Title
Task-Space / Joint-Space Damping Transformations for Passive Redundant Manipulators

Abstract
We consider here passive mechanical wrists, capable of imparting a desired damping matrix to a grasped workpiece. Previous work has shown how to select a damping matrix such that an assembly operation can be made force-guided. The passive mechanical wrist is programmable -- it can adopt a wide range of damping matrices -- by virtue of a number of tunable dampers which interconnect the joints.

We have been studying the range of damping matrices that such a wrist can adopt, purely by tuning its dampers. A kinematic Jacobian relates the task-space damping matrix to a similar matrix in the hydraulic space of the tunable dampers (joint-space). We find that a redundant wrist has a broader range of realizable damping matrices than a non-redundant wrist.

However for redundant wrists the transformation of damping matrices between task-space and joint-space is not straightforward. In this paper we identify the causal directions along which the transformations are linear. We show that the joint-space matrices which are obtained as linear transformations of desired task-space matrices are all singular. Many realizable joint-space matrices (corresponding to a desired task-space damping matrix) are shown to exist which are not discovered by linear transformations.

Source: Proceedings of the IEEE 1993 International Conference on Robotics and Automation, Atlanta, GA

Title
Mechanical Computation for Passive Force Control

Abstract
Force control implemented by a passive mechanical device (perhaps a wrist) has inherent advantages over active implementations. A passive mechanical device can regain some of the versatility of its active counterpart if it incorporates mechanical elements with programmable parameters, e.g. damping coefficients or spring stiffnesses. We wish to characterize the range of accommodation matrices that a passive device may be programmed to possess..

Source: Proceedings of the IEEE 1993 International Conference on Robotics and Automation, Atlanta, GA