Time-optimality of robots by minimizing the motion times in terms of spin, circular arc, and tangential motion

In this paper, three omniwheels are positioned at an equilateral triangle having the vertices with wheel axles connected from the center of the triangle with the rays to every individual wheel in a typical mobile robot configuration. Omniwheels as normal wheels are moving perpendicularly to the direction of the wheel axle by the motors, however, unlike normal wheels, they may slide parallelly to the axle direction. Apart from a directed automobile, a time-optimal robot with such architecture may travel in either direction without rotating initially, and that can spin while doing so. Straight lines seem to be the shortest pathways for this time-optimal robot with minimum motion timing. The robot, on the other hand, might drive faster in certain various directions with minimum motion time. In this paper, we use a robot kinematic model to set independent speed boundaries with minimum motion time for the wheel and calculate the quickest analytical paths between setups. In this paper, the robot with minimum motion timing is analyzed in terms of spins, circular arcs, as well as a tangential motion to the wheel axles, which appear in the time-optimal trajectories of the robot. Thus, the sequence of various segments in time-optimal robot trajectories is analyzed.