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

Abstract

This article presents a systematic and fully general modelbased 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 concepts 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 representations 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 corresponding 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.

Classification and Kinematic Equivalents of Contact Types for Fingertip-Based Robot Hand Manipulation

“…The introduced contact model is based on an extension of the Bruyninckx-Hunt approach of surfacesurface contact [10,11]. Thanks to such extension, a general classification of non-frictional and frictional contact types suitable for both robot hand manipulation analyses and robot hand design is proposed.…”

“…Independently from Hunt's work and in the context of compliant robot motion, Bruyninckx et al [11] proposed a kinematic-chain-based model of point contact that logically resolves all the weaknesses of the Hunt's approach; it can be indeed seen as an extension of such perspective. The Bruyninckx's model, which we call the generalized kinematicchain-based model of point contact, or the Bruyninckx-Hunt model, consists of five serially-connected passive revolute joints whose location and direction are unequivocal.…”

“…The instantaneous kinematics analysis of the introduced contact types should follow straightforwardly from the methods presented in [11,18,19], but this is certainly an aspect that deserves further research.…”

Operating High-DoF Articulated Robots Using Virtual Links and Joints

“…They treated only smaller examples which could be solved analytically on paper. Bruyninckx [4] also showed an example where a virtual closed chain minimizes the otherwise unconstrained twist motion about the axis of a round tool on a revolute-jointed industrial manipulator.…”

Multi-Link Multi-Contact Force Control for Manipulators

“…This kinematic model is more general than the Raibert-Craig model [9] which provides only an orthogonal decomposition of the operational space. It is noted that other work has also been done which presents a general kinematic contact model [1] [6] [10].…”