Duality-based Convex Optimization for Real-time Obstacle Avoidance between Polytopes with Control Barrier Functions
arXiv:2107.08360 · doi:10.23919/ACC53348.2022.9867246
Abstract
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.
arXiv commentAccepted to 2022 American Control Conference (ACC) with full version of proofs in the appendix
References in corpus (4)
- Discontinuous Dynamical Systems: A tutorial on solutions, nonsmooth analysis, and stability
- Safe Control Synthesis via Input Constrained Control Barrier Functions
- Safety Embedded Differential Dynamic Programming Using Discrete Barrier States
- Duality-based Convex Optimization for Real-time Obstacle Avoidance between Polytopes with Control Barrier Functions