Algorithm to construct invariant ellipsoids in the problem of stabilization of wheeled robot motion

Design of the control law for planar motion of the wheeled robot was studied. The aim of control lies in driving the robot to the desired smooth curvilinear trajectory and stabilizing its motion. At that, the control resource and the domain of variations of the phase variables are bounded. It was previously suggested to construct the criterion for control law stabilizability as invariant ellipsoids, that is, quadratic approximations of the attraction domains of the target trajectory. Then construction of the invariant ellipsoids came to solving a system of linear matrix inequalities and testing a scalar inequality. The paper was devoted to practical application of the previous results. Choice of the parameters of the system of linear matrix inequalities was discussed. An algorithm to construct an invariant ellipsoid in at most three iterations was developed. It also determines the maximal ellipsoid for a given maximal permissible deviation of the robot from the target trajectory.