Developing controllers for obstacle avoidance between polytopes is a challenging and necessary problem for navigation in a tight space. 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 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 demonstrate the proposed controller on a moving sofa problem where non-conservative maneuvers can be achieved in a tight space.

翻译：开发控制器,以避免在多顶楼之间形成障碍,这是在紧凑的空间航行时遇到的一个具有挑战性和必要的问题。传统方法只能将避免障碍的问题发展成一个离线优化问题。为了应对这些挑战,我们建议使用控制屏障功能进行基于双重性的安全临界最佳控制,以避免在多顶楼之间形成障碍,这可以通过基于QP的优化问题实时解决。引入了双重优化问题,以代表多顶楼与Lagrangian功能之间的最短距离,用两种形式构建控制屏障功能。我们向拟议的控制器展示了移动的沙发问题,在那里可以在紧凑的空间进行非保守的操纵。