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Kinematic isotropy of omnidirectional mobile robots with powered caster wheels is discussed and utilized in optimizing the design parameters of the robots. The analysis is done to cover the most general cases, by observing the mathematical expression of the equations of motion rather than by numerical evaluation of specific parameters or actuation schemes. Optimal design guidelines are provided. Singularity analysis is given to support the proposed design guidelines. Simulation results are presented to verify the conclusions drawn.