Kinematic Models for Model-Based Compliant Motion in the Presence of Uncertainty

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Abstract
This article presents a systematic and fully general model- based approach to compliant robot motion, taking into account uncertainties in the geometry of the manipulated object and the environment with which it is in contact. The emphasis is not on control but on modeling, instantaneous motion specification, and on-line uncertainty identification. The presented models are intuitive and yet sufficiently flexible to deal with multiple and time-varying motion constraints between nonpolyhedral objects. The description of the interaction between the manipulated object and its environment starts from first- and second-order approximations of the objects' geometry at the contact points. From these geometric descriptions, the manipulated object's motion freedom—and its dual, the set of possible reaction forces—is modeled up to second order (i.e., accelerations) using the similarity with the kinematics of manipulators. Geometric uncertainties of the manipulated object and the environment, also up to second order (i.e., curvature), are integrated into these kinematic models. The on-line identification of uncertainties is based on the measured motion and/or the reaction forces. Two basic con cepts underlie the identification approach: consistency and reciprocity. These concepts give rise to linear identification equations in the uncertainty parameters by applying them to the first-order series expansions of the mathematical representa tions of the motion constraints. Both approaches are shown to be equivalent. The theoretical developments are illustrated by real-world experiments: the motion specification of a complex three-point contact situation between a cylindrical peg and the corre sponding chamferless hole; and force-controlled 2D contour tracking of an unknown object, with recursive identification of the curvature. Redundancy resolution and robot calibration are suggested as other potential applications.

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