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.

Robotic posture optimization and control is an important issue for industrial applications, particularly for the automobile assembly line automation workcells. The optimal posture means that a robot reaches the best configuration in order to operate on a force-related task. It can be modeled as an even joint-torque distribution problem. Through the model, four possible potential functions are developed for the posture optimization in a redundant robotic system. One of the four shows higher effectiveness than others in a simulation study. These potential functions can be more suitably applied to a dual-redundant robotic system for its multi-subtask optimization aided by a nonlinear null space control scheme for the subtask weighting factors determination.