Georgy Moiseev

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.

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.
We study constant voltage dynamics for the symmetric model of the vehicle and get a general analytical solution for arbitrary initial conditions which is shown to be Lyapunov stable. Piecewise combination of the trajectories produces a solution to boundary-value problems for arbitrary initial and terminal mass center coordinates, course angles and their derivatives with one switch point. The proposed control combining translation and rotation of the vehicle is shown to be more energy-efficient than a control splitting these two types of motion.
For the nonsymmetrical vehicle configuration, we propose a numerical procedure of solving boundary-value problems that uses parametric continuation of the solution obtained for the symmetric vehicle. It shows that the proposed type of control can be used for an arbitrary vehicle configuration.