Synthesis of Barrier Certificate-Based Controllers for Safe Robotic Task Execution

Abstract

Safety critical control applications are ubiquitous, and hence synthesizing control algorithms with formal guarantees on safety and task satisfaction is of great importance. Tasks such as motion planning in unknown environments or planning for autonomous vehicles require controllers that satisfy a sequence of operations. In addition, the system must execute trajectories which are dynamically feasible, safe, and respect actuator constraints. In this thesis, a barrier certificate-based approach to synthesize controllers for safe robotic task execution is detailed. Control barrier functions have recently emerged as a tool to guarantee safety and reachability for dynamical systems, and they can be conveniently encoded in computationally efficient quadratic programs, making them amenable to real-time implementation. Leveraging these useful features, a framework for translating a given user defined specification to a sequence of barrier certificate-based controllers is introduced. The specification is formalized using linear temporal logic, a tool from formal methods literature. Executing such a sequence of controllers results in satisfaction of the given specification. Implementation results on a multi-robot test bed are provided. Furthermore, in order to guarantee task satisfaction, it is important to address certain assumptions that are prevalent in barrier functions-based literature such as feasibility of the quadratic programs, negligence of system volume when guaranteeing safety, and knowledge of the safe sets in unknown operating environments. We thus provide techniques to address the above assumptions and discuss simulation and experimental results to demonstrate the efficiency of the proposed approaches.