Optimizing Curvature and Clearance of Piecewise Bézier Paths.

Path optimization typically involves finding a smooth and short path that satisfies motion constraints of a given vehicle or simulated agent. In this paper, we propose a new path optimization scheme based on convex optimization of a piecewise quadratic Bézier path. Our method addresses $C^{1}$ continuity and a target minimum clearance to obstacles while minimizing path length and maximum curvature. The user is able to customize the objective function by assigning different weights to the clearance, length, and curvature terms. As a result our method is versatile and suitable for a variety of path planning applications in robotics and autonomous vehicles. We present several results demonstrating the ability to achieve paths according to different values for the curvature, length, and clearance parameters. Our benchmark scenarios apply our method directly to low-quality paths generated by a sampling-based planner, and as well in comparison to a heuristic shortcut-based smoothing method. Our results show that the quality of the paths produced by our method outperforms other approaches, and that our method is responsive to the weights chosen by the user. Our method is able to control the main path properties of interest in a unified fashion, and therefore represents an excellent option for several path planning applications in robotics and autonomous vehicles.