A Convex Optimization Approach to Smooth Trajectories for Motion Planning with Car-Like Robots
This work addresses trajectory smoothing for car-like robots, offering a fast heuristic that is incremental over prior elastic band methods.
The paper tackles the problem of jagged trajectories from sampling-based motion planning for car-like robots by introducing the Convex Elastic Smoothing (CES) algorithm, which iteratively optimizes shape and speed via convex programming, achieving high-quality solutions in a few hundred milliseconds.
In the recent past, several sampling-based algorithms have been proposed to compute trajectories that are collision-free and dynamically-feasible. However, the outputs of such algorithms are notoriously jagged. In this paper, by focusing on robots with car-like dynamics, we present a fast and simple heuristic algorithm, named Convex Elastic Smoothing (CES) algorithm, for trajectory smoothing and speed optimization. The CES algorithm is inspired by earlier work on elastic band planning and iteratively performs shape and speed optimization. The key feature of the algorithm is that both optimization problems can be solved via convex programming, making CES particularly fast. A range of numerical experiments show that the CES algorithm returns high-quality solutions in a matter of a few hundreds of milliseconds and hence appears amenable to a real-time implementation.