Estimating the attraction domain of the invariant set in the problem of wheeled robot control

Consideration was given to the problem of controlling the planar motion of a wheeled robot with the driving rear wheels and forewheels intended for chassis rotation. The aim of control is to drive the goal point to the prescribed trajectory and stabilize the motion along it. The trajectory consists of segments of straight lines and circles. The forewheel rotation mechanism has inertiality due to its dynamic characteristics. Disregard for the dynamic properties of the forewheel drive at designing the control law leads in the course of motion to transients in the closed-loop system at passing from one trajectory segment to another. It was assumed that the drive dynamics obeys a first-order differential equation whose right-hand side satisfies the “sector condition”. To estimate these transients, in the system state space an invariant set is defined and estimated together with the estimate of the attraction domain.