|Devin J. Balkcom, Paritosh
A. Kavathekar Department of Computer Science, Dartmouth College,
Hanover, NH 03755 and Matthew T. Mason Robotics Institute,
Carnegie Mellon University, Pittsburgh, PA 15213
|A common mobile robot design
consists of three ‘omniwheels’ arranged at the vertices of an
equilateral triangle, with wheel axles aligned with the rays from the center
of the triangle to each wheel. Omniwheels, like standard wheels, are driven
by the motors in a direction perpendicular to the wheel axle, but unlike
standard wheels, can slip in a direction parallel to the axle. Unlike a
steered car, a vehicle with this design can move in any direction without
needing to rotate first, and can spin as it does so. The shortest paths
for this vehicle are straight lines. However, the vehicle can move more
quickly in some directions than in others. What are the fastest trajectories?
We consider a kinematic model of the vehicle and place independent bounds
on the speeds of the wheels, but do not consider dynamics or bound accelerations.
We derive the analytical fastest trajectories between configurations. The
time-optimal trajectories contain only spins in place, circular arcs, and
straight lines parallel to the wheel axles. We classify optimal trajectories
by the order and type of the segments; there are four such classes, and
there are no more than 18 control switches in any optimal trajectory.