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Robust Safety Critical Control Under Multiple State and Input Constraints: Volume Control Barrier Function Method

Jinyang Dong, Shizhen Wu, Rui Liu, Xiao Liang, Biao Lu, Yongchun Fang

Abstract

In this paper, the safety-critical control problem for uncertain systems under multiple control barrier function (CBF) constraints and input constraints is investigated. A novel framework is proposed to generate a safety filter that minimizes changes to reference inputs when safety risks arise, ensuring a balance between safety and performance. A nonlinear disturbance observer (DOB) based on the robust integral of the sign of the error (RISE) is used to estimate system uncertainties, ensuring that the estimation error converges to zero exponentially. This error bound is integrated into the safety-critical controller to reduce conservativeness while ensuring safety. To further address the challenges arising from multiple CBF and input constraints, a novel Volume CBF (VCBF) is proposed by analyzing the feasible space of the quadratic programming (QP) problem. % ensuring solution feasibility by keeping the volume as a positive value. To ensure that the feasible space does not vanish under disturbances, a DOB-VCBF-based method is introduced, ensuring system safety while maintaining the feasibility of the resulting QP. Subsequently, several groups of simulation and experimental results are provided to validate the effectiveness of the proposed controller.

Robust Safety Critical Control Under Multiple State and Input Constraints: Volume Control Barrier Function Method

Abstract

In this paper, the safety-critical control problem for uncertain systems under multiple control barrier function (CBF) constraints and input constraints is investigated. A novel framework is proposed to generate a safety filter that minimizes changes to reference inputs when safety risks arise, ensuring a balance between safety and performance. A nonlinear disturbance observer (DOB) based on the robust integral of the sign of the error (RISE) is used to estimate system uncertainties, ensuring that the estimation error converges to zero exponentially. This error bound is integrated into the safety-critical controller to reduce conservativeness while ensuring safety. To further address the challenges arising from multiple CBF and input constraints, a novel Volume CBF (VCBF) is proposed by analyzing the feasible space of the quadratic programming (QP) problem. % ensuring solution feasibility by keeping the volume as a positive value. To ensure that the feasible space does not vanish under disturbances, a DOB-VCBF-based method is introduced, ensuring system safety while maintaining the feasibility of the resulting QP. Subsequently, several groups of simulation and experimental results are provided to validate the effectiveness of the proposed controller.

Paper Structure

This paper contains 12 sections, 3 theorems, 51 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Control Barrier Function
  4. RISE-based Disturbance Observer
  5. Problem Formulation
  6. Main Results
  7. Robust Safety With Disturbance Estimation
  8. DOB-VCBF-based Robust Safety Critical Control Framework
  9. Simulation and Experimental Results
  10. Simulation results
  11. Experimental results
  12. Conclusions

Key Result

Theorem 1

Consider system (equ:sys2) and the disturbance estimation law given in (equ:obs) and (equ:obs1). Suppose that Assumption assumption:bounded_continuity holds and $\phi^{i-1}(\bar{\bm{x}}(0))>0, i\in[r]$. If the parameters are selected such that $\beta>\delta_2+\delta_3/\max\{1,\alpha-\gamma\}$, $\bet with $\bm K$ and $\bm \eta(\bar{\bm{x}})$ defined below (equ:highorder_limit_U1), will guarantee $h

Figures (4)

  • Figure 1: Simulation results of blimp avoiding a single obstacle.
  • Figure 2: Simulation results of blimp avoiding multiple obstacles.
  • Figure 3: Trajectories to the target position with obstacle avoidance under different safety filters
  • Figure 4: Trajectories for the five cases of $k_p = 0.2, 0.4, 0.6, 0.8, 1.0$.

Theorems & Definitions (8)

  • Proof 1
  • Remark 1
  • Theorem 1
  • Proof 2
  • Theorem 2
  • Proof 3
  • Theorem 3
  • Proof 4