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Obstacle avoidance between polytopes is a challenging topic for optimalcontrol and optimization-based trajectory planning problems. Existing workeither solves this problem through mixed-integer optimization, relying onsimplification of system dynamics, or through model predictive control withdual variables using distance constraints, requiring long horizons for obstacleavoidance. In either case, the solution can only be applied as an offlineplanning algorithm. In this paper, we exploit the property that a smallerhorizon is sufficient for obstacle avoidance by using discrete-time controlbarrier function (DCBF) constraints and we propose a novel optimizationformulation with dual variables based on DCBFs to generate a collision-freedynamically-feasible trajectory. The proposed optimization formulation haslower computational complexity compared to existing work and can be used as afast online algorithm for control and planning for general nonlinear dynamicalsystems. We validate our algorithm on different robot shapes using numericalsimulations with a kinematic bicycle model, resulting in successful navigationthrough maze environments with polytopic obstacles.

Safety-Critical Control and Planning for Obstacle Avoidance between Polytopes with Control Barrier Functions