Recent advances in multi-body dynamics and nonlinear control

Abstract

This paper presents some recent advances in the dynamics and control of constrained multi-body systems. The constraints considered need not satisfy D'Alembert's principle and therefore the results are of general applicability. They show that in the presence of constraints, the constraint force acting on the multi-body system can always be viewed as made up of the sum of two components whose explicit form is provided. The first of these components consists of the constraint force that would have existed were all the constraints ideal; the second is caused by the non-ideal nature of the constraints, and though it needs specification by the mechanician who is modeling the specific system at hand, it nonetheless has a specific form. The general equations of motion obtained herein provide new insights into the simplicity with which Nature seems to operate. They are shown to provide new and exact methods for the tracking control of highly nonlinear mechanical and structural systems without recourse to the usual and approximate methods of linearization that are commonly in use

A contribution on modeling methodologies for multibody systems.

“…The same happens when the methodology described in Sections 4.1 and 4.2 is applied. In these cases, adopting a correct interpretation of the Principle of Relaxation of Constraints, active forces due to control inputs can be interpreted as constraint forces and vice versa, once their primary function is to enforce the system to follow an specific trajectory in the state space, constraining the the system to it (UDWADIA, 2006). Such an analogy allows the development of an approach, based on Theorem 4.3, that leads to expressions to compute some of the constraint forces acting in a multibody system when convenient.…”