Ball on a beam: stabilization under saturated input control with large basin of attraction

This article is devoted to the stabilization of two underactuated planar systems, the well-known straight beam-and-ball system and an original circular beam-and-ball system. The feedback control for each system is designed, using the Jordan form of its model, linearized near the unstable equilibrium. The limits on the voltage, fed to the motor, are taken into account explicitly. The straight beam-and-ball system has one unstable mode in the motion near the equilibrium point. The proposed control law ensures that the basin of attraction coincides with the controllability domain. The circular beam-and-ball system has two unstable modes near the equilibrium point. Therefore, this device, never considered in the past, is much more difficult to control than the straight beam-and-ball system. The main contribution is to propose a simple new control law, which ensures by adjusting its gain parameters that the basin of attraction arbitrarily can approach the controllability domain for the linear case. For both nonlinear systems, simulation results are presented to illustrate the efficiency of the designed nonlinear control laws and to determine the basin of attraction

An original walking composed of a ballistic single-support and a finite time double-support phases

International audienceThe paper aim is to define an original walking for a 2D biped with a trunk, two identical legs with knees and massless feet. This walking is composed of a ballistic single-support phase and a distributed in time double-support phase. The ballistic movement in single support is defined by solving a boundary value problem with initial and final biped configurations and velocity conditions. These conditions ensure that at the beginning of the single support the toe of the rear leg rises without touching the ground again and at the landing of the heel there is no impact. In the double-support phase, the orientation of the two feet and other generalized coordinates which are used to define the configuration of the biped, are chosen as Bezier functions of time. The torques and ground reaction forces resulting from this double-support phase are determined by solving for the biped the inverse dynamic problem. Statement of the problem The walking motion We design biped periodic walking, which consist of distributed in time single-and double-support phases. Ballistic single-support motion is designed. During this motion the torques in all joints are zeroes except the torque in the ankle-joint of the stance leg. The torque in the ankle-joint of the stance leg is applied in order to keep its foot in the equilibrium. During double-support motion the torques are applied in all the six joints; during this time both feet rotate: foot of the rear leg-around its toe, foot of the front leg-around its heel. To explain our statement of the problem more clearly, we show Fig. 1 with several stick-figures, which results from our numerical investigations. a) b) c) d) e

Control Algorithms of the Longitude Motion of the Powered Paraglider

International audienceThe design of remotely controlled and autonomous Unmanned Aerial Vehicles (\emph{UAVs}) is an actual direction in modern aircraft development. A promising aircraft of this type is a powered paraglider (\emph{PPG}). In this paper, a new mathematical model is suggested for the paraglider's longitudinal motion aimed at the study of \emph{PPG} dynamics and the synthesis of its automatic control. \emph{PPG} under consideration is composed of a wing (canopy) and a load (gondola) with propelling unit. The \emph{PPG} mechanical model is constructed as the system of two rigid bodies connected by an elastic joint with four degrees of freedom that executes a 2D motion in a vertical plane. The details of \emph{PPG}'s motion characteristics including steady-states regimes and its stability have been studied. A nonlinear control law, based on the partial feedback linearization, has been designed for the thrust of \emph{PPG}. Simulation results are analyzed. Simulation tests show that the internal dynamics are stable near the steady-state flight regime

Study and choice of actuation for a walking assist device

International audienceA walking assist device (WAD) with bodyweight support reduces energy expenditure of a walking person. However, it is also important that the location of actuators in the WAD will be optimally chosen. For this purpose a wearable assist device composed of a bodyweight support, legs and shoes articulated with hip (upper joint), knee (middle joint), and ankle (lower joint) is discussed. Since human walk involves large displacements only in sagittal plane, a planar model is considered. In order to evaluate the optimal distribution of input torques, a bipedal model of a seven-link system with several walking velocities is coupled with the mentioned WAD. To study the efficiency of the WAD and to choose an appropriate actuation, the torque cost is evaluated when the same walking pattern are tracked with and without a WAD. The paper deals with the torque cost for the human and the WAD with several types of actuation. It is shown that full actuation with six motors or partial actuation with two motors located at the upper joints are two more efficient solutions while an actuation at the middle joints or lower joints only is ineffective. The numerical simulations carried out for several walking velocities confirm the mentioned observations

