Minimum Time Kinematic Trajectories for Self-propelled Rigid Bodies in the Unobstructed Plane

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.