Generalizing Dubins Curves: Minimum-time Sequences of Body-fixed Rotations and Translations in the Plane

This paper presents the minimum-time sequences of rotations and translations that connect two configurations of a rigid body in the plane. The configuration of the body is its position and orientation, given by (x, y, ) coordinates, and the rotations and translations are velocities ( x, y, ) that are constant in the frame of the robot. There are no obstacles in the plane. We completely describes the structure of the fastest trajectories, and present a polynomialtime algorithm that, given a set of rotation and translation controls, enumerates a finite set of structures of optimal trajectories. These trajectories are a generalization of the well-known Dubins and Reeds-Shepp curves, which describe the shortest paths for steered cars in the plane.

• Type: Journal
• Year: 2010
• Where: IJRR
• Authors: Andrei A. Furtuna, Devin J. Balkcom
• Keywords: Fastest Trajectories, IJRR 2010, Rotations, Trajectories