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We have introduced a methodology for the kinematic modeling of wheeled mobile robots. In this paper, we apply our methodology to Uranus, an omnidirectional wheeled mobile robot which is being developed in the Robotics Institute of Carnegie Mellon University. We assign coordinate systems to specify the transformation matrices and write the kinematic equations-of-motion. We illustrate the actuated inverse and sensed forward solutions; i.e., the calculation of actuator velocities from robot velocities and robot velocities from sensed wheel velocities. We apply the actuated inverse and sensed forward solutions to the kinematic control of Uranus by: calculating in real-time the robot position from shaft encoder readings (i.e., dead reckoning); formulating an algorithm to detect wheel slippage; and developing an algorithm for feedback control.
Muir et al. (Wed,) studied this question.