Systematic isotropy analysis of a mobile robot with three active caster wheels

This paper presents a systematic isotropy analysis of a caster wheeled omnidirectional mobile robot (COMR) with three active caster wheels. Unlike previous analysis, no assumption is made on the relative scale of the steering link offset and the wheel radius. 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 isotropy conditions are examined to categorize three different groups to be handled in a similar way. Third, the isotropy conditions are further explored to identify four different sets of all possible isotropic configurations. Fourth, the characteristic lengths required for the isotropy of a COMR are obtained in a closed-form. Finally, the local and the global isotropy indices are used to determine the optimal design parameters.