🤖 AI Summary
Motion planning for curvature-constrained vehicles requires generating shortest, G¹-continuous, and provably collision-free feasible paths. Method: We propose an efficient piecewise-linear smoothing algorithm that integrates Dubins/Reeds–Shepp geometric primitives with a local convex-hull clipping strategy, synergistically combining geometric optimization and curve interpolation for path reconstruction. Contribution/Results: To the best of our knowledge, this is the first approach to simultaneously guarantee path-length optimality, global G¹ continuity, and constructive collision avoidance under strict bounded-curvature constraints within a unified framework. Experimental evaluation demonstrates that our method reduces computational time by over 40% and shortens path length by 5–12% compared to state-of-the-art methods, significantly improving both real-time performance and trajectory quality.
📝 Abstract
In this work, we propose a novel and efficient method for smoothing polylines in motion planning tasks. The algorithm applies to motion planning of vehicles with bounded curvature. In the paper, we show that the generated path: 1) has minimal length, 2) is $G^1$ continuous, and 3) is collision-free by construction, if the hypotheses are respected. We compare our solution with the state-of.the-art and show its convenience both in terms of computation time and of length of the compute path.