Industrial robots have found great potential in applications to assembly-line automation. Programmable robotbased assembly systems are often needed, in particular for circumstances in which special assembly equipment is not available or well-trained operators could not be employed economically. Robots with enough compliance can perform not only classic automation tasks, such as spot welding, cargo carrying, etc., but also can operate those tasks which demand the compliant motion capacity of robots. Therefore, the research on robot compliance is especially important for parts assembly by robots, where robot compliant motions and manipulations are essential requirements. This paper presents a number of important issues in robot compliance research, including the specification of robot end-effector compliance; properties of a robot compliance matrix at its end-effector; discussions on passive compliance and active compliance and their comparisons; and derivation of the compliance at the endeffector required for tasks.

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, i.e., a diffeomorphism between its combined C-manifold and the minimum embeddable C-manifold 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 subsystem 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. One of the examples is simulated in computer to verify its trajectory-tracking adaptive control process.

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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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