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Francesco Braghin

Publications and source records attributed to Francesco Braghin.

At least 37 records · Page 2Linked to original sources

RoboMorph: In-Context Meta-Learning for Robot Dynamics Modeling

The landscape of Deep Learning has experienced a major shift with the pervasive adoption of Transformer-based architectures, particularly in Natural Language Processing (NLP). Novel avenues for physical applications, such as solving Partial Differential Equations and Image Vision, have been explored. However, in challenging domains like robotics, where high non-linearity poses significant challenges, Transformer-based applications are scarce. While Transformers have been used to provide robots with knowledge about high-level tasks, few efforts have been made to perform system identification. This paper proposes a novel methodology to learn a meta-dynamical model of a high-dimensional physical system, such as the Franka robotic arm, using a Transformer-based architecture without prior knowledge of the system's physical parameters. The objective is to predict quantities of interest (end-effector pose and joint positions) given the torque signals for each joint. This prediction can be useful as a component for Deep Model Predictive Control frameworks in robotics. The meta-model establishes the correlation between torques and positions and predicts the output for the complete trajectory. This work provides empirical evidence of the efficacy of the in-context learning paradigm, suggesting future improvements in learning the dynamics of robotic systems without explicit knowledge of physical parameters. Code, videos, and supplementary materials can be found at project website. See https://sites.google.com/view/robomorph/

cs.RO↗

Real-time optimal control of high-dimensional parametrized systems by deep learning-based reduced order models

Steering a system towards a desired target in a very short amount of time is challenging from a computational standpoint. Indeed, the intrinsically iterative nature of optimal control problems requires multiple simulations of the physical system to be controlled. Moreover, the control action needs to be updated whenever the underlying scenario undergoes variations. Full-order models based on, e.g., the Finite Element Method, do not meet these requirements due to the computational burden they usually entail. On the other hand, conventional reduced order modeling techniques such as the Reduced Basis method, are intrusive, rely on a linear superimposition of modes, and lack of efficiency when addressing nonlinear time-dependent dynamics. In this work, we propose a non-intrusive Deep Learning-based Reduced Order Modeling (DL-ROM) technique for the rapid control of systems described in terms of parametrized PDEs in multiple scenarios. In particular, optimal full-order snapshots are generated and properly reduced by either Proper Orthogonal Decomposition or deep autoencoders (or a combination thereof) while feedforward neural networks are exploited to learn the map from scenario parameters to reduced optimal solutions. Nonlinear dimensionality reduction therefore allows us to consider state variables and control actions that are both low-dimensional and distributed. After (i) data generation, (ii) dimensionality reduction, and (iii) neural networks training in the offline phase, optimal control strategies can be rapidly retrieved in an online phase for any scenario of interest. The computational speedup and the high accuracy obtained with the proposed approach are assessed on different PDE-constrained optimization problems, ranging from the minimization of energy dissipation in incompressible flows modelled through Navier-Stokes equations to the thermal active cooling in heat transfer.

math.OC↗

Optimal Design of Broadband, Low-Directivity Graded Index Acoustic Lenses for Underwater Applications

Manipulating underwater pressure waves is crucial for marine exploration, as electromagnetic signals are strongly absorbed in water. However, the multi-path phenomenon complicates the accurate capture of acoustic waves by receivers. Although graded index lenses, based on metamaterials with smoothly varying properties, successfully focus pressure waves, they tend to have high directivity, which hinders practical application. This work introduces three 2D acoustic lenses made from a metamaterial composed of solid inclusions in water. We propose an optimization scheme where the pressure dynamics is governed by Helmholtz's equation, with control parameters affecting each lens cell's density and bulk modulus. Through an appropriate cost function, the optimization encourages a broadband, low-directivity lens. The large-scale optimization is solved using the Lagrangian approach, which provides an analytical expression for the cost gradient. This scheme avoids the need for a separate discretization step, allowing the design to transition directly from the desired smooth refractive index to a practical lattice structure. As a result, the optimized lens closely aligns with real-world behavior. The homogenized numerical model is validated against finite elements, which considers acoustic-elastic coupling at the microstructure level. When homogenization holds, this approach proves to be an effective design tool for achieving broadband, low-directivity acoustic lenses.

math.OC↗

High Bulk Modulus Pentamodes: the Three-Dimensional Metal Water

Despite significant advances in the field of phononic crystals, the development of acoustic metafluids that replicate the behaviour of liquids in three dimensions remains elusive. For instance, water - the quintessential pentamode (PM) material - has a bulk modulus two orders of magnitude higher than current state-of-the-art PMs. The need for a low shear modulus inherently conflicts with the desire of high bulk modulus and density. In this letter, we shed light on the limitations of existing PM geometries and propose an innovative shape for the links that constitute the network. Inspired by the kinematics of ropes, these links are constructed from thin fibres and demonstrate the potential to create PMs with properties akin to those of liquids. As a prime example, we present the design of the first metamaterial that fully deserves the name 3D metal water, since its acoustic properties in the low frequency regime are indistinguishable with water. Additionally, we highlight a shear band gap in the lattice dispersion diagram, and illustrate the influence of geometric parameters on the dynamic properties at higher frequencies. This novel design of metafluids holds promise for applications requiring anisotropic materials such as acoustic lenses, waveguides, and cloaks.

