Optimal model-based trajectory planning with static polygonal constraints

TL;DR

This paper introduces a hybrid trajectory planning method that combines graph search and convex optimization to compute globally optimal paths respecting exact polygonal constraints for various dynamical systems.

Contribution

It presents a novel approach that leverages the exact geometry of polygonal constraints, improving optimality and flexibility over previous approximation-based methods.

Findings

Successfully plans distance-optimal trajectories for a Dubins car.

Generates time-, distance-, and energy-optimal paths for marine vehicles.

Demonstrates improved accuracy and flexibility in trajectory planning.

Abstract

The main contribution of this paper is a novel method for planning globally optimal trajectories for dynamical systems subject to polygonal constraints. The proposed method is a hybrid trajectory planning approach, which combines graph search, i.e. a discrete roadmap method, with convex optimization, i.e. a complete path method. Contrary to past approaches, which have focused on using simple obstacle approximations, or sub-optimal spatial discretizations, our approach is able to use the exact geometry of polygonal constraints in order to plan optimal trajectories. The performance and flexibility of the proposed method is evaluated via simulations by planning distance-optimal trajectories for a Dubins car model, as well as time-, distance- and energy-optimal trajectories for a marine vehicle.