Date of Award


Document Type

Thesis (Ph.D.)


Department of Computer Science

First Advisor

Devin Balkcom


The problem of moving rigid bodies efficiently is of particular interest in robotics because the simplest model of a mobile robot or of a manipulated object is often a rigid body. Path planning, controller design and robot design may all benefit from precise knowledge of optimal trajectories for a set of permitted controls. In this work, we present a general solution to the problem of finding minimum time trajectories for an arbitrary self-propelled, velocity-bounded rigid body in the obstacle-free plane. Such minimum-time trajectories depend on the vehicle’s capabilities and on and the start and goal configurations. For example, the fastest way to move a car sideways might be to execute a parallel-parking motion. The fastest longdistance trajectories for a wheelchair-like vehicle might be of a turn-drive-turn variety. Our analysis reveals a wide variety of types of optimal trajectories. We determine an exhaustive taxonomy of optimal trajectory types, presented as a branching tree. For each of the necessary leaf nodes, we develop a specific algorithm to find the fastest trajectory in that node. The fastest trajectory overall is drawn from this set.


Originally posted in the Dartmouth College Computer Science Technical Report Series, number TR2011-694.