physics.app-ph↗

Tactical Game-theoretic Decision-making with Homotopy Class Constraints

We propose a tactical homotopy-aware decision-making framework for game-theoretic motion planning in urban environments. We model urban driving as a generalized Nash equilibrium problem and employ a mixed-integer approach to tame the combinatorial aspect of motion planning. More specifically, by utilizing homotopy classes, we partition the high-dimensional solution space into finite, well-defined subregions. Each subregion (homotopy) corresponds to a high-level tactical decision, such as the passing order between pairs of players. The proposed formulation allows to find global optimal Nash equilibria in a computationally tractable manner by solving a mixed-integer quadratic program. Each homotopy decision is represented by a binary variable that activates different sets of linear collision avoidance constraints. This extra homotopic constraint allows to find solutions in a more efficient way (on a roundabout scenario on average 5-times faster). We experimentally validate the proposed approach on scenarios taken from the rounD dataset. Simulation-based testing in receding horizon fashion demonstrates the capability of the framework in achieving globally optimal solutions while yielding a 78% average decrease in the computational time with respect to an implementation without the homotopic constraints.

cs.MA↗

An optimal control strategy to design passive thermal cloaks of arbitrary shape

In this paper we describe a numerical framework for achieving passive thermal cloaking of arbitrary shapes in both static and transient regimes. The design strategy is cast as the solution of an optimal control problem (OCP) for the heat equation where the coefficients of the thermal diffusivity matrix take the role of control functions and the distance between the uncloaked and the cloaked field is minimized in a suitable observation domain. The control actions enter bilinearly in the heat equation, thus making the resulting OCP nonlinear, and its analysis nontrivial. We show that optimal diffusivity coefficients exist both for the static and the transient case; we derive a system of first-order necessary optimality conditions; finally, we carry out their numerical approximation using the Finite Element Method. A series of numerical test cases assess the capability of our strategy to tackle passive thermal cloaking of arbitrarily complex two-dimensional objects.

math.OC↗

ZAPP! Zonotope Agreement of Prediction and Planning for Continuous-Time Collision Avoidance with Discrete-Time Dynamics

The past few years have seen immense progress on two fronts that are critical to safe, widespread mobile robot deployment: predicting uncertain motion of multiple agents, and planning robot motion under uncertainty. However, the numerical methods required on each front have resulted in a mismatch of representation for prediction and planning. In prediction, numerical tractability is usually achieved by coarsely discretizing time, and by representing multimodal multi-agent interactions as distributions with infinite support. On the other hand, safe planning typically requires very fine time discretization, paired with distributions with compact support, to reduce conservativeness and ensure numerical tractability. The result is, when existing predictors are coupled with planning and control, one may often find unsafe motion plans. This paper proposes ZAPP (Zonotope Agreement of Prediction and Planning) to resolve the representation mismatch. ZAPP unites a prediction-friendly coarse time discretization and a planning-friendly zonotope uncertainty representation; the method also enables differentiating through a zonotope collision check, allowing one to integrate prediction and planning within a gradient-based optimization framework. Numerical examples show how ZAPP can produce safer trajectories compared to baselines in interactive scenes.

cs.RO↗

Model Predictive Control Strategies for Electric Endurance Race Cars Accounting for Competitors Interactions

This paper presents model predictive control strategies for battery electric endurance race cars accounting for interactions with the competitors. In particular, we devise an optimization framework capturing the impact of the actions of the ego vehicle when interacting with competitors in a probabilistic fashion, jointly accounting for the optimal pit stop decision making, the charge times and the driving style in the course of the race. We showcase our method for a simulated 1h endurance race at the Zandvoort circuit, using real-life data of internal combustion engine race cars from a previous event. Our results show that optimizing both the race strategy as well as the decision making during the race is very important, resulting in a significant 21s advantage over an always overtake approach, whilst revealing the competitiveness of e-race cars w.r.t. conventional ones.

eess.SY↗

Controlling surface acoustic waves (SAWs) via temporally graded metasurfaces

In this manuscript, the temporal rainbow effect for surface acoustic waves (SAW) is illustrated through a temporal analog of space metagradings. We show that a time-modulated array of mechanical resonators induces a wavenumber-preserving frequency transformation which, in turn, dictates Rayleigh-to-Shear wave conversion. The process is unfolded through the adiabatic theorem, which allows us to delineate the transition between a solely frequency-converted wave packet and a temporally-driven mode conversion. In other words, our paper explores the role of time modulation in the context of elastic metasurfaces, and we envision our implementation to be suitable for designing a new family of SAW devices with frequency conversion, mode conversion, and unusual transport capabilities.

physics.app-ph↗

Nonlinear In-situ Calibration of Strain-Gauge Force/Torque Sensors for Humanoid Robots

High force/torque (F/T) sensor calibration accuracy is crucial to achieving successful force estimation/control tasks with humanoid robots. State-of-the-art affine calibration models do not always approