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On the Computational Complexity of Stackelberg Planning and Meta-Operator Verification
No full textInternational audienceStackelberg planning is a recently introduced single-turn two-player adversarial planning model, where two players are acting in a joint classical planning task, the objective of the first player being hampering the second player from achieving its goal. This places the Stackelberg planning problem somewhere between classical planning and general combinatorial two-player games. But, where exactly? All investigations of Stackelberg planning so far focused on practical aspects. We close this gap by conducting the first theoretical complexity analysis of Stackelberg planning. We show that in general Stackelberg planning is actually no harder than classical planning. Under a polynomial plan-length restriction, however, Stackelberg planning is a level higher up in the polynomial complexity hierarchy, suggesting that compilations into classical planning come with a worst-case exponential plan-length increase. In attempts to identify tractable fragments, we further study its complexity under various planning task restrictions, showing that Stackelberg planning remains intractable where classical planning is not. We finally inspect the complexity of meta-operator verification, a problem that has been recently connected to Stackelberg planning
Réduction du seuil d'instabilité de modulation d'un résonateur Fabry-Pérot fibré
No full textNational audienceDans l'intention de générer des peignes Kerr de fréquences, nous démontrons par une analyse complète la possibilité de réduire de 15.6% la puissance de seuil de déclenchement d'instabilité de modulation dans un résonateur Fabry-Pérot fibré de 7 cm de long
Les lentilles diffractives : une base pour l’optimisation de meta-surfaces de grande dimension ?
No full textNational audienceL’optimisation des performances des metasurfaces est usuellement présenté sous l’angle de l’optimisation des éléments sub-longueur d’onde élémentaires permettant leur réalisation. Cependant, la réalisation de meta-surfaces de grande dimension reposera sur l’agencement macroscopique de ces éléments simples. De ce point de vue, les lentilles diffractives sont un système physique simple permettant de tester et valider des méthodologies d’optimisation de cet agencement macroscopique. Nous présentons des stratégies d’optimisation de performances de ce type de systèmes présentant un très grand nombre de paramètres libres
Periodic Event-Triggered and Self-Triggered Control of Spacecraft Rendezvous System With Input Delay
No full textInternational audienceThis paper solves the problem of spacecraft rendezvous with input delay by designing the periodic event triggered control (PETC) and periodic self-triggered control (PSTC), respectively. Firstly, a PETC based on the discrete-timeparametric Lyapunov equation (DPLE) is designed to stabilize the delayed spacecraft rendezvous systems. Moreover, in order to avoid monitoring the measurement errors, a PSTC algorithm that the updates of the next control law depend on the previous triggered states is also designed. Specially, by using the properties of the DPLE, this new approach is not only simple, but also provides an easy and explicit condition on the only parameter of DPLE to guarantee the non-triviality of the designed PETC and PSTC. Finally, the effectiveness of theoretical results is verified by simulations
Sequential Trajectory Optimization for Externally-Actuated Modular Manipulators with Joint Locking
No full textInternational audienceIn this paper, we present a novel trajectory planning method for externally-actuated modular manipulators (EAMMs), consisting of multiple rotor-actuated links with joints that can be either locked or unlocked. This joint-locking feature allows effective balancing of the payload capacity and dexterity of the robot but significantly complicates the planning problem by introducing binary decision variables. To address this challenge, we leverage the problem’s intrinsic structure, i.e., the payload at the end-effector being enhanced by merely locking its immediate connected links; this allows us to break down the complex planning problem into a series of manageable subproblems and solve them sequentially. Our approach significantly reduces the problem’s complexity: in a serial n-link EAMM with m joint-lock mechanisms, where there could potentially be 2 m distinct configurational dynamics, we require solving only n + 1 trajectory optimization problems for single rigid body dynamics sequentially, thereby rendering the problem tractable. We substantiate the efficacy of our method through various simulation and experimental studies, covering ground-free and ground-bound configurations as well as both motion-only and manipulation tasks
FRENCHDIAM : Vers une filière Diamant Française pour l'électronique de puissance
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Control design for beam stabilization with self-sensing piezoelectric actuators: managing presence and absence of hysteresis
No full textInternational audienceThis paper deals with the modeling and stabilization of a flexible clamped beam controlled with a piezoelectric actuator in the self-sensing config- uration. We derive the model starting from general principles, using the general laws of piezoelectricity. The obtained model is composed by a PDE, describing the flexible deformations dynamics, interconnected with an ODE describing the electric charge dynamics. Firstly, we show that the derived linear model is well-posed and the origin is globally asymptot- ically stable when a voltage control law, containing the terms estimated in the self-sensing configuration, is applied. Secondly, we make the more realistic assumption of the presence of hysteresis in the electrical domain. Applying a passive control law, we show the well-posedness and the origin’s global asymptotic stability of the nonlinear closed-loop system
Contact Models in Robotics: a Comparative Analysis
No full textInternational audiencePhysics simulation is ubiquitous in robotics. Whether in model-based approaches (e.g., trajectory optimization), or model-free algorithms (e.g., reinforcement learning), physics simulators are a central component of modern control pipelines in robotics. Over the past decades, several robotic simulators have been developed, each with dedicated contact modeling assumptions and algorithmic solutions. In this article, we survey the main contact models and the associated numerical methods commonly used in robotics for simulating advanced robot motions involving contact interactions. In particular, we recall the physical laws underlying contacts and friction (i.e., Signorini condition, Coulomb's law, and the maximum dissipation principle), and how they are transcribed in current simulators. For each physics engine, we expose their inherent physical relaxations along with their limitations due to the numerical techniques employed. Based on our study, we propose theoretically grounded quantitative criteria on which we build benchmarks assessing both the physical and computational aspects of simulation. We support our work with an open-source and efficient C++ implementation of the existing algorithmic variations. Our results demonstrate that some approximations or algorithms commonly used in robotics can severely widen the reality gap and impact target applications. We hope this work will help motivate the development of new contact models, contact solvers, and robotic simulators in general, at the root of recent progress in motion generation in robotics
