Computational Reference Dynamical Model of a Multibody System With First Order Constraints

The paper presents a development of a computational based procedure for generation of constrained system dynamical models. The constraints may be both holonomic and first order nonholonomic, either material or nonmaterial. The latter ones are referred to as programmed and they are imposed by a designer, a control engineer as a control goal, or may come from controlled system performance requirements. The procedure for generation of constrained dynamics provides then reference dynamical models, i.e. models whose solutions satisfy all the constraints put upon them. These models may serve as motion planners for control. The distinctions between the presented approach and the ones reported in the literature are that the constraints may be material or nonmaterial and the final equations of motion are derived in the reduced state form, i.e. constraint reaction forces are eliminated at the equations derivation level but not afterwards as in the case of the Lagrange approach. This is the essential advantage of our approach and this one computational procedure may serve both reference and control oriented dynamical models derivation. The procedure is applied to a manipulator model whose end effector is subjected to a programmed constrained.