Séminaire AID/CIEDS « Essaims de drones » et « FARO » des 9 et 10 novembre 2023

Amphi Rose Dieng Kuntz, Télécom Paris. Le 9 novembre à partir de 12:00, et 10 novembre jusqu’à 12:00 puis salle 4A301 jusqu'à 15:30.

Le social event est au Zeyer, à 7:30pm précises, le 9 novembre.

Jeudi 9 novembre

12:00am-1:30pm déjeuner - salle 0A128 (buffet)

1:30pm-2:15pm Luc Jaulin (ENSTA Bretagne), " Inertial control of a flat spinning disk "

Abstract: We propose a Lyapunov approach to control the rotation of a flat disk spinning in a three-dimensional space without gravity nor any other external forces. The motion of the disk is governed by the Euler's rotation equation for spinning objects. The control is made through the inertia matrix of the disk. Only a partial control of the rotation can be done since the angular momentum should remain constant. The assumption that the disk is flat creates a difficulty since masses used to change the inertia matrix are not allowed to move along the axis normal to the disk plane.

2:25pm-3:10pm, Abdelmouaiz Tebjou (ENSTA Paris): " Data-driven Reachability using Christoffel Functions and Conformal Prediction "

Abstract : An important mathematical tool in the analysis of dynamical systems is the approximation of the reach set, i.e., the set of states reachable after a given time from a given initial state. This set is difficult to compute for complex systems even if the system dynamics are known and given by a system of ordinary differential equations with known coefficients. In practice, parameters are often unknown and mathematical models difficult to obtain. Data-based approaches are promised to avoid these difficulties by estimating the reach set based on a sample of states. If a model is available, this training set can be obtained through numerical simulation. In the absence of a model, real-life observations can be used instead. A recently proposed approach for data-based reach set approximation uses Christoffel functions to approximate the reach set. Under certain assumptions, the approximation is guaranteed to converge to the true solution. In this paper, we improve upon these results by notably improving the sample efficiency and relaxing some of the assumptions by exploiting statistical guarantees from conformal prediction with training and calibration sets. In addition, we exploit an incremental way to compute the Christoffel function to avoid the calibration set while maintaining the statistical convergence guarantees. Furthermore, our approach is robust to outliers in the training and calibration set.

3:20pm-3:35pm, Break

3:35pm-4:20pm Danil Berrah (ENSTA Paris): " Autocoding sCvx Algorithm "

Abstract: We address the embedded code generation for an optimal control algorithm, sCvx, which is particularly suitable for solving trajectory planning problems with collision avoidance constraints. Existing uses of sCvx on drones or embedded platform are currently handcrafted coded. On the other hand, recent toolboxes such as SCPToolbox provide a simpler access to these trajectory planning algorithms, based on the resolution of a sequence of convex sub-problems. We define here a framework, in Python, enabling the automatic code generation for sCvx, in C, based on CvxPyGen and the \ecos solver. The framework is able to address problems involving non-convex constraints such as obstacle avoidance. This is a first step towards a more streamlined process to autocode trajectory planning algorithms and convex optimization solvers.

4:30pm-5:15pm, Damien Masse (Universite Bretagne Occidentale): " Guaranteed integration over Lie groups  "

Abstract : We consider a differential equation where the state of the system is described as an element of a matrix Lie group, using SE2 or SO3 as examples. We show that an intuitive approach based on using matrix exponentiation on boxes can give incorrect bounds on the result of the integration. We provide a correction to get guaranteed bounds on the result, and present an example of application.

Vendredi 10 novembre

9:30am-10:15am, Xavier Thirioux (ISAE): " Equation-Directed Axiomatization of Lustre Semantics to Enable Optimized Code Validation.  "

Abstract : Model-based design tools like SCADE Suite and Simulink are often used to design safety-critical embedded software. Consequently, generating correct code from such models is crucial. We tackle this challenge on Lustre, a dataflow synchronous language that embodies the concepts that base such tools. Instead of proving correct a whole code generator, we turn an existing compiler into a certifying compiler from Lustre to C, following a translation validation approach. We propose a solution that generates both C code and an attached specification expressing a correctness result for the generated and optionally optimized code. The specification yields proof obligations that are discharged by external solvers through the Frama-C platform.

10:25am-11:10am, Nuwan Herath Mudiyanselage (ENSTA Bretagne): " High-resolution drawing of algebraic curves and surfaces  "

Abstract: Scientific visualization allows users to build an intuition and to get an understanding of their data. We address the problem of visualizing implicit algebraic plane curves and surfaces, that are solutions of a polynomial equation P(x, y) = 0 or Q(x, y, z) = 0. More specifically, we handle the problem of drawing high degree curves or surfaces at a high resolution. In this case, most state-of-the-art approaches fail to produce drawings in a reasonable time due to the high evaluation cost of the polynomial. Our main contribution is to combine standard visualization algorithms from computer graphics with multipoint evaluation methods from computer algebra. More precisely, we use the fast Discrete Cosine Transform (DCT), which can be computed efficiently with the Fast Fourier Transform (FFT) algorithm. In most of our algorithms, we have combined that idea with a classical subdivision process in order to reduce the number of evaluations. Using exact error bound computation and interval arithmetic, we propose new algorithms which produce certified drawings. We compare them experimentally on two classes of high degree polynomials. Notably, some of those approaches are faster than state-of-the-art drawing software.

11:25am-11:40am Break

11:40pm-12:25pm Rizwann Parveen (Télécom Paris):, " Harmony in Motion: The Role of Model-Driven Design for Drone Swarms  "

Abstract: Commencing with a brief overview of my Ph.D. background and work, which focused on utilizing Timed Automata and the UPPAAL model checker for precise system design, this talk transitions to explore the application of Model-Driven Design in drone swarm architectures. The talk delves into the critical properties that demand consideration in the realm of drone swarms, prompting questions about facilitating seamless coordination and collaboration among drones, enable scalable and adaptable architectures, optimize mission planning, support real-time decision-making. By adopting a model-driven lens, this talk aims to unveil novel methods and research directions, paving the way for a deeper understanding of how critical challenges in drone swarm design can be effectively addressed. The talk opens up the discussion and research questions on how model-driven approaches can elevate the autonomy, adaptability, and overall performance of drone swarms in diverse scenarios.

12:35am-1:30pm déjeuner - salle 1A422 (buffet)

1:30pm-2:15pm Aloysio Galvao Lopes (LIX), " Assurances for machine learning trajectory predictors : guaranteed probabilistic bounds with conformal prediction"  "

Abstract : Machine learning models have become the rule in the domain of trajectory prediction. That has happened mainly because of the inherit uncertainty and multimodality involved in the process of predicting other humans’ interacting behaviour, which makes it nearly impossible to model a predictor that takes all factors into account. In this context, when, possibly, human lives depend on the reliability of those predictions, safety assurances need to be provided. This presentation will consider these circumstances to motivate our problem, and will introduce the theory of conformal prediction. We will start with the base formalism, then, we will show how the theory can be useful for machine learning models and time-series. Finally, we will make a link with our ongoing work and present our open questions.

2:25pm-3:25pm Eric Goubault, Laurent Pautet, Luc Jaulin, Christophe Garion, Jean-Daniel Masson. Réunion de travail