Kinematic Modeling Of Wheeled Mobile Robots - Patrick Muir, Charles Neuman
Carnegie Mellon University (1986)
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We farmulate the kinematic equation-of--motion of wheeled mobile robots incorporating conventional,
omnidirectional, and ball wheels. While our approach parallels the kinematic modeling of stationary manipulators, we extend the methodology to accomodate such specid characteristics of wheeled mobile robot
to multiple closed-link chains, higher-pair contact points between a wheel and a surface, and unactuated
and unsensed wheel degreed-fredam. We survey existing wheeled mobile robots to motivate our development. To communicate the kinematic features of wheeled mobile robots, we introduce a diagrammatic
convention and nomenclature. We apply the Seth-Uicker convention to assign cooodizmte a m and develop a matrix coordinate transformation algebra to derive the equations-of-motion. A wheel Jacobian
matrix is formulated to relate the motions of each wheel to the motions of the robot. We combine the individual
wheel equations to form the composite robot equation-of-motion. We calculate the m c d forward
and actuated inverse solutions and interpret the conditions which guarauta their existence. We interprete
the properties of the composite robot equation to characterize the mobility of a whceled mobile robot
according to the mobility characterization tree. S-, we apply actuation and sensing characteritstion
trccs to dclincatc the robot motions prodaciblc by the wheel actuators and discernable by the wheel sensors,
respectively. We apply OUT kinematic model to design, kinanatidmsed control, dead-reckoning, and wheel
slip detection. To illustrate the development, we formulate and interpret the kinematic equations-of-motion
of six prototype wheeled mobile robots.

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