An input-sample method for zonotopic obstacle avoidance with discrete-time control barrier functions

Abstract:

Generating safe and feasible trajectories for autonomous robots in an obstacle-cluttered environment is a vital problem in robotics research. In this thesis, we propose an input sampling algorithm leveraging discrete-time control barrier function conditions (DCBF) to address this problem. Specifically, an optimization-based control barrier function that takes into account the geometric shapes of the vehicle and obstacles is constructed and verified. We then propose a discrete-time CBF that guarantees safety during the inter-sampling intervals. It is worth noting that we do not need an explicit expression of the barrier function, but instead, a numerically efficient algorithm is proposed to evaluate and implement the CBF/DCBF conditions. Finally, an RRT algorithm is incorporated that draws the input sampling from the input space restricted to DCBF condition. Thanks to our proposed DCBF and input sampling method approach, our proposed method is less conservative, computationally efficient, and guarantees safety during the sampling intervals. Numerical simulation with a unicycle model has been done to demonstrate the favorable properties of the algorithm.