Efficient Clothoid Tree-Based Local Path Planning for Self-Driving Robots

In this paper, we propose a real-time clothoid tree-based path planning for self-driving robots. Clothoids, curves that exhibit linear curvature profiles, play an important role in road design and path planning due to their appeal- ing properties. Nevertheless, their real-time applications face considerable challenges, primarily stemming from the lack of a closed-form clothoid expression. To address these chal- lenges, we introduce two innovative techniques: 1) an efficient and precise clothoid approximation using the Gauss-Legendre quadrature; and 2) a data-efficient decoder for interpolating clothoid splines that leverages the symmetry and similarity of clothoids. These techniques are demonstrated with numerical examples. The clothoid approximation ensures an accurate and smooth representation of the curve, and the clothoid spline decoder effectively accelerates the clothoid tree exploration by relaxing the problem constraints and reducing the problem size. Both techniques are integrated into our path planning algorithm and evaluated in various driving scenarios.