Guaranteed computation of robot trajectories

Calcul garanti de trajectoires de robots

Simon Rohou (1, 2) , Luc Jaulin (1, 2) , Lyudmila Mihaylova (3) , Fabrice Le Bars (1, 2) , Sandor M Veres (3)

1 Lab-STICC_ENSTAB_CID_PRASYS
2 Pôle STIC_OSM
3 University of Sheffield [Sheffield]

This paper proposes a new method for guaranteed integration of state equations. Within this framework, the variables of interest are trajectories submitted to both arithmetic and differential equations. The approach consists in formalizing a problem thanks to a constraint network and then apply these constraints to sets of trajectories. The contribution of the paper is to provide a reliable framework to enclose the solutions of these differential equations. Its use is shown to be simple, more general and more competitive than existing approaches dealing with guaranteed integration, especially when applied to mobile robotics. The flexibility of the developed framework allows to deal with non-linear differential equations or even differential inclusions built from datasets, while considering observations of the states of interest. An illustration of this method is given over several examples with mobile robots.

Mots clés: guaranteed integration; tube programming; mobile robotics; constraints; contractors; ODE

Domaines: Robotique [cs.RO]; Systèmes dynamiques [math.DS]; Analyse numérique [math.NA]; Automatique / Robotique; Intelligence artificielle [cs.AI]

Simon Rohou, Luc Jaulin, Lyudmila Mihaylova, Fabrice Le Bars, Sandor M Veres. Guaranteed computation of robot trajectories. Robotics and Autonomous Systems, 2017, 93, pp.76 - 84. ⟨10.1016/j.robot.2017.03.020⟩. ⟨hal-01516228⟩