Gap-singular systems: definition and consequences in trajectory planning

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

Induction d'une ovulation post-partum chez la vache creole a l'aide d'une separation temporaire du veau et de l'utilisation prealable d'un implant de Norgestomet

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Optimal trajectory tracking for differentially flat systems with singularities

The purpose of this paper is twofold: on one hand to analyse some properties of a class of differentially flat systems having particular singularities, and, on the other hand, to propose an adaptation of existing online optimal control strategies like NTG in order to take into account those singularities as well as constraints like bounds on the inputs.The system we are interested in is a mobile robot with several steering wheels, but we will present the main ideas for a simpler system called "symmetric crane" which has similar structural properties. The optimal control problem considered is to minimize an error w.r.t. a reference traject

Stability analysis of a vision-based control design for an autonomous mobile robot

We propose a simple control design allowing,a mobile robot equipped with a camera to track a line on the ground. The control algorithm, as well as the image-processing algorithm, are very simple. We discuss the existence and the practical stability of an equilibrium trajectory of the robot when tracking a circular reference line. We then give a complementary analysis for arbitrary reference lines with bounded curvature. Experimental results confirm the theoretical analysis