Free-body-diagram method for the uniqueness analysis of reactions and driving forces in redundantly constrained multibody systems with nonholonomic constraints

Abstract

Overconstrained and overactuated multibody systems are problematic in modeling. Under the rigid body assumption, redundantly constrained systems have, in general, nonunique reactions. However, despite this fact, some of the reactions may be unique. A similar problem pertains to driving forces. There are methods that may be used to check the uniqueness. One of them is the free-body-diagram-based approach considered in this paper. The former formulations of this method are unified and extended to the case of systems with affine nonholonomic constraints. Moreover, the previously proposed methods are partially reformulated to obtain a unified description. Four numerical approaches are considered—three based on the direct sum (namely, rank comparison, SVD and QR methods) and the nullspace approach. The numerical efficiency of these four methods is estimated and compared. In order to illustrate the reaction uniqueness analysis, a mobile platform with a trailer is examined in three actuation cases (non-actuated, fully actuated and overactuated). The obtained results are summarized and a brief guidance for exploiting the outcomes of the uniqueness analysis is provided.