Duality-based Convex Optimization for Real-time Obstacle Avoidance between Polytopes with Control Barrier Functions
This work addresses the problem of real-time navigation in constrained environments for robotics, offering an incremental improvement over traditional offline optimization methods.
The paper tackled real-time obstacle avoidance between polytopes in tight spaces by proposing a duality-based safety-critical optimal control method using nonsmooth control barrier functions, which enabled real-time solving via QP optimization and demonstrated successful avoidance in scenarios like a moving sofa problem with nonlinear dynamics.
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.