Using Spherical Harmonics for Navigating in Dynamic and Uncertain Environments
Steven D. Patrick, Efstathios Bakolas · IFAC-PapersOnLine · 2022
In this paper, we present a novel approach for local motion planning in an unknown environment populated by static and dynamic obstacles. A key component of our planner is the use of harmonic basis functions defined over the unit sphere, known as spherical harmonics (SH), to represent a collision-free space near an agent. In contrast with our previous approach, which only applies to unknown static environments, the approach proposed herein handles dynamic obstacles as well. It is done by efficiently calculating the coefficients of a spherical harmonics approximation of the local collision-free space for each step of a given planning horizon. Our method for approximating the collision-free space with spherical harmonics allows us to plan trajectories in challenging environments (e.g., planning through narrow passages) where other methods for generating search-spaces fail. To accurately approximate the collision-free space for future time steps along a planning horizon, we use a Kalman Filter (KF) to propagate the measured point cloud through time. Our use of the KF allows us to better approximate obstacles moving in space in comparison to inaccurate constant obstacle velocity assumptions used by other methods. Finally, we show the effectiveness of our proposed trajectory planner using two different non-trivial scenarios.