A robot safety-critical control method based on on-demand activation of robust control barrier function

Abstract

The application belongs to the technical field of robot control, and particularly relates to a kind of safety-critical control method for robot arm based on on-demand activation robust control barrier function, aiming at solving the technical bottleneck that existing robust control barrier function is limited by over-conservative control behavior in processing high relative order system. By introducing relaxation technology, a continuous derivable lower bound of safety constraint about disturbance is constructed, which promotes the construction of high-order control barrier function. At the same time, a kind of "on-demand activation" cascade barrier function structure is designed by combining with modified linear unit activation function. The safety filter remains dormant in the absolute safety region, realizing zero intervention to the nominal controller; only the modified action is activated when facing safety risk. The experimental results show that the method can ensure safety under both differentiable and non-differentiable disturbances, reduce unnecessary control modification and control conservatism, perfectly balance the safety and tracking performance of robot, and has good engineering application value.

Description

Technical Field

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

[0002] In recent years, autonomous systems such as drones, self-driving cars, and robots have been widely used in complex and dynamic environments. Due to increasingly complex mission scenarios and growing environmental uncertainty, ensuring absolute safety during system operation has become a fundamental issue in safety-critical control. Control barrier functions have attracted considerable attention because they can directly transform safety requirements into inequality constraints on control inputs, achieving minimal correction to the nominal controller while ensuring the positive invariance of the safety set.

[0003] However, traditional control barrier function methods typically rely on accurate system models, making it difficult to directly address the uncertainties and external disturbances prevalent in real-world systems. To enhance safety assurance capabilities, robust control barrier functions have been proposed, establishing more conservative safety constraints by explicitly considering the effects of disturbances. However, existing robust control barrier function methods usually require continuous application of safety corrections throughout the entire operation. Even when the system is far from potentially hazardous areas, the safety mechanism continues to intervene in the nominal control input, introducing additional control regulation and degrading system performance. On the other hand, for high-relative-order safety constraints in complex nonlinear systems, existing methods typically employ high-order control barrier functions for recursive construction. However, when the system is affected by unknown and non-differential disturbances, the recursive differentiation process inevitably introduces disturbance derivative terms of different orders, posing significant theoretical challenges to safety constraint construction and controller design. Therefore, how to reduce unnecessary safety interventions while ensuring robust safety and avoid dependence on disturbance derivative information remains an urgent problem to be solved in the safety control of high relative order nonlinear systems. To this end, this invention provides a robotic arm safety-critical control method based on on-demand activation of robust control barrier functions, which can solve the problem of insufficient robotic arm control accuracy caused by the overly conservative limitations of existing robust control barrier function methods. Summary of the Invention

[0004] The purpose of this invention is to provide a safety-critical control method for robotic arms based on on-demand activation of robust control barrier functions, which can solve the problem of insufficient control accuracy of robotic arms caused by the overly conservative limitations of existing robust control barrier function methods.

[0005] The specific technical solution adopted by this invention is as follows: A safety-critical control method for a robotic arm based on a robust control obstacle function activated on demand includes the following steps: S1: Construct a dynamic model of a single-link robotic arm, convert it into an affine nonlinear system, and define the safety constraint function and the upper bound of the disturbance; S2: Using relaxation techniques, construct a continuously differentiable lower bound for the safety constraint function with respect to the disturbance, thus completing the construction of the higher-order control barrier function; S3: Design a robust control barrier function for on-demand activation, embedding a modified linear unit activation function in the stepwise construction to establish an on-demand activation mechanism; S4: Based on the constructed on-demand activation robust control barrier function, a safety-critical quadratic programming controller is designed to generate control signals to drive the robotic arm actuator.

[0006] The technical effects achieved by this invention are as follows: This invention discloses a solution to the overly conservative limitations of existing robust control barrier function methods. Firstly, for a robotic arm dynamics model, this method innovatively constructs a continuously differentiable lower bound for safety constraints with respect to disturbances using relaxation techniques, facilitating the construction of higher-order control barrier functions. This design significantly broadens the framework's applicability to differentiable / non-differentiable and matched / mismatched disturbances. Next, a modified linear unit activation function is introduced to implement an "on-demand activation" strategy. Within the absolutely safe region, the safety filter remains dormant, ensuring zero intervention on the nominal controller; only when the system faces a safety violation risk will the control action be instantaneously activated to provide safety correction. Based on this theoretical framework, a corresponding quadratic programming controller is designed, ensuring the feasibility of optimization. Simulation results demonstrate the effectiveness of this method in handling differentiable and non-differentiable disturbances, maintaining strict safety constraints, and preserving optimal control performance with minimal intervention. Attached Figure Description