La citadelle de Brouage et la dynamique paléoenvironnementale du marais charentais: l’apport de la malacologie et palynologie

International audienceL'ancien port de Brouage est situé face à l'île d'Oléron, aujourd'hui en plein marais, à quelques kilomètres de la mer. Si le chenal est aujourd'hui inaccessible à tout bateau de fort tonnage, cela n'a pas été le cas à l'époque moderne. La fouille de la maison Champlain, initiée dès 2003 par K. Robin (Conseil Général de la Charente-Maritime) et reprise depuis par A. Champagne, a donc la particularité de se situer dans un milieu humide dont la géomorphologie et la dynamique sédimentaire ont considérablement fluctué. La compréhension de ces évolutions est au cœur de nos préoccupations au niveau à la fois de l'implantation de cette citadelle en zone littorale mais aussi de la gestion des ressources alimentaires et matériaux de construction. La prospection géophysique entreprise en 2010 par V. Mathé, a été confrontée à des données géotechniques anciennes (Mathé 2010). Elle a précisé l'hypothèse d'une ville établie sur un banc de sable, reposant sur du bri, et non sur un banc de galets de lest. Les différentes phases de terrain avaient permis de reconnaître ces sables sur lesquels les diverses structures anthropiques s'installent

3D Walking Biped: Optimal Swing of the Arms

International audienceA ballistic walking gait is designed for a 3D biped with two identical two-link legs, a torso, and two identical one-link arms. In the single support phase, the biped moves due to the existence of a momentum, produced mechanically, without applying active torques in the inter-link joints. This biped is controlled with impulsive torques at the instantaneous double support to obtain a cyclic gait. The impulsive torques are applied in the seven inter-link joints. Then an infinity of solutions exists to find the impulsive torques. An effort cost functional of these impulsive torques is minimized to determine a unique solution. Numerical results show that for a given time period and a given length of the walking gait step, there is an optimal swinging amplitude of the arms. For this optimal motion of the arms, the cost functional is minimum

Finite Time Stabilization of a Double Integrator - Part I: Continuous Sliding Mode-based Position Feedback Synthesis

International audienceThe twisting and supertwisting algorithms, generating important classes of second order sliding modes (SOSM's), are well-recognized for their finite time stability and robustness properties. In the present paper, a continuous modification of the twisting algorithm and an inhomogeneous perturbation of the supertwisting algorithm are introduced to extend the class of SOSM's that present the aforementioned attractive features. Thus modified, the twisting and supertwisting algorithms are utilized in the state feedback synthesis and, respectively, velocity observer design, made for the finite time stabilization of a double integrator if only position measurements are available. Performance and robustness issues of the resulting output feedback synthesis are illustrated by means of numerical simulations

La citadelle de Brouage et la dynamique paléoenvironnementale du marais charentais: l’apport de la malacologie et palynologie

International audienceL'ancien port de Brouage est situé face à l'île d'Oléron, aujourd'hui en plein marais, à quelques kilomètres de la mer. Si le chenal est aujourd'hui inaccessible à tout bateau de fort tonnage, cela n'a pas été le cas à l'époque moderne. La fouille de la maison Champlain, initiée dès 2003 par K. Robin (Conseil Général de la Charente-Maritime) et reprise depuis par A. Champagne, a donc la particularité de se situer dans un milieu humide dont la géomorphologie et la dynamique sédimentaire ont considérablement fluctué. La compréhension de ces évolutions est au cœur de nos préoccupations au niveau à la fois de l'implantation de cette citadelle en zone littorale mais aussi de la gestion des ressources alimentaires et matériaux de construction. La prospection géophysique entreprise en 2010 par V. Mathé, a été confrontée à des données géotechniques anciennes (Mathé 2010). Elle a précisé l'hypothèse d'une ville établie sur un banc de sable, reposant sur du bri, et non sur un banc de galets de lest. Les différentes phases de terrain avaient permis de reconnaître ces sables sur lesquels les diverses structures anthropiques s'installent