In this paper we study the tracking control of Lagrangian systems subject to frictionless unilateral constraints. The stability analysis incorporates the hybrid and nonsmooth dynamical feature of the overall system. The difference between tracking control for unconstrained systems and unilaterally constrained ones, is explained in terms of closed-loop desired trajectories and control signals. This work provides details on the conditions of existence of controllers which guarantee stability.It is shown that the design of a suitable transition phase desired trajectory, is a crucial step. Some simulation results provide information on the robustness aspects. Finally the extension towards the case of multiple impacts, is considered.

In this paper we study the tracking control of Lagrangian systems subject to frictionless unilateral constraints. More precisly it concerns a class of specific nonsmooth systems which perform cyclic impacting tasks. The stability analysis incorporates the hybrid and nonsmooth dynamical feature of the overall system. This work provides details on the conditions of existence of a such controller which guarantees an asymptotic strongly stability. Some tests in simulation give some result on the robustness of this controller. And finally it clarifies some concepts related to multiple impacting systems.

Results relevant to path-tracking control for a tractor-2-trailers vehicle with one coupling joint on axle and the other off axle , are developed. In the case of off axle hitchings with a negative offset, these results are based on input/output linearization and extend controllers design procedures already available for vehicles of which the coupling joints are all on axle , or all off axle . In the case of off axle hitchings with a positive offset, exact linearization is no longer applicable and the problem is solved using Jacobian linearization. Convergence and robustness properties of the ensuing controllers are illustrated by means of simulation. Extension of these results to more general tractor-n-trailers vehicles is discussed.

Biped robots have specific dynamical constraints and stability problems which reduce significantly their motion range. In these conditions, motion planning used for mobile robots cannot be applied to biped robots. In this paper, the path planning problem is seen as finding a sequence of footholds in a 3D environment, keeping robot stability, motion continuity and working within the structural constraints of the biped. The designed path planner contains two parts : The first one determines a reference path which maximises success rate in view of biped capabilities. This reference track is computed by the well know A* search in the graphs algorithm. The second part of the path planner is a path tracking algorithm which makes the robot follow the reference track. Simulation results concern the anthropomorphic 15 degrees of freedom robot BIP2000.

In this paper we study the tracking control of Lagrangian systems subject to frictionless unilateral constraints. The stability analysis incorporates the hybrid and nonsmooth dynamical feature of the overall system. The difference between tracking control for unconstrained systems and unilaterally constrained ones, is explained in terms of closed-loop desired trajectories and control signals. This work provides details on the conditions of existence of a controller which guarantees asymptotic stability.

In this poster we study the tracking control of Lagrangian systems subject to frictionless unilateral constraints. The stability analysis incorporates the hybrid and nonsmooth dynamical feature of the overall system. The difference between tracking control for unconstrained systems and unilaterally constrained ones, is explained in terms of closed-loop desired trajectories and control signals. This work provides details on the conditions of existence of controllers which guarantee stability.It is shown that the design of a suitable transition phase desired trajectory, is a crucial step.

In this poster we study the tracking control of Lagrangian systems subject to frictionless unilateral constraints. The stability analysis incorporates the hybrid and nonsmooth dynamical feature of the overall system. The difference between tracking control for unconstrained systems and unilaterally constrained ones, is explained in terms of closed-loop desired trajectories and control signals. This work provides details on the conditions of existence of controllers which guarantee stability.It is shown that the design of a suitable transition phase desired trajectory, is a crucial step.

Dans ce papier nous étudions la poursuite de trajectoire pour des systèmes mécaniques Lagrangiens soumis à des contraintes unilatérales sans frottements. L'analyse de la stabilité de tels systèmes doit prendre en compte le caractère hybride (ou non-régulier) de la dynamique du système complet. Les différences entre la poursuite de trajectoire pour un système non-contraint et un système soumis à une contrainte unilatérale sont expliquées en termes de trajectoires invariantes et de trajectoires désirées. Ces travaux donnent des détails sur les conditions d'existence de loi de commande asymptotiquement stable.

Dans ce papier nous étudions la poursuite de trajectoire pour des systèmes mécaniques Lagrangiens soumis à des contraintes unilatérales sans frottements. L'analyse de la stabilité de tels systèmes doit prendre en compte le caractère hybride (ou non-régulier) de la dynamique du système complet. Les différences entre la poursuite de trajectoire pour un système non-contraint et un système soumis à une contrainte unilatérale sont expliquées en termes de trajectoires invariantes et de trajectoires désirées. Ces travaux donnent des détails sur les conditions d'existence de loi de commande asymptotiquement stable

Les robots bipèdes présentent de par leur structure complexe, une forte instabilité, et des contraintes dynamiques et cinématiques qui restreignent leurs mouvements. Cette étude, en deux parties, porte sur la génération automatique de trajectoires (au niveau articulaire) entre deux postures stables pour un robot bipède. Ceci est fait en adaptant la méthode du gradient projeté au robot bipède. La deuxième partie de l'étude porte sur la planification de chemin en environnement non structuré. La planification est réalisée en faisant le suivi d'un chemin déterminé à l'avance en fonction des données topographiques du terrain. Ces deux études sont appliquées au robot BIP, un robot anthropomorphe comportant 15 articulations actionnées.

In this paper we study the tracking control of Lagrangian systems subject to frictionless unilateral constraints. The stability analysis incorporates the hybrid and nonsmooth dynamical feature of the overall system. The difference between tracking control for unconstrained systems and unilaterally constrained ones, is explained in terms of closed-loop desired trajectories and control signals. This work provides details on the conditions of existence of controllers which guarantee stability. It is shown that the design of a suitable transition phase desired trajectory, is a crucial step. Some simulation results provide information on the convergence of such controller. Finally the extension towards the case of multiple impacts, is considered.

In this paper we study the robustness of tracking controllers for Lagrangian systems subject to frictionless unilateral constraints. The stability analysis incorporates the hybrid and nonsmooth dynamical features of the overall system. This work provides details on the robustness of such controllers with respect to the modelling errors of the dynamic, the uncertainty on the constraint position, and with respect to the measurement noise.