Weighted polar finite time control barrier functions with applications to multi-robot systems

M. Srinivasan, N.-s. Hyun, S. Coogan
IEEE Conference on Decision and Control, 2019


In this paper, we introduce a class of functions inspired by the weighted Lp norm which is used for the control of unicycle robots in planar space. In particular, we prove that these functions are valid finite time control barrier functions. Finite time control barrier functions (FCBFs) provide a formal guarantee for finite time convergence to desired sets in the state space. Traditionally, these barrier functions consider only the position of the robot and not the heading, which makes it difficult to apply this framework in cases where the heading is important in addition to the position. In this paper, a new barrier function defined with the full state of the robot is proposed to achieve finite time convergence to the desired set in the state space and the desired heading angle with controllable error bounds. We propose a quadratic program (QP) based controller, which guarantees finite time convergence to a desired region in the state space. We show that there exists singular sets in the state space where the QP is infeasible. By virtue of the structure of the proposed barrier function, feasibility of the QP is guaranteed. A multi-robot case study is presented, along with simulation and experimental results.