Optimal Design of Multibody Systems Using the Adjoint Method

Optimal design of multibody systems (MBS) is of primary importance to engineers and researchers working in various fields, e.g.: in robotics or in machine design. The goal of this paper is a development and implementation of systematic methods for finding design sensitivities of multibody system dynamics with respect to design parameters in the process of optimization of such systems. The optimal design process may be formulated as finding a set of unknown parameters such that the objective function is minimized under the assumption that design variables may be subjected to a variety of differential and/or algebraic constraints. The solutions of such complex optimal problems are inevitably connected with evaluation of a gradient of the objective function. Herein, a multibody system is described by redundant set of absolute coordinates. The equations of motion for MBS are formulated as a system of differential-algebraic equations (DAEs) that has to be discretized and solved numerically forward in time. The design sensitivity analysis is addressed by using the adjoint method that requires determination and numerical solution of adjoint equations backwards in time. Optimal design of sample planar multibody systems are presented in the paper. The properties of the adjoint method are also investigated in terms of efficiency, accuracy, and problem size.