Tractable Compositions of Discrete-Time Control Barrier Functions with Application to Lane Keeping and Obstacle Avoidance [article]

Matthew Cavorsi, Mohammad Khajenejad, Ruochen Niu, Qiang Shen, Sze Zheng Yong
<span title="2020-04-04">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This paper introduces control barrier functions for discrete-time systems, which can be shown to be necessary and sufficient for controlled invariance of a given set. Moreover, we propose nonlinear discrete-time control barrier functions for partially control affine systems that lead to controlled invariance conditions that are affine in the control input, leading to a tractable formulation that enables us to handle the safety optimal control problem for a broader range of applications with
more &raquo; ... complicated safety conditions than existing approaches. In addition, we develop mixed-integer formulations for basic and secondary Boolean compositions of multiple control barrier functions and further provide mixed-integer constraints for piecewise control barrier functions. Finally, we apply these discrete-time control barrier function tools to automotive safety problems of lane keeping and obstacle avoidance, which are shown to be effective in simulation.
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="">arXiv:2004.01858v1</a> <a target="_blank" rel="external noopener" href="">fatcat:off4tgdeavdnpmcn3m5gp3jefq</a> </span>
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