Optimal control tuning of a redundant robot

International audienceA robot can generally be described by a vector first-order differential equation, named state equations. A robot is said to be redundant if it has more actuators than necessary. In this case, the number of inputs is higher than the number of outputs (variables to be controlled) and there exists many different ways to achieve the control requirements. We can thus take advantage of the extra number of freedom degrees in order to optimize some performance criterion (involving energy, security, longevity or speed). The resulting problem can be formalized into an parametric optimization problem with equality constraints where the free variables (or the parameters) of the optimization problem correspond to the outputs. Due the non-convexity of the optimization problem, the paper proposes to use an interval approach for the resolution. The approach is illustrated on the optimal sail tuning of a sailboat robot

Consistency techniques for the localization of a satellite

International audienceThis paper recalls that the problem of estimating the state vector of a nonlinear dynamic system can be interpreted as a constraint satisfaction problem over continuous domains with a large number (several thousands) of variables and constraints. Consistency techniques are then shown to be particularly efficient to contract the domains for the variables involved. This is probably due to the large number of redundancies naturally involved in the constraints of the problem. The approach is illustrated on the estimation of the position of a satellite in orbit around the earth

Nonlinear bounded-error state estimation of continuous-time systems

International audienceThis paper presents a first study on the application of interval analysis and consistency techniques to state estimation of continuous-time systems described by nonlinear ordinary differential equations. The approach is presented in a bounded-error context and the resulting methodology is illustrated on an example

Solving set-valued constraint satisfaction problems

WOSInternational audienceIn this paper, we consider the resolution of constraint satisfaction problems in the case where the variables of the problem are subsets of Rn. In order to use a constraint propagation approach, we introduce set intervals (named i-sets), which are sets of subsets of Rn with a lower bound and an upper bound with respect to the inclusion. Then, we propose basic operations for i-sets. This makes possible to build contractors that are then used by the propagation to solve problem involving sets as unknown variables. In order to illustrate the principle and the efficiency of the approach, a testcase is provided

Estimation d'état de systèmes non-linéaires à temps continus par une approche ensembliste

Cet article illustre l'utilisation de l'analyse par intervalles et des méthodes de propagation de contraintes pour l'estimation de systèmes à temps continu décrit par des équations différentielles ordinaires. Cette approche est présentée dans un contexte ensembliste, c'est-à-dire que les incertitudes sur les quantités manipulés sont représentées par un ensemble et non plus par une loi de propabilité

Inertial control of a spinning flat disk

This paper proposes a Lyapunov based approach to control the rotation of a flat disk spinning in the space without external forces. The motion of the disk is governed by the Euler's rotation equation for spinning objects. The control is made through the inertia matrix of the disk.Comment: 14 pages, 6 figure

Modelisation of a rolling disk with Sympy

This paper proposes a Lagrangian approach to find the state equations of a disk rolling on a plane without friction. The approach takes advantage of a symbolic computation to simplify the reasoning.Comment: 10 pages, 4 figure

Asymptotically minimal contractors based on the centered form;Application to the stability analysis of linear systems

This paper proposes a new interval-based contractor for nonlinear equations which is minimal when dealing with narrow boxes. The method is based on the centered form classically used by interval algorithms combined with a Gauss Jordan band diagonalization preconditioning. As an illustration in stability analysis, we propose to compute the set of all parameters of a characteristic function of a linear dynamical system which have at least one zero in the imaginary axis. Our approach is able compute a guaranteed and accurate enclosure of the solution set faster than existing approaches.Comment: 19 page

A Priori Error Analysis and Spring Arithmetic

WOSInternational audienceError analysis is defined by the following concern: bounding the output variation of a (nonlinear) function with respect to a given variation of the input variables. This paper investigates this issue in the framework of interval analysis. The classical way of analyzing the error is to linearize the function around the point corresponding to the actual input, but this method is local and not reliable. Both drawbacks can be easily circumvented by a combined use of interval arithmetic and domain splitting. However, because of the underlying linearization, a standard interval algorithm leads to a pessimistic bound, and even simply fails (i.e., returns an infinite error) in case of singularity. We propose an original nonlinear approach where intervals are used in a more sophisticated way through the so-called "springs". This new structure allows to represent an (infinite) set of intervals constrained by their midpoints and their radius. The output error is then calculated with a spring arithmetic in the same way as the image of a function is calculated with interval arithmetic. Our method is illustrated on two examples, including an application of geopositioning