This paper presents a configuration manifold embedding model that provides a new approach to dynamic model reduction and adaptive control of redundant robotic systems. The proposed model is developed based on a geometrical and topological analysis of configuration manifolds (C-manifolds) hidden behind every robotic dynamic system that commonly obeys the Lagrange equation. With a detailed study of the C-manifold immersion and embedding into Euclidean space, we show that for a redundant robotic system, a subtask decision by choosing a certain null solution is technically equivalent to the C-manifold embedization. A direct adaptive control strategy is then developed based on the C-manifold embedding model for a specific application to model reduction and control of redundant robotic systems with both main tasks and subtasks represented in Cartesian space. It is also demonstrated that making only a kinematics model for a redundant robot can do the dynamic control job. Finally, a computer simulation study shows the effectiveness of this adaptive control algorithm.
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