Submitted, 1997 European Control Conference Trajectory tracking for fully actuated mechanic.pdf

Submitted, 1997 European Control Conference Trajectory tracking for fully actuated mechanical systemsFrancesco Bullo and Richard M. MurrayyControl and Dynamical SystemsCalifornia Institute of TechnologyPasadena, CA 91125bullo@September 1, 1996AbstractThis paper presents a general framework for thecontrol of mechanical systems with as many inputsas degrees of freedom. The notions of error func-tion and transport map are introduced to properlydene a conguration and a velocity error. Theseare the crucial ingredients in designing a propor-tional derivative feedback and feedforward control.The proposed approach includes various results oncontrol of manipulators, autonomous vehicles andpointing devices.Keywords: mechanical systems, nonlinear control1. IntroductionThis work is a contribution in the area of nonlin-ear control theory for mechanical systems (Murray1995) and it is the completion of our previousworks (Bullo and Murray 1995) and (Bullo, Mur-ray and Sarti 1995). Given a fully actuated controlsystem, that is a system with as many inputs as de-grees of freedom, our control objective is to track atrajectory with exponential convergence rates andto guarantee performance and robustness.Exponential tracking for a robotic manipulatorwas achieved in the late 1980s using a Lyapunovtechnique, see (Wen and Bayard 1988) for example,and is now standard in textbooks (Murray, Li andSastry 1994). Since then, similar techniques havebeen applied to other elds in robotics, like posi-tion and attitude stabilization for satellites (Wenand Kreutz-Delgado 1991) and autonomous under-water vehicles (Fjellstad and Fossen 1994). Ad-ditionally, global stability issues were addressedby Koditschek (1989).Here we consider general mechanical systemsdened on Riemannian manifolds and extendKoditscheks approach to the exponential trackingResearch supported in part by the National ScienceFoundation under Grant CMS-9502224.yResearch supported in part by the National ScienceFoundation under Gra