Yuri A. Kapitanyuk

Yuri A. Kapitanyuk, Anton V. Proskurnikov, Ming Cao

Roll stabilization is an important problem of ship motion control. This problem becomes especially difficult if the same set of actuators (e.g. a single rudder) has to be used for roll stabilization and heading control of the vessel, so that the roll stabilizing system interferes with the ship autopilot. Finding the "trade-off" between the concurrent goals of accurate vessel steering and roll stabilization usually reduces to an optimization problem, which has to be solved in presence of an unknown wave disturbance. Standard approaches to this problem (loop-shaping, LQG, $H_{\infty}$-control etc.) require to know the spectral density of the disturbance, considered to be a \colored noise". In this paper, we propose a novel approach to optimal roll stabilization, approximating the disturbance by a polyharmonic signal with known frequencies yet uncertain amplitudes and phase shifts. Linear quadratic optimization problems in presence of polyharmonic disturbances can be solved by means of the theory of universal controllers developed by V.A. Yakubovich. An optimal universal controller delivers the optimal solution for any uncertain amplitudes and phases. Using Marine Systems Simulator (MSS) Toolbox that provides a realistic vessel's model, we compare our design method with classical approaches to optimal roll stabilization. Among three controllers providing the same quality of yaw steering, OUC stabilizes the roll motion most efficiently.

Yuri A. Kapitanyuk, Anton V. Proskurnikov, Ming Cao

In this paper we propose an algorithm for path following control of the nonholonomic mobile robot based on the idea of the guiding vector field (GVF). The desired path may be an arbitrary smooth curve in its implicit form, that is, a level set of a predefined smooth function. Using this function and the robot's kinematic model, we design a GVF, whose integral curves converge to the trajectory. A nonlinear motion controller is then proposed which steers the robot along such an integral curve, bringing it to the desired path. We establish global convergence conditions for our algorithm and demonstrate its applicability and performance by experiments with real wheeled robots.

Hector Garcia de Marina, Yuri A. Kapitanyuk, Murat Bronz et al.

This paper presents an algorithm for solving the problem of tracking smooth curves by a fixed wing unmanned aerial vehicle travelling with a constant airspeed and under a constant wind disturbance. The algorithm is based on the idea of following a guiding vector field which is constructed from the implicit function that describes the desired (possibly time-varying) trajectory. The output of the algorithm can be directly expressed in terms of the bank angle of the UAV in order to achieve coordinated turns. Furthermore, the algorithm can be tuned offline such that physical constraints of the UAV, e.g. the maximum bank angle, will not be violated in a neighborhood of the desired trajectory. We provide the corresponding theoretical convergence analysis and performance results from actual flights.