  Developing controllers for obstacle avoidance between polytopes is a
challenging and necessary problem for navigation in tight spaces. Traditional
approaches can only formulate the obstacle avoidance problem as an offline
optimization problem. To address these challenges, we propose a duality-based
safety-critical optimal control using nonsmooth control barrier functions for
obstacle avoidance between polytopes, which can be solved in real-time with a
QP-based optimization problem. A dual optimization problem is introduced to
represent the minimum distance between polytopes and the Lagrangian function
for the dual form is applied to construct a control barrier function. We
validate the obstacle avoidance with the proposed dual formulation for L-shaped
(sofa-shaped) controlled robot in a corridor environment. We demonstrate
real-time tight obstacle avoidance with non-conservative maneuvers on a moving
sofa (piano) problem with nonlinear dynamics.
