Gap-singular systems: definition and consequences in trajectory planning†

Abstract

This article introduces the concept of gap-singularities to underline particular phenomena related to the choice of the outputs in some non-linear systems. It is shown that, when bounds on the variables are considered, this property induces a topological isolation of the gap-singular trajectories in the outputs domain. In the context of differentially flat systems, a procedure to detect gap-singularities is provided because it is related to the existence of a singularity of flatness. The examples that are presented in this article show that taking gap-singularities into account can improve some trajectory planning algorithms based on an optimal control approach like in the Nonlinear Trajectory Generation software. †This article presents research results of the Belgian Programme on Interuniversity Attraction Poles, initiated by the Belgian Federal Science Policy Office. The scientific responsibility rests with its authors.