[0007] Figure 1 This is a schematic diagram of the tracking performance of the system of the present invention under minute perturbations. Figure 2 This is a schematic diagram of the control input of the present invention under minute perturbation. Figure 3 This is a schematic diagram illustrating the evolution of the security function of this invention under differentiable perturbations. Figure 4 This is the perturbation curve of the present invention. Figure 5 This is a schematic diagram of the tracking performance of the system of the present invention under non-indeterminate perturbation. Figure 6 This is a schematic diagram of the control input of the present invention under non-indeterminate perturbation. Figure 7 This is a schematic diagram illustrating the evolution of the security function of this invention under non-differentiable perturbations. Figure 8 This is a non-indeterminate perturbation curve diagram of the present invention; Figure 9This is the system response of the Franka Emika Panda robot of this invention under small perturbations; in the figure, Figure 9 (a) is a graph showing the tracking performance under indeterminate perturbations; Figure 9 (b) is the input curve under differentiable perturbations; Figure 9 (c) is the evolution diagram of the security function under differentiable perturbations; Figure 9 (d) is a graph of the differentiable perturbation; Figure 10 The figure shows the system response of the Franka Emika Panda robot of this invention under non-differentiable perturbations. Figure 10 (a) is a graph showing the tracking performance under non-differentiable perturbations; Figure 10 (b) is the input curve under non-differentiable perturbation; Figure 10 (c) is the evolution diagram of the security function under non-differentiable perturbations; Figure 10 (d) is a non-differentiable perturbation curve. Detailed Implementation

[0008] 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.

[0009] like Figures 1-10 As shown, a method for safety-critical control of a robotic arm based on on-demand activation of a robust control obstacle function is characterized by the following steps: S1: Construct a dynamic model of a single-link robotic arm, convert it into a strictly feedback affine nonlinear system, and define the safety constraint function and the upper bound of the disturbance; S2: Using relaxation techniques, construct a continuously differentiable lower bound for the safety constraint function with respect to the disturbance, thus completing the construction of the higher-order control barrier function; S3: Design a robust control barrier function that can be activated on demand. In the hierarchical construction, a modified linear unit activation function is embedded to establish an on-demand activation mechanism, so that the safety filter remains dormant when the robotic arm system is in an absolutely safe area, and the correction action is activated only when a safety risk is faced. In S3, the robust control barrier function is designed for on-demand activation. First, consider the disturbed single-link robotic arm, whose dynamic equation is: (1) in, To output the angle, To control the torque. and These are the moment of inertia and the coefficient of viscous friction, respectively. , and These represent the load mass, link length, and gravitational acceleration, respectively. This indicates an external disturbance.

[0010] Introducing state variables The dynamic equation (1) is transformed into a nonlinear system (2): (2) make , , and Then the nonlinear system (2) can be written in affine form: (3) in ; The given positive constant is .

[0011] To ensure safety, the output angle must not exceed the safe range. Accordingly, safety constraints are defined as follows: (4) Its safe set is: (5); The main feature of this method is the adoption of an on-demand activation strategy to mitigate the over-control costs caused by continuous activation of control actions, while effectively suppressing disturbances. Furthermore, this control strategy exhibits strong robustness, capable of handling differentiable and non-differentiable disturbances, as well as disturbances randomly generated or driven by exogenous systems. For ease of theoretical analysis and implementation, the output angle safety boundary is set to a constant, and a linear extension is employed. Class function, represented as A safe set is defined by a continuously differentiable function. Characterization. To handle the perturbation term, based on the known upper bound of the perturbation. The worst-case perturbation lower bound is constructed and expressed as: (6) Since the relative order is greater than 1, it satisfies It is easy to prove that... Established A lower bound on the perturbation. However, Its non-differentiability prevents it from being directly used to construct higher-order control barrier functions. Therefore, inequalities are used... ; We can obtain: (7) although It is not differentiable, but its upper bound is obtained through relaxation. Satisfying the required smoothness condition makes it possible to construct higher-order control barrier functions. Therefore, it is possible to construct... The smooth lower bound of the time derivative is: (8) in One is an adjustable design parameter used to mitigate the conservatism introduced by the relaxation process.

[0012] Based on the above analysis, by... The exact derivative of is replaced by its smooth lower bound, and an auxiliary function is defined: (9) in; ; and It is a design parameter.

[0013] Higher-order control barrier functions apply control barrier function-like conditions: To indirectly ensure Thus ensuring Evolution along the trajectory in the positive direction. However, even This persistent constraint still generates additional control actions, leading to excessive control costs. In contrast, the proposed method introduces an on-demand activation strategy, activating only when needed. Control inputs are invoked only when necessary, thereby reducing unnecessary control costs.

[0014] Therefore, this invention proposes the following candidate control barrier function: (10) in, Represents a rectifier linear unit. It is a continuously differentiable function that satisfies If and only if .

