73 Cupyright © 1996 IFAC 13th Triennial Wurld Congress. San Franciscu. USA VIBRATION DAMPING IN FLEXmLE FINGERS OF AN UNDERWATER ROBOT HAND VIA SLIDING MODES G. Bartolini*, W. Capnto*, M. Cecchi*, A. Ferrara*, L. Fridman+ *Department of Communication. Computer and System of Genova Via Opera Pia 13 16145 Genova -lrALY rel.- +39/0 3532207 - Fax.' +39 103532948 E-mail: jerrara@dist.unige.it + School of Mathematical Sciences - TeI Aviv University Ramat-Aviv 69978 rei Aviv - ISRAEL rel.- 972-3-6408031 - Fax .' 972-3-6409357 E-mail.' shustin@math.tau.ac.il Abstract. The aim of the present paper is to formulate a simple model of a flexible robotic structure and to propose a class of control strategies based on the sliding mode concept. In the first part, a simplified model of a finger of an unconventional gripper is presented. In the second part the problem of suppressing vibrations in flexible structures by means of the sliding mode technique is considered. Then an adaptive control strategy allowing to damp oscillations also in presence of delay is proposed, Simulation examples are provided to complement the theoretical discussion. Keywords. Discontinuous control, Vibration dampers, Sliding mode, Delay analysis, Robot control. Ib-03 2 I. INTRODUCTION! The work presented in this paper is relevant to the project AMADEUS (Advanced MAnipulator for DEep Underwater Sampling, EEC MAST program) whose goal is that of achieving good underwater sampling capabilities by using advanced grippers with flexible fingers. For the mechanical realization of the fingers of the AMADEUS gripper the so-called "elephant's trunk" technology (Davies, 1994), which appears to be particularly suitable for operating underwater, has been adopted. This technology allows the motion of the fingers (or tentacles, for very wide structures) without requiring the presence of rotative or prismatic joints. The aim of this paper is to define a model for the flexible finger of the AMADEUS gripper and design a control strategy for damping its vibrations around the equilibrium configurations. More precisely, a lumped parameters formulation of the model will be presented. This model relies on the assumption that the whole mass of the system is concentrated at the free cnd of the finger. Moreover, linear relationships for elasticity have been adopted. [Work supported by Project MAST AMADEUS under contract "MAS2- funded by the European Community. In the second part of the paper, the problem of suppressing vibrations in flexible structures, and in particular in the robotic element considered, by means of sliding mode control will be dealt with. Sliding mode control gives rise