Incursive anticipatory control of a chaotic robot arm

Abstract

This paper deals with an innovative mathematical tool for modelling, simulating and controlling systems in automation engineering. Classically, feedback processes are based on recursive loops where the future state of a system is computed from the present and past states. With the new concept of incursion, an inclusive recursion, the future state of a system is taken into account for computing this future state in a self-referential way. The future state is computed from the mathematical model of the system. With incursion, numerical instabilities in the simulation of finite difference equations can be stabilised. The incursive control of systems can also stabilise feedback loops by anticipating the effect of the control what I call a feed-in-time control. In this short paper, the particular case of the modelling, simulation and control of a robot arm in a working space is studied. The highly non-linear model is based on recursive finite difference equations which give rise to instabilities, bifurcations and fractal chaos. The anticipatory control by incursion, called feed-in-time control, of such a robot arm stabilises its trajectory. Numerical simulations show that the robot arm reaches set points in a few steps in any point of the working space.