No-Overturn Conditions for Omnivehicle Motion

We consider the dynamics of an omnidirectional vehicle moving on a perfectly rough horizontal plane. The vehicle has three omniwheels controlled by three direct current motors.
To find out the limits of the scope where the bilateral constraints model is applicable, we study the normal reactions of the vehicle. We present a step-by-step algorithm for finding out reaction components in the case of controlled motion. Based on these results, no-overturn conditions of the vehicle are proposed.
We apply this approach to study a specific model, that of a symmetrical omnivehicle. As a consequence, vehicle design recommendations are proposed.