Cable-Driven Robots with Wireless Control Capability for Pedagogical Illustration in Science

Science teaching in secondary schools is often abstract for students. Even if some experiments can be conducted in classrooms, mainly for chemistry or some physics fields, mathematics is not an experimental science. Teachers have to convince students that theorems have practical implications. We present teachers an original and easy-to-use pedagogical tool: a cable-driven robot with a Web-based remote control interface. The robot implements several scientific concepts such as 3D-geometry and kinematics. The remote control enables the teacher to move freely in the classroom.Comment: CAR - 8th National Conference on "Control Architecure of Robots" (2013

Confidence-based contractor, propagation and potential clouds for differential equations

A novel interval contractor based on the confidence assigned to a random variable is proposed in this paper. It makes possible to consider at the same time an interval in which the quantity is guaranteed to be, and a confidence level to reduce the pessimism induced by interval approach. This contractor consists in computing a confidence region. Using different confidence levels, a particular case of potential cloud can be computed. As application, we propose to compute the reachable set of an ordinary differential equation under the form of a set of confidence regions, with respect to confidence levels on initial value

Confidence-based Contractor, Propagation and Potential Cloud for Differential Equations

International audienc

Validated trajectory tracking using flatness

The problem of a safe trajectory tracking is addressed in this paper. It consists in using the results of a validated path planner providing a set of safe trajectories to produce the set of controls to apply to remain inside this set of planned trajectories while avoiding static obstacles. This computation is performed using the differential flatness of many dynamical systems. The method is illustrated in the case of the Dubins car

Tuning PI controller in non-linear uncertain closed-loop systems with interval analysis

The tuning of a PI controller is usually done through simulation, except for few classes of problems, e.g., linear systems. With a new approach for validated integration allowing us to simulate dynamical systems with uncertain parameters, we are able to design guaranteed PI controllers. In practical, we propose a new method to identify the parameters of a PI controller for non-linear plants with bounded uncertain parameters using tools from interval analysis and validated simulation. This work relies on interval computation and guaranteed numerical integration of ordinary differential equations based on Runge-Kutta methods. Our method is applied to the well-known cruise-control problem, under a simplified linear version and with the aerodynamic force taken into account leading to a non-linear formulation

Validated Computation of the Local Truncation Error of Runge-Kutta Methods with Automatic Differentiation

International audienceIn this paper, we propose a novel approach to bound the local truncation error based on the order condition which is usable for explicit and implicit Runge-Kutta methods

Interval Methods for Model Qualification: Methodology and Advanced Application

It is often too complex to use, and sometimes impossible to obtain, an actual model in simulation or command field . To handle a system in practice, a simplification of the real model is then necessary. This simplification goes through some hypotheses made on the system or the modeling approach. In this paper, we deal with all models that can be expressed by real-valued variables involved in analytical relations and depending on parameters. We propose a method that qualifies the simplification validity by verifying a quality threshold on the hypothesis relevance. This method, based on interval analysis, can check the acceptance of the hypothesis in a full range of the whole model space, and can give bounds to the quality threshold and to the model parameters.% to keep the simplified model acceptable. Our approach is experimentally validated on a robotic application.Ce document présente une méthode base sur l'analyse par intervalle servant a la vérification d'une hypothèse utilisée dans le cadre d'une simplification de modèle. Une application en robotique est présentée

Optimal switching instants for the control of hybrid systems

The problem of determining the optimal switching instants for the control of hybrid systems under reachability constraints is considered. This optimization problem is cast into an interval global optimization problem with differential constraints, where validated simulation techniques and a dynamic time meshing are used for the computation of its solution. The approach is applied on two examples, one being the well-known example of the Goddard’s problem where a rocket has to reach a given altitude while consuming the smallest amount of fuel, the second one considers a system with an higher dimension and a more complex optimization problem