[0015] The motivation behind formula (10) is that when the uncontrolled dynamics of system (3) satisfy the safety conditions At this time, the second term in (10) is inactive. In this case, safety can be guaranteed without additional control overhead, and the function degenerates into... The function defined by formula (10) is called the on-demand activation robust control barrier function. The following theorem shows that, under certain assumptions, the on-demand activation robust control barrier function is an effective control barrier function.

[0016] Theorem 1: Consider a disturbed nonlinear robotic arm system (2), whose control affine form is shown in (3), the safety set Given a continuously differentiable function of relative order 2 Definition. If the design parameters satisfy... Then the candidate on-demand activation robust control barrier function An effective control barrier function that constitutes the system.

[0017] Proof: To prove It is an effective control barrier function; it only needs to be verified for all There is a control input The following conditions are met: (11) Define the activation item as .because and ,function It is continuously differentiable, and its derivative is: If , ;like ,but . The time derivative along the system dynamics can be expressed as: (12) Note the control input Only appears In the item. Therefore, Central control input The coefficient is: (13) because The relative order is 2, and we have ,thereby: (14) This invention is analyzed in two scenarios: Scenario 1: Activated area ; In this area, due to Strictly increasing, its derivative satisfies Therefore, the derivative of the activation function is .

[0018] review The definition, and note We can obtain: (15) Note It depends only on the previous state variables, therefore we have Therefore, (15) can be simplified to the following second-order Lie derivative form. (15) Will Substituting the control coefficients, we get: (17) Given a relative order of 2, we have Combining It can be seen that the control coefficient is strictly non-zero. Since the control input is unconstrained, there always exists a sufficiently large control input. The control barrier function condition (11) is satisfied.

[0019] Scenario 2: Safe Zone ; Within this region, the activation function satisfies Therefore, the correction function degenerates into the original constraint function. The control coefficient disappears. At this point, the control barrier function condition (11) must be in effect when no need for... In the case of assistance, the system's natural drift ensures performance.

[0020] Considering the worst-case drift of second-order synthesis ,because The drift term is independent of the control input. Structurally, it degenerates into an uncontrolled form: (18) because We can obtain: (19) use and It can be deduced that: (20) in It is a design parameter. This satisfies condition (11), thus proving... This constitutes a control barrier function.

[0021] Combining scenarios 1 and 2, we can conclude that robust control barrier functions should be activated on demand. It is an effective control barrier function, proof complete.

[0022] To demonstrate the security of the underlying physical system, a backstepping-based recursive analysis is conducted. Consider the recursive expression given by equation (10). (twenty one) Recursively deriving this algebraic logic, nonnegativity will be propagated down layer by layer to the lowest level: (twenty two) Therefore, for all They all This ensures system security.

[0023] S4: Based on the constructed on-demand activation robust control barrier function, a safety-critical quadratic programming controller is designed to generate control signals to drive the robotic arm actuator, minimizing the correction to the nominal controller while ensuring the strict safety of the robotic arm system.

[0024] In step S4, during the specific design process of the safety-critical secondary programming controller... This invention has proven that the proposed on-demand robust control barrier function method can strictly guarantee system safety under disturbances, that is, for all... satisfy Based on this conclusion, the present invention constructs a safety-critical quadratic programming controller that ensures system safety constraints while minimizing the correction of nominal control input.

[0025] let To implement the nominal control law for tracking the target; and to achieve safety assurance with minimal intervention, consider the following quadratic programming problem: (twenty three) The above constraints are related to the control quantity Since it is affine, the optimization problem is a convex quadratic programming problem.

[0026] During the feasibility analysis process: Activated area: When Make Sometimes, This indicates that safety constraints can be achieved through control inputs. Since control inputs are unconstrained, feasibility is always satisfied.

[0027] Safe zone: when For all ,have The constraints degenerate into This condition can be automatically satisfied by the system dynamics itself. In this case, the quadratic programming problem degenerates into... That is, ensuring system safety without intervention from controlled inputs.

[0028] To verify the effectiveness of the proposed control scheme, this invention conducts simulation experiments on a closed-loop system. The reference signal is selected as... At the same time, ensure safety constraints It is always satisfied. First, the auxiliary function. The condition for activating the robust control barrier function on demand can be expressed as follows: .function Characterize the activation conditions of safety constraints: when At this time, the system state remains within the safe set, and no security intervention is required. Related items can be written as , , On the contrary, when The system enters the activation zone, security constraints are triggered, and the corresponding items are modified as follows: , , .

[0029] A proportional-derivative nominal controller is used to achieve reference trajectory tracking, and the control gains are set to [values ​​to be filled in]. , The system parameters selected in this invention are as follows: , , , , Meanwhile, the relevant parameters of the control barrier function are configured as follows: , , .

[0030] Based on the differentiability and non-differentiability of the perturbation, this invention implements two sets of methods. The first set selects a differentiable perturbation. The second group chooses non-differential perturbations. .

