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

Abstract

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.

Dynamics modeling method dedicated to system models with open- and closed-loop structures subjected to kinematic and task based constraints

“…Among them, there are special methods dedicated to constrained systems in both analytical and computational approaches. As reported in [11], constrained system dynamical models constitute a significant class of models essential to engineering applications. They are used so videly, e.g.…”

Dynamics Modeling Method Dedicated to System Models with Open- and Closed-loop Structures Subjected to Kinematic and Task Based Constraints

“…Among them, there are special methods dedicated to constrained systems in both analytical and computational approaches. As reported in [12], constrained system dynamical models constitute a significant class of models essential to engineering applications. They are used in so many applications, e.g.…”

“…[34 -38]. For systems subjected to such constraints the preliminary results for obtaining the computationally efficient dynamical models were presented in [12,39,40]. There, constraints of this kind, referred to as programmed, at the position level, were incorporated into a rigid-flexible system dynamics for open loop structures.…”

Comparison of Kane’s and Lagrange’s Methods in Analysis of Constrained Dynamical Systems

“…10 A large number of research studies were conducted to improve the Lagrange's method such as a representation of a matrix form of the Lagrangian equations for constrained systems 11 and introducing a novel approach to derive the motion equations of nonholonomic constrained systems by the elimination of the constraint reaction forces. 12 However, this method has a few drawbacks, including constraint violation and computational error accumulation. These are the result of applying constraint equations in acceleration form and a large number of differential equations in the solving process.…”