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In the recent past, several sampling-based algorithms have been proposed tocompute trajectories that are collision-free and dynamically-feasible. However,the outputs of such algorithms are notoriously jagged. In this paper, byfocusing on robots with car-like dynamics, we present a fast and simpleheuristic algorithm, named Convex Elastic Smoothing (CES) algorithm, fortrajectory smoothing and speed optimization. The CES algorithm is inspired byearlier work on elastic band planning and iteratively performs shape and speedoptimization. The key feature of the algorithm is that both optimizationproblems can be solved via convex programming, making CES particularly fast. Arange of numerical experiments show that the CES algorithm returns high-qualitysolutions in a matter of a few hundreds of milliseconds and hence appearsamenable to a real-time implementation.

A Convex Optimization Approach to Smooth Trajectories for Motion Planning with Car-Like Robots