Robust Collision Avoidance of Quadric and Polygonal Surfaces Moving in Planar Environments

The determination of robot trajectories that can achieve reactive collision avoidance with moving objects is of great interest. In cluttered environments with tight spaces, it becomes important to consider the shapes of the objects in computing these trajectories. The literature largely models the shapes of the objects as circles, and this can make the avoidance maneuvers very conservative, especially when the objects are elongated and/or non-convex. In this paper, we model the shapes of the objects using combinations of quadric surfaces or polygons, and employ a collision cone approach to achieve reactive collision avoidance, in the presence of measurement noise. The collision avoidance design employs a dual-loop control architecture where the inner loop uses a dynamic inversion-based method and the outer loop uses Linear Matrix Inequalities (LMIs). Simulation results demonstrating the collision avoidance laws for dynamic, heterogeneous quadric and polygonal surfaces are presented.