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

TL;DR

This paper introduces a duality-based convex optimization approach using control barrier functions for real-time obstacle avoidance between polytopes, enabling safe navigation in tight spaces with nonlinear dynamics.

Contribution

It presents a novel duality-based method that formulates obstacle avoidance as a real-time solvable QP, improving upon traditional offline approaches.

Findings

Successful real-time obstacle avoidance demonstrated in corridor environments.

Effective avoidance of moving obstacles with nonlinear dynamics.

Non-conservative, tight maneuvering achieved in experiments.

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.