Design of Ball Wheel Mechanisms for Omnidirectional Vehicles With Full Mobility and Invariant Kinematics

Abstract

A new ball wheel design for fully mobile omnidirectional vehicles is presented. This ball wheel mechanism yields a unique vehicle design that is not only omnidirectional with no kinematic singularity but is configuration-invariant in kinematic behavior. Invariant kinematics greatly simplifies the control of smooth and precise vehicle motion. Multiple displacement sensors are easily incorporated into each ball wheel mechanism to enhance the accuracy of vehicle motion control. Two fundamental requirements of functioning ball wheel designs are established: one is the translational form closure requirement for holding a spherical tire, and the other is the non-overconstraint requirement to allow each ball to rotate in two directions. It is proved that a class of mechanisms in which a ball is held by rollers whose axes are fixed directly to the vehicle chassis cannot satisfy the fundamental requirements. A class of modified mechanisms are then analyzed and the necessary and sufficient conditions for the modified mechanisms the fundamental requirements are obtained. For this class of ball wheels (Class 1), conditions for configuration-invariant kinematics are found and two possible actuation schemes are discussed. Two prototype vehicles have been built: both have three Class 1 ball wheels but each uses a different actuation scheme. Performance data of the two prototypes are compared. Both achieve smooth motion and precise dead reckoning.