Kinematic modeling of wheeled mobile robots

TLDR

The study formulates kinematic equations for wheeled mobile robots—including conventional, omnidirectional, and ball wheels—by extending manipulator models to account for closed‑link chains, higher‑pair contacts, and unactuated wheel degrees of freedom. The authors derive these equations using the Sheth‑Uicker convention, matrix coordinate transformations, and a wheel Jacobian, combine wheel equations into a composite robot motion model, analyze mobility, actuation, and sensing via characterization trees, and validate the approach on the CMU Mobile Robot Laboratory’s Uranus robot.

Abstract

Abstract We formulate the kinematic equations of motion of wheeled mobile robots incorporating conventional, omnidirectional, and ball wheels. 1 We extend the kinematic modeling of stationary manipulators to accommodate such special characteristics of wheeled mobile robots as multiple closed‐link chains, higher‐pair contact points between a wheel and a surface, and unactuated and unsensed wheel degrees of freedom. We apply the Sheth‐Uicker convention to assign coordinate axes and develop a matrix coordinate transformation algebra to derive the equations of motion. We introduce a wheel Jacobian matrix to relate the motions of each wheel to the motions of the robot. We then combine the individual wheel equations to obtain the composite robot equation of motion. We interpret the properties of the composite robot equation to characterize the mobility of a wheeled mobile robot according to a mobility characterization tree. Similarly, we apply actuation and sensing characterization trees to delineate the robot motions producible by the wheel actuators and discernible by the wheel sensors, respectively. We calculate the sensed forward and actuated inverse solutions and interpret the physical conditions which guarantee their existence. To illustrate the development, we formulate and interpret the kinematic equations of motion of Uranus, a wheeled mobile robot being constructed in the CMU Mobile Robot Laboratory.