Hybrid Control of Flexible Manipulators with Multiple Contact

This paper proposes a hybrid positiodforce controller for flexible link manipulators that make contact with the environment at more than one point. The manipulator maintains contact at the bracing point to reduce its strucruraI vibrations, and at the same time, rhe end effector may make contact with the workpiece to perform the task. This approach requires hybrid control not only at the end effector but also at the bracing point. In this paper, the dynamic equations of the motion with multiple contact constraints are derived. The dynamic equations are transformed into two subspaces, the constrained and constraint-pee subspace, using the singular value decomposition of the constraint equations. Each force and position controller are developed based on the orthogonality of these two subspaces. A hybrid controller is proposed from the new coordinates, and its stability is proved analytically under the quasi-static condition. Finally, an experimental study is carried out to justifi the feasibility and application of proposed ideas.