UC Berkeley

Control barrier functions (CBFs) are one of the many used approaches for achieving safety in robot autonomy. This thesis tackles several challenges present in control barrier functions in different aspects, including optimization, control, planning and navigation.

This thesis is composed of three parts. In Part I, we point out the optimization infeasibility between CBF constraint and input constraint, and address the feasibility problem in optimal control for quadratic programming using control barrier functions under input constraints. We also notice that the potential conflict between input constraints and safety constraints also exists in the discrete-time domain together with model predictive control. This conflict is formally identified in reachability analysis and reachability is later enhanced in proposed formulations.

In the Part II, we focus on obstacle avoidance for control and trajectory generation in a tight environment, which requires polytopic obstacle avoidance. We analyze the optimization problem for obstacle avoidance between polytopes. The novel optimizations for obstacle avoidance in continuous domain and discrete-time domain are proposed to solve this challenge.

In Part III of the thesis, we discuss several applications of motion planning and navigation using control barrier functions.We firstly address the motion planning problem within a finite state machine which unifies a mid-level planner and a low-level safety-critical controller with application to autonomous driving. Next, we propose parallelism for motion planning with control barrier functions with application to autonomous racing. Finally, we explore the possibility of safety-critical motion planning for high dimensional systems such as Cassie, a life-size bipedal robot.