  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.
