Control of underactuated mechanical systems

点击翻译按钮获取中文摘要

The proposed research project aims at the systematic design of control facilities for underactuated nonlinear mechanical systems, i.e., systems with fewer actuators (control inputs) than mechanical degrees of freedom. The project is subdivided into the three parts analysis, design and implementation, which will be worked on in this ordering, with some expected parallelisms.The analysis part on the one hand deals with the classification of underactuated systems from the viewpoint of control theory, i.e., in terms of the influence that is exerted by the input to the dynamics. Thereby, a possible tool is the representation of the systems in a suited normal form. One the other hand the roll of the inherent inertial coupling as well as discrete and continuous symmetries is investigated. Furthermore, the applicability of approaches based on orbital flatness are assayed, i.e., obtaining a differentially flat system using a suited transformation of time.A central feature of underactuated systems is the compliance or violation of the so called Brockett condition, which states necessary conditions for the existence of a continuous differentiable control law asymptotically stabilizing an equilibrium point. Subject of the second part of the project is the design of control algorithms for both cases. As a reaction to the difficulties occurring when standard methods are applied, various different approaches are proposed. In many cases the transition between equilibrium points is desired, requiring the computation and stabilization of a reference trajectory. To avoid adverse controllability properties near equilibrium points it is possible to design the motion such that desired positions are reached with vanishing velocity but nonzero acceleration. If this motion is performed periodically, it is possible to consider the stabilization of a limit cycle instead of a general trajectory. Further possibilities for controller design for systems violating the Brockett condition include the stabilization of submanifolds of the state space (instead of an isolated equilibrium) and the formulation of discontinuous control laws.In the implementation part of the project the developed analysis and design methods, whose scope is aimed to be as general as possible, are experimentally verified on existing test beds.Additionally, to ease the applicability of the developed methods and algorithms for the control community it is planned to provide a software toolbox for an open source computer algebra system.