Outer flatness: trajectory generation for a model helicopter

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Michiel van Nieuwstadt and Richard M. Murray
1997 European Control Conference

This paper introduces the concept of outer flatness, a derivative of differential flatness. Outer flatness describes a system that can be split in 2 subsytems, a non-flat inner system and a flat outer system. The outputs of the outer system are the tracking outputs of interest. The inputs of the outer system are the outputs of the inner system, and not subject to our direct control. The inputs of the inner system are the real actuator inputs. This system structure is also present in backstepping and dynamic inversion. We present two theorems on exponential and bounded tracking for outer flat systems, based on Lyapunoff arguments. We validate the approach with simulations and experiments on a model helicopter.