Modeling and PD control of closed-chain mechanical systems

In this paper, we review the structure of a reduced model for closed-chain mechanical systems originally proposed by Ghorbel, Chetelat and Longchamp (1994), and highlight the fact that the model has two special characteristics which make it different from models of open-chain mechanical systems. First, it is defined locally, and second it is an implicit model. We show that closed-chain systems satisfy the property of skew symmetry. We therefore propose PD-based control strategies with full as well as simple gravity compensation and discuss and compare the computational issues involved in the implementation of both controllers.