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Developing controllers for obstacle avoidance between polytopes is achallenging and necessary problem for navigation in tight spaces. Traditionalapproaches can only formulate the obstacle avoidance problem as an offlineoptimization problem. To address these challenges, we propose a duality-basedsafety-critical optimal control using nonsmooth control barrier functions forobstacle avoidance between polytopes, which can be solved in real-time with aQP-based optimization problem. A dual optimization problem is introduced torepresent the minimum distance between polytopes and the Lagrangian functionfor the dual form is applied to construct a control barrier function. Wevalidate the obstacle avoidance with the proposed dual formulation for L-shaped(sofa-shaped) controlled robot in a corridor environment. We demonstratereal-time tight obstacle avoidance with non-conservative maneuvers on a movingsofa (piano) problem with nonlinear dynamics.

Duality-based Convex Optimization for Real-time Obstacle Avoidance between Polytopes with Control Barrier Functions