Constrained Parametric Design of Motion Laws

A new method to design motion laws is proposed, featuring the ability of imposing constraints over sequences of functions, each defined by parameters. User constraints may require, for example, continuity between segments, acceleration or position at given time values, and so on. The optimal value for function parameters is obtained applying a modified Newton-Lagrange process over a constrained optimization problem. The outer Newton loop adopts a linear solver which exploits the sparsity of the coefficient matrix, hence allowing high computational efficiency even in case of many constraints. The resulting method has been implemented into a custom software for multibody simulation, thus providing a powerful yet expandable way to design motion laws for mechatronic devices.