Sensitivity analysis and optimization of the dynamics of multibody systems using analytical gradient based methods

Abstract

Sensitivity analysis of the dynamics of multibody systems is an extraordinarily useful tool for the design optimization and optimal control problems. In this tesis document, the sensitivity analysis of joint-coordinate formulations is studied using purely analytical differentiation methods. The recursive foundations of joint coordinate modeling are reviewed and extended to support the definition of recursive kinematic relations and accumulation schemes with an arbitrary selection of reference points. Two different solutions of the equations of motion of unconstrained open-loop systems are developed, leading to a semi-recursive and a fully-recursive approach. Moreover, the dynamics of constrained multibody systems is described using Matrix R and ALI3-P formulations combined with semi-recursive methods. The main contribution of this thesis consists on the analytical development of each derivative required in the sensitivity analysis of joint-coordinate formulations. As a result, two sensitivity analyses for unconstrained open-loop systems and six sensitivity formulations for constrained systems are achieved. All dynamic and sensitivity formulations have been implemented in the multibody library MBSLIM as general formulations.