Зобова Александра Александровна

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.

В статье рассматривается новый лаконичный метод вывода динамических уравнений неголономных систем, предложенный Я.В. Татариновым в 2003 году, в применении к описанию динамики колесных систем трех различных типов (рояльное колесо, экипажи с роликонесущими колесами, с дифференциальным приводом).