, the system performance will be easily deteriorated, and even the state will be out of bounds, thereby bringing serious safety hazards, affecting the accuracy of task completion and the stability of the system, 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 the uncertainty of the system to a certain extent, but it is often difficult to guarantee the real-time safety constraints of the system while taking into account the control performance. In addition, most of these methods rely on ideal model assumptions, and it is difficult to achieve real-time response and active defense in the face of sudden disturbances or rapidly changing environments. Therefore, the application proposes a robot robust safety control method based on a control barrier function. SUMMARY

[0004] The application aims to provide a robot robust safety control method based on a control barrier function, which can overcome the problems of insufficient safety control ability and weak robustness of robots in the prior art in an interference environment, so as to realize the control goal of balancing the safety and tracking performance of the system in an uncertain environment.

[0005] The technical solutions adopted by the application are as follows:

[0006] A robot robust safety control method based on a control barrier function comprises the following steps:

[0007] Step S1: establishing a robot system model containing state variables, control inputs and disturbance terms;

[0008] Step S2: designing a disturbance observer to estimate and compensate the disturbance of the system in real time;

[0009] Step S3: Based on the interference estimation results, define the system safety goal, construct a control barrier function to convert the system safety constraints into inequality conditions that the control input must satisfy, and perform system safety analysis to prove the forward invariance of the system 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 the present invention are:

[0012] In this method, safety is the core objective of control design. A disturbance observer is introduced to perform online estimation and dynamic compensation for unknown disturbances in the system, effectively improving the robustness of the system in uncertain environments. By accurately modeling and compensating for disturbances in real time, the system can more accurately respond to environmental changes and dynamic disturbances, reducing the risk of the system deviating from its safe range. Furthermore, by utilizing a control barrier function, the previously intractable safety constraint problem is transformed into an inequality constraint that can be directly implemented in the controller, ensuring that the system state always remains within a preset safe region, thereby ensuring the safety of system operation. Furthermore, while satisfying safety constraints, this method can still achieve precise control of the tracking target, enhancing the flexibility and practicality of the control strategy. This method comprehensively considers the coordination between task execution and safety constraints, exhibiting excellent robustness, safety, and tracking performance. It is suitable for robotic systems exposed to disturbances and has high engineering application value and potential for widespread adoption.

[0013] The control method proposed in the present invention is both robust and flexible. It can ensure 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 interference conditions. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0016] Figure 3 Schematic diagram of external interference and interference estimation;

[0017] Figure 4 Schematic diagram comparing the safe state trajectory of the robot based on the present application method and the existing worst-case method;

[0018] Figure 5 Schematic diagram of control input of the present application method and the existing robot based on the worst-case method. DETAILED DESCRIPTION

[0019] In order to make the purpose and advantages of the present invention more clearly understood, the present invention is described in detail below with reference to the following examples. It should be understood that the following text is only used to describe one or more specific embodiments of the present invention and does not strictly limit the scope of protection of the present invention.

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

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

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

[0023]

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

[0025] In order to facilitate the design and analysis of the controller, the state space variable x1=θ is introduced. Then formula (1) can be 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, is the interference estimation, c is the adjustment parameter;

[0031] The interference error function is defined as:

[0032]

[0033] Since the actual interference is bounded, define |d|≤μ; take the time derivative of the error function and get

[0034]

[0035] Define the Lyapunov function as:

[0036]

[0037] Combined with Young's inequality, V ed Taking the time derivative, we get

[0038]

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

[0040] For all Both Established, according to formula (7) and the comparison lemma, we can get

[0041]

[0042] From formula (8), we can see that the interference estimation error e d Bounded.

[0043] Step S3: Based on the interference estimation results, define the system safety objectives, construct a control barrier function to convert the system 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:

[0045] C1={x1∈R|h1≥0} (9)

[0046] Then the control barrier function h is constructed as

[0047]

[0048] Among them, s1 is a virtual controller, and Taking the derivative of the control barrier function, we can get:

[0049]

[0050] Therefore, the system's safety constraints are transformed into the inequality conditions that the control input must satisfy:

[0051]

[0052] Where γ is a positive constant,

[0053] Security Analysis:

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

[0055]

[0056] The given controller is

[0057]

[0058] Substituting (14) into (13), we have

[0059]

[0060] Note that is scaled to

[0061]

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

[0063]

[0064] Substituting the inequality into (17), we have

[0065]

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

[0067]

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

[0069]

[0070] Further, the system is always safe to operate.

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

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

[0073]

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

[0075] Define a=ξ0+γh,b=||ξ1||,the Lagrangian factor λ solved by 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, the present invention:

[0080] To verify the effectiveness and superiority of the robust safety control method based on the control obstacle function on a single-link robot, this application conducted a simulation experiment on the single-link robot in MATLAB2024a. The simulation was run on a computer equipped with an NVIDIA RTX4060 GPU, and the total task duration was 40 seconds. In order to truly evaluate the performance of the algorithm in a practical 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 goal is Tracking target is y d =2sin(t)+cos(0.5t).

[0081] The main goal of this simulation is to make the robot state x1 always keep running in the safe area. When the tracking target is outside the safe area, the system state runs along the safe boundary. When the tracking target is not in the safe area, the system state can be stably tracked. The simulation results are shown in Figure 1-Figure 3 . Figure 1 Shows the robot's safe tracking performance, Figure 2 The control input u is shown. Figure 3 The actual disturbance d is compared with the estimated disturbance d. From the results, it can be seen that throughout the simulation process, the trajectory of the single-link robot strictly remains within its respective safety range, verifying the effectiveness and practicality of the proposed control strategy.

[0082] In order to highlight the advancement and superiority of the method proposed in this application, the method proposed in this application is compared with the latest research results - the safety control method based on the worst case scenario. The dynamic model of the single-link robot is shown in formula (1). The other control parameter configurations remain unchanged, the safety target remains unchanged, and the initial state is [x1(0), x2(0)] T=[0.05,0.05] T , the tracking target is y d =0.5sin(t)+sin(0.5t), and the external interference is set to d=0.1sin(t)+0.1cos(0.5t). The simulation results are shown in Figure 4-Figure 5 . Figure 4 The safety status trajectory of the robot based on the proposed method and the existing worst-case method is shown. Figure 5 The control input u of the robot based on the present application method and the existing worst-case method is shown.

[0083] From the simulation results, it can be observed that throughout the simulation process, both control methods can effectively ensure that the system state always remains within their respective preset safety zones, meeting basic safety requirements. However, by comparison, it can be found that compared with the traditional control strategy based on the worst-case assumption, the method of the present application exhibits better trajectory tracking performance within the safety zone, and the control input is smoother, indicating that the controller has a more ideal effect. This not only verifies that the proposed method has higher control accuracy and efficiency while ensuring system safety, but also further demonstrates its feasibility and practical value in practical applications.

[0084] The foregoing is merely a preferred embodiment of the present invention. It should be noted that those skilled in the art may make various improvements and modifications without departing from the principles of the present invention, and such improvements and modifications are also within the scope of protection of the present invention. Structures, devices, and operating methods not specifically described or explained herein shall, unless otherwise specified or limited, be implemented in accordance with conventional means in the art.

Claims

1. A robot robust safety control method based on a control obstacle function, characterized by: The following steps are involved: Step S1: Establish a robot system model including state variables, control inputs and disturbance terms; Step S2: Design a disturbance observer to estimate and compensate for system disturbances in real time; Step S3: Based on the interference estimation results, define the system safety objectives, construct a control barrier function to convert the system 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; 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.

2. A robot robust safety control method based on control obstacle function according to claim 1, characterized in that: In step S1, the single-link robot is modeled as: Wherein, Equation (1) describes the dynamic characteristics of the single-link system; θ represents the joint angle, Represent angular velocity and angular acceleration respectively; I = ml 2 is the moment of inertia, where m is the mass of the rod and l is the length of the rod; b is the viscous friction coefficient, g is the acceleration due to gravity, mglsinθ is the nonlinear gravity term, τ∈R is the joint torque, and d∈R n is the disturbance term; Introduce state space variable x1=θ, Then formula (1) can be written as 3. The robot robust safety control method based on the control obstacle function according to claim 1, characterized in that: In step S2, the interference observer is designed as follows: Where p is the internal state function, is the interference estimation, c is the adjustment parameter; The interference error function is defined as: Since the actual interference is bounded, define |d|≤μ; μ is the known limit of the interference; take the time derivative of the error function and get Define the Lyapunov function as: Combined with Young's inequality, V ed Finding the time derivative, we can get in, ω is a positive constant and satisfies 0<ω<2c; For all Both Established, according to formula (7) and the comparison lemma, we can get From formula (8), we can see that the interference estimation error e d Bounded.

4. The robot robust safety control method based on the control obstacle function according to claim 1, characterized in that: In step S3, the system security objective function is defined as h1 and its security set is: C1={x1∈R|h1≥0} (9) Then the control barrier function h is constructed as Among them, s1 is a virtual controller, and is the partial derivative of h1 with respect to x1. γ0 is a positive constant and β is a design parameter. Derivative of the control barrier function yields: Therefore, the system's safety constraints are transformed into the inequality conditions that the control input must satisfy: Where γ is a positive constant. Security Analysis: Define the function as h s =h-βV ed , for h s The time derivative is: Given a controller: Substituting formula (14) into formula (13), we can get Note that in formula (15) Scale to Substituting formula (16) into formula (15), we have The inequality Substituting into formula (17), we can get According to the comparison lemma and formula (18), for all initial values ​​x1(0)∈C,x2(0)∈C, we have Therefore, the set C is forward invariant with respect to the system, i.e. As a result, the system always runs safely.

5. The robot robust safety control method based on the control obstacle function according to claim 1, characterized in that: In step S4, according to formula (12), the quadratic programming problem can be written as: in, ξ1=-(x2-s1),k d is the desired controller. Define a=ξ0+γh,b=||ξ1||,the Lagrangian factor λ solved by equation (13) is where λ is the Lagrangian factor, a and b represent the equations above, σ is the smoothing factor, log(·) is the logarithmic function, and exp(·) is the exponential function. After safety filtering along the ξ1 direction, the safety controller is: t * =k d +λξ1 (23).

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