Computation of bounded feed‐forward control for underactuated multibody systems using nonlinear optimization

Abstract

AbstractUnderactuation occurs, when only some generalized coordinates have a control input. For end‐effector trajectory tracking a combined feed‐forward and feedback control is often a suitable approach. Feed‐forward control design based on an inverse model for underactuated multibody systems is presented. The starting point is the transformation of the multibody system into a nonlinear input‐output normal‐form. The inverse model follows from this and consists of chains of differentiators, driven internal dynamics and an algebraic part. Especially when using the end‐effector as system output the internal dynamics is often unbounded. In order to obtain a viable feed‐forward control, a bounded solution must be determined. For this task the internal dynamics is solved as a nonlinear optimization problem. Thereby, the coordinates of the internal dynamics define the objective function which is minimized. The equation of the internal dynamics must be fulfilled at each point of a discrete time grid. In addition continuity of the solution is achieved by adding as equality constraint an integration formula, e.g. trapezoidal rule. The optimization problem is then solved by a SQP‐method. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)