Synergistic control barrier functions with application to obstacle avoidance for nonholonomic vehicles

Abstract

Control barrier functions (CBFs) have recently emerged as a means to ensure safety of controlled dynamical systems. CBFs are suitable for obstacle avoidance, where the CBF is often constructed from the distance and relative velocity between the vehicle and the obstacle. For vehicles required to maintain non-zero forward speed, ordinary (non-hybrid) CBFs cannot ensure safety due to vanishing control authority when the vehicle is oriented directly towards the obstacle. In this paper, synergistic CBFs are proposed, which is an intuitive extension of CBFs using ideas from synergistic Lyapunov functions. A synergistic CBF for obstacle avoidance for nonholonomic vehicles is constructed by shifting the orientations with vanishing control authority. This induces a penalty for traversing the obstacle in the counterclockwise or clockwise direction, where a logic variable is used to determine the preferred direction. The performance of the CBF is illustrated by a case study.

Guiding Vector Fields for Following Occluded Paths

“…In fact, many existing studies in the literature have adopted hybrid controllers. The paper [46] proposes a synergistic control barrier function that enables switching between overlapping non-hybrid control barrier functions to guarantee collision avoidance. The algorithm is still effective for nonholonomic vehicles.…”

Finite-Time Output-Feedback Formation Control for High-Order Nonlinear Multiagent Systems With Obstacle Avoidance

“…Consequently, the best result one can achieve is almost global asymptotic stability. To overcome these constraints, a number of hybrid control approaches for global robot navigation with, obstacle avoidance, have been proposed recently [30]- [35].…”

Safety-Critical Control for Systems with Impulsive Actuators and Dwell Time Constraints

“…CBFs thus provide a computationally tractable solution to many nonlinear constrained control problems. While the original formulations of CBFs [3]- [5] considered continuous-time systems, subsequent authors have published numerous extensions to sampled systems [6]- [11], discrete-time systems [12], [13], and hybrid systems [14]- [17], among others. In this paper, we develop set invariance rules for a specific class of hybrid systems: systems with impulsive actuators that are only permitted to be used after a minimum dwell time has elapsed since their previous use.…”

“…Impulsive systems are a special class of hybrid systems, and there has been much work on stability of hybrid systems over the past two decades [18]- [23], and more recently work on set invariance [4], [17], [24] and CBFs [14]- [16], [25], [26] for hybrid systems. A hybrid system is a combination of a set of time intervals where a system flows according to a state differential equation called the flow map, and a set of times where the state jumps (changes instantaneously) according to an algebraic function called the jump map.…”

“…In this letter, due to the minimum dwell time constraint, rather than applying control to render the state always inside such a controlled-invariant set, we must apply control to render the state into a set whose forward reachable set remains a subset of the CBF set at least until the dwell time has elapsed. This is an inherently different problem than that addressed by typical CBFs [1], [5] or by the hybrid CBFs in [4], [14]- [17], [24]- [26], and has more in common with set invariance conditions for sampled controllers such as [6]- [9], [28], [29]. That said, we are also interested in much longer dwell times than were present in [6], [7], [28], [29], and address this challenge in Section III-E1.…”