Non-holonomic, omnidirectional undercarriages that are composed of steered standard wheels seem to provide a solid compromise between versatility, flexibility and high robustness against various ground conditions. However, such undercarriages are characterized by the occurrence of a number of singular configurations. To avoid these singular configurations most control-approaches restrict the admissible configuration-space thus eventually reducing the mobility and flexibility of the undercarriage. Within this work a state-space representation that forms a locally singularity-free atlas of the admissible configurationspace is presented. Based on this state-space description a switching based controller is developed that incorporates the former singular regions into the used configuration space and thus allows to exploit the full flexibility of non-holonomic, omnidirectional undercarriages. The implemented controller is quantitatively and qualitatively evaluated and compared to one approach that avoids the singular regions and one that completely neglects the non-holonomic bindings
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