LAUSR

A recently developed index reduction method is applied to comparatively complicated underactuated mechanical systems in the context of inverse dynamics. The inverse dynamics formulation is carried out by employing servo constraints in which the outputs (specified in time) are expressed by state variables. The dynamic equations are governed by differential-algebraic equations (DAEs) with high index. If redundant coordinates are used to formulate servo-constraint problems, the algebraic equations in the DAEs contain both servo and holonomic constraints. It is highly challenging to solve the DAEs with high index. Hence index reduction approaches are required. Index reduction by minimal extension facilitates the desired index reduction and thus makes possible the stable numerical integration of the index-reduced DAEs. In this paper we apply the advocated method to a very general and versatile formulation of comparatively complicated crane systems. In contrast to other schemes previously developed for underactuated systems subject to servo constraints, the present approach makes feasible numerically solving the challenging inverse dynamics problems presented herein.