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I thought I would be clever and use TWO shopping-cart-style casters (more stable) instead of the ONE usual omnidirectional ball caster. Now that I am running it I am almost positive that the kinematics are totally different and in fact very hard to model.

Can someone confirm or deny this belief, and give any context (links etc.) so I can dig deeper?

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You might take a look at this paper dealing with a powered wheelchair, which has two caster wheels. https://hal.inria.fr/hal-02124781/document

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