Control Barrier Function Based Quadratic Programs for Safety Critical Systems

Control Barrier Function Based Quadratic Programs for Safety Critical Systems

5 Dec 2016 | Aaron D. Ames, Xiangru Xu, Jessy W. Grizzle, Paulo Tabuada
This paper presents a methodology for integrating safety and performance objectives in safety-critical systems using control barrier functions (CBFs) and control Lyapunov functions (CLFs) within quadratic programs (QPs). Safety conditions are expressed as CBFs, which ensure forward invariance of a set, while performance objectives are expressed as CLFs, which ensure asymptotic stability. The paper develops two types of barrier functions: reciprocal barrier functions (RBFs) and zeroing barrier functions (ZBFs), which provide conditions for forward invariance of a set. These barrier functions are extended to CBFs, which impose inequality constraints on the control input to ensure safety. The paper shows how CBFs can be unified with CLFs in a QP to achieve control objectives subject to safety constraints. The approach is demonstrated on two automotive control problems: adaptive cruise control (ACC) and lane keeping (LK). The paper also discusses the relationships between RBFs, ZBFs, and set invariance, and shows how higher relative degree barrier functions can be used to design CBFs. The paper concludes with a discussion of the theoretical and practical implications of using QPs to mediate safety and performance in control systems.This paper presents a methodology for integrating safety and performance objectives in safety-critical systems using control barrier functions (CBFs) and control Lyapunov functions (CLFs) within quadratic programs (QPs). Safety conditions are expressed as CBFs, which ensure forward invariance of a set, while performance objectives are expressed as CLFs, which ensure asymptotic stability. The paper develops two types of barrier functions: reciprocal barrier functions (RBFs) and zeroing barrier functions (ZBFs), which provide conditions for forward invariance of a set. These barrier functions are extended to CBFs, which impose inequality constraints on the control input to ensure safety. The paper shows how CBFs can be unified with CLFs in a QP to achieve control objectives subject to safety constraints. The approach is demonstrated on two automotive control problems: adaptive cruise control (ACC) and lane keeping (LK). The paper also discusses the relationships between RBFs, ZBFs, and set invariance, and shows how higher relative degree barrier functions can be used to design CBFs. The paper concludes with a discussion of the theoretical and practical implications of using QPs to mediate safety and performance in control systems.
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[slides and audio] Control Barrier Function Based Quadratic Programs for Safety Critical Systems