A Parameterized Cubic Bézier Spline-based Informed RRT* for Non-holonomic Path Planning

Abstract

This paper proposes a new path planning algorithm for robotics called Informed SRRT <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">*</sup> . Compared to conventional RRT <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">*</sup> algorithms with Euclidean metrics, our algorithm extends the approach by incorporating a local planner from SRRT to satisfy both external and internal constraints. To compute the path to the goal region, we use parameterized cubic curves instead of computationally expensive numerical methods. We add two extra lines at the endpoints of the Bézier spline to leave rooms for the rewiring process. Kinematic constraints require at least three state connections to be tweaked during rewiring. The algorithm always ensures that the path has G <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> continuity of curvature within upper-bound constraints. Simulation results demonstrate that the proposed method finds shorter paths than SRRT while maintaining the same iteration of node sampling.