Configuration manifolds and their applications to robot dynamic modeling and control

This paper presents a configuration manifold (C-manifold) embedding model for robot dynamic systems analysis and control algorithms development from a geometrical and topological perspective. The concepts of C-manifolds and their isometric embeddings are introduced, and the explicit forms of their representations are then developed. For an open serial-chain robotic system, a topological equivalence is found and demonstrated to be useful for dynamic model reduction. The study further shows that kinematics of a dynamic system determines the topology of its C-manifold so that the kinematics becomes a structure of the dynamics. By taking advantage of adaptive control, developing a kinematic model is shown to be sufficient for dynamic control purpose. Furthermore, we discover that the entire dynamic model of a robot can be significantly reduced, and the lower bound of the model reduction is a sub-system with the minimum embeddable C-manifold in the sense of topology. The paper also gives examples to illustrate the procedure of determining their C-manifold embedding models.