Program

8h45-9h00 Présentation de la journée

9h00-9h45 Mehdi Benallegue (Chercheur à l’AIST, Japon)

Title: About theoretical guarantees for controlling dynamic motions of legged and complex robots

Abstract: The control of complex systems has been resorting for a long time to open-loop motion generation coupled to high-gain simple feedback loops. This scheme offered efficient implementation and robustness to small perturbations. However, when dealing with dynamic motions or in the case of underactuated robots, this solution meets easily the limits of its application domain. While these issues triggered an important trend of model-free machine-learning-based motion control, there was a symmetric movement towards more theoretically grounded solutions. In this talk, I will present my recent works to provide theoretical guarantees of stability, feasibility, and convergence to the generation and control of dynamic motions for these systems. In particular, three examples will be developed: the state estimation for humanoids, the generation of motor torques, and the production of joint angle trajectories.

9h45-10h30 Frédéric Jean (Directeur de l'Unité de Mathématiques Appliquées à l’ENSTA)

Titre: Periodical body's deformations are optimal strategies for locomotion

Résumé: A periodical cycle of body's deformation is a common strategy for
locomotion (see for instance birds, shes, humans). The aim of this talk
is to establish that the auto-propulsion of deformable object is
optimally achieved using periodic strategies of body's deformations.
This property is proved for a simple model using optimal control theory
framework.

10h30-10h45 Pause Café

10h45-11h30 Emmanuel Trélat (Directeur du Laboratoire Jacques-Louis Lions)

Titre: La propriété de turnpike.

Résumé: La propriété de turnpike a été découverte dans les années 50 par le prix Nobel Samuelson en économétrie. Elle stipule que la trajectoire optimale d'un problème de contrôle optimal en temps long reste essentiellement proche d'un état stationnaire, lui-même solution d'un problème de contrôle optimal statique associé.

Nous avons établi la propriété de turnpike dans un cadre très général en contrôle optimal non linéaire en dimension finie et infinie, montrant que la trajectoire optimale est, à part au début et à la fin de l'intervalle de temps, exponentiellement proche d'un état stationnaire (optimal), et que cette propriété est également vraie pour le contrôle et pour le vecteur adjoint obtenus par le principe du maximum de Pontryagin. Nous montrons que la propriété de turnpike exponentiel est due à un phénomène d'hyperbolicité qui est intrinsèque au caractère symplectique des équations extrémales. Nous en déduisons une méthode simple et efficace pour le calcul numérique des trajectoires optimales dans ce cadre, notamment une variante appropriée de la méthode de tir. Cela peut s'avérer utile dans les problèmes de motion planning.

La propriété de turnpike s'avère être universelle et l'ensemble de turnpike peut être plus général qu'un simple état stationnaire, comme par exemple une trajectoire périodique. Nous montrons aussi la propriété de turnpike de forme pour des modèles EDP dans lesquels un sous-domaine évolue en temps selon un critère d'optimisation.

Ces travaux sont en collaboration avec Gontran Lance, Can Zhang et Enrique Zuazua.

11h30-12h15 Bastien Berret (PR, Université Paris Saclay)

Titre: Stochastic optimal open-loop control as a theory of human movement planning

Résumé: Understanding human movement is an important issue in neuroscience and for applications such as restoration/prevention of motor deficits in patients/workers using robots. Optimal control has emerged as a leading theory to achieve such an understanding in computational terms. While optimal control theory has yielded valuable insights regarding the principles that may guide motor planning and execution in humans, two key features of limb movements were not well predicted by existing models without using ad hoc fixes: muscle co-contraction and movement vigor. Co-contraction refers to the simultaneous contraction of opposing muscles, a strategy for purposely modulating the mechanical impedance of a limb (e.g., joint stiffness). Vigor refers to the speed of movement that an individual chooses to perform an action (e.g., movement duration). In this talk, I will present recent results in the context of arm reaching movements regarding the possible origin of co-contraction and vigor from the optimal control viewpoint. I will show that if one primary goal of motor planning is to issue an optimal open-loop motor command considering the stochasticity of the nonlinear system under control, co-contraction and vigor can be explained from a common principle: the minimization of a trade-off between effort and variance. This open-loop command can be complemented by a high-level feedback command that will correct task-relevant errors using online sensory information. The proposed framework highlights the potential role of open-loop control in well-learned behaviors and extends the standard optimal feedback control theory of voluntary motor control.

12h30-14h00 Buffet Déjeuner

14h00-14h45 Bachir El Khadir (Goldstine Fellow at IBM Research, NY)

Titre: Piecewise-linear approximate optimal solutions to "calculus of variations" via moment-sos formulations

Abstract: We propose a novel method for planning shortest length piecewise-linear motions through complex environments punctured with static, moving, or even morphing obstacles. Using a moment optimization approach, we formulate a hierarchy of semidefinite programs that yield increasingly refined lower bounds converging monotonically to the optimal path length. For computational tractability, our global moment optimization approach motivates an iterative motion planner that outperforms competing sampling-based and nonlinear optimization baselines. Our method natively handles continuous time constraints without any need for time discretization, and has the potential to scale better with dimensions compared to popular sampling-based methods.. Ces travaux sont en collaboration avec JB Lasserre et Vikas Sindhwani

14h45-15h30 Francis Bach (INRIA, Académie des sciences)

Titre: Sommes de carrés en dimension infinie pour l’optimisation et le contrôle.

15h30-15h45 Pause Café

15h45-16h30 Justin Carpentier (Chercheur INRIA, Paris)

Title: Robotics: Recent Progress for online Optimal Control of Nonsmooth Dynamical Systems in Robotics.

Abstract: Optimal Control is an essential and powerful framework for generating complex motions on robots. In this talk, I will cover recent contributions for efficient and numerically robust resolution of constrained optimal control which are common in robotics. In particular, I will introduce (i) recent variations of the well-established Differential Dynamic Programming methods to account for constraints, (ii) enhancements of forward dynamics problems involving contact interactions and (iii) new but simple techniques to deal with non-smoothness in the dynamics of robots. I will conclude this talk with important but yet unsolved problems of the field.

16h30-18h00 Discussion

Online user: 3

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