Algorithms of Adaptive and Robust Output Control for a Robotic Prototype of a Surface Vessel

Abstract

The paper is devoted to development of a dynamic positioning system for a robotic vessel prototype. Two control laws, each intended to solve the posed problem, are proposed in the work. The mathematical model of MIMO plant boils down to a static function, as well as three independent dynamical channels with single input and single output, which correspond to the coordinates of the vessel (two linear ones and an angle one). They define its position in the plane uniquely. The 1st order linearized Nomoto model, which approximately describes the surface vessel behavior, is used as a mathematical description of each channel. The parameters of the considered MIMO plant are assumed to be unknown. Elements of the state vector are not measured, i.e. the feedback is provided using only the position and orientation of the prototype. It is implemented using a digital camera attached to a tripod above the workspace. The video signal is processed in a computer by image binarization according to the color of the deck and the red mark on the bow. The centers of the obtained spots are detected and after simple calculations three required coordinates become available. Error signals between the specified values and outputs at each channel enter the regulators, which shape the so called virtual control inputs distributed by the inverse transformation among the actuators of the robot. Control commands in the required format are sent to the prototype via a radio channel. The first proposed regulator is robust and it has fixed control parameters in its structure. The second one has adaptation laws of these parameters. Both algorithms are implemented on the robotic setup of surface vessel motion modeling. During the experimental approval of the obtained algorithms the stabilization problem of the vessel prototype in the specified area is performed.