Phasor-Like Interpretation of the Angular Velocity of the Wheels of Omnidirectional Mobile Robots

Omnidirectionality is a feature that allows motion in any direction without orientation maneuvers. Omnidirectional mobile robots are usually based on omni or mecanum wheels. The motion of an omnidirectional mobile robot is defined by a target motion command M = (v,a,?), where v is the module of the translational velocity; a is the angular orientation of the translational velocity, and ? is the angular velocity of the mobile robot. The motion is achieved by converting the target motion command into the target angular velocities that must be applied to the active wheels of the robot. This work proposes a simplified phasor-like interpretation of the relationship between the parameters of a specific motion command and the angular velocities of the wheels. The concept of phasor-like notation is validated from the analysis of the kinematics of omnidirectional mobile robots using omni wheels and mecanum wheels. This simplified phasor-like notation fosters unconstrained conceptual design of single-type and hybrid multi-wheeled omnidirectional mobile robots without the distribution or type of wheels being a design constraint.