[0031] Simulation results are displayed in Figures 1-8 . Figure 1 The tracking graph is displayed; Figure 2 The corresponding control input response curves are provided, where the safety controller is activated as needed based on the system's safety status. Specifically: when the system is operating within the safe region, the control input remains at the nominal control value, without any additional intervention; when approaching the safety boundary, the safety filter is activated to adjust the nominal control input and ensure system safety. Figure 3 As the safety function undergoes dynamic changes, even in the face of external disturbances, the algorithm in this paper can still guarantee that the safety function is always non-negative, thereby strictly restricting the system state within the safety set; Figure 4 Provide the corresponding disturbance response results. Figures 5 to 8 The simulation results for non-differentiable perturbations are given.

[0032] To further verify the applicability of the proposed method in practical systems, physical experiments were conducted based on the Franka Emika Panda robot platform. Experiments were performed on systems with differentiable perturbations. , With non-indeterminate perturbation , In this case, a comprehensive evaluation of the system's security protection capabilities and trajectory tracking performance is conducted. Figure 9 and 10Experimental results show that the proposed method can effectively ensure system security and achieve good tracking performance under various complex disturbances. 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 safety-critical control method for a robotic arm based on a robust control obstacle function activated on demand, characterized in that: Includes the following steps: S1: Construct a dynamic model of a single-link robotic arm, convert it into an affine nonlinear system, and define the safety constraint function and the upper bound of the disturbance; S2: Using relaxation techniques, construct a smooth lower bound that is continuously differentiable with respect to the disturbance for the safety constraint function, thus completing the construction of the higher-order control barrier function; S3: Design a robust control barrier function for on-demand activation, embedding a modified linear unit activation function in the stepwise construction to establish an on-demand activation mechanism; S4: Based on the constructed on-demand activation robust control barrier function, a safety-critical quadratic programming controller is designed to generate control signals to drive the robotic arm actuator.

2. The robotic arm safety-critical control method based on on-demand activation of robust control obstacle function according to claim 1, characterized in that: In step 1, considering the disturbed single-link robotic arm, its dynamic equation is: （1） in, To output the angle, To control the torque; and These are the moment of inertia and the coefficient of viscous friction, respectively. , and These represent the load mass, link length, and gravitational acceleration, respectively. Indicates external disturbance; Introducing state variables The dynamic equation (1) is transformed into a nonlinear system (2): （2） make , , and Then the nonlinear system (2) can be written in affine form: （3） in, x These are states, where F, G, and B are known specific Lipschitz continuous functions. , , and All of them are in matrix form; ; Given positive constants; The output angle must not exceed the safe range. Accordingly, safety constraints are defined as: （4） in, This is the safety boundary, set as a constant; The output angle of the robotic arm is converted into a nonlinear system using... x 1 represents; Its safe set is: （5） Among them, when If the result is greater than or equal to 0, it means that set C is forward invariant and the system is safe.

3. The robotic arm safety-critical control method based on on-demand activation robust control obstacle function according to claim 2, characterized in that: In step 2, based on the known upper bound of the perturbation The worst-case perturbation lower bound is constructed and expressed as: （6）； It is derived by taking the derivative of formula (3) and considering the worst-case effect of the disturbance; structure The smooth lower bound of the time derivative is: （8） in One is an adjustable design parameter used to mitigate the conservatism introduced by the relaxation process; By The exact derivative of is replaced by its smooth lower bound, and an auxiliary function is defined: （9） in; ; and It is a design parameter.

4. The robotic arm safety-critical control method based on on-demand activation of robust control obstacle function according to claim 3, characterized in that: In S3, a robust control barrier function is designed to be activated on demand. （10） in, Represents a rectifier linear unit. It is a continuously differentiable function that satisfies If and only if .

5. The robotic arm safety-critical control method based on on-demand activation of robust control obstacle function according to claim 4, characterized in that: In step S4, during the specific design process of the safety-critical secondary programming controller... Construct a safety-critical quadratic programming controller that ensures system safety constraints while making small corrections to the nominal control input; let To implement the nominal control law for tracking the target; and to achieve safety assurance with minimal intervention, consider the following quadratic programming problem: （23） Where u is the controller, It is a nominal controller. These are constraints of the quadratic programming, ensuring system security. It is a constant; The above constraints are related to the control quantity Since it is affine, the optimization problem is a convex quadratic programming problem. During the feasibility analysis process: Activated area: When Make Sometimes, This indicates that safety constraints can be achieved through control inputs; since control inputs are unconstrained, feasibility is always satisfied. Safe zone: when For all ,have The constraints degenerate into This condition can be automatically satisfied by the system dynamics itself; in this case, the quadratic programming problem degenerates into... That is, ensuring system safety without intervention from controlled inputs.

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