Systematic Isotropy Analysis of Caster Wheeled Mobile Robots with Steering Link Offset Different from Wheel Radius

Previous isotropy analysis of a caster wheeled omnidirectional mobile robot (COMR) has been made under the assumption that the steering link offset is equal to the caster wheel radius. Nevertheless, many practical COMRs in use take advantage of the steering link offset different from the wheel radius. This paper presents a systematic isotropy analysis of a fully actuated COMR with variable steering link offset, which can be considered as the generalization of the previous analysis. First, with the characteristic length introduced, the kinematic model of a COMR is obtained based on the orthogonal decomposition of the wheel velocities. Second, the necessary and sufficient conditions for the isotropy of a COMR are examined to categorize three different groups, each of which can be dealt with in a similar way. Third, the isotropy conditions are further explored to identify four different sets of all possible isotropic configurations. Fourth, the expressions of the isotropic characteristic length required for the isotropy of a COMR are obtained.