Abstract
This paper presents a configuration manifold model for the analysis of dynamic systems and the development of control algorithms from both geometrical and topological points of view. The fundamental theory of surfaces and differential manifolds endowed with Riemannian metrics is overviewed. The concepts of configuration manifolds (C-manifolds) and their immersions and embeddings are then introduced and applied to dynamic systems modeling. An explicit form of the smooth embedding for a given dynamic system with its C-manifold is derived. In an open serial-chain robotic system, a topological equivalence, i.e. a homeomorphism, is found and shown to be useful for dynamic model reduction. With topology being viewed as the structure of geometry, we discover and prove that the kinematics of a dynamic system determines its topology so that the kinematics is virtually a structure of the system's dynamics. This key point of view is further extended to the development of an adaptive control strategy. A computer simulation study is finally performed to verify the proposed model and adaptive control scheme.
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Gu, E.Y.L. Dynamic Systems Analysis and Control Based on a Configuration Manifold Model. Nonlinear Dynamics 19, 113–134 (1999). https://doi.org/10.1023/A:1008374216291
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DOI: https://doi.org/10.1023/A:1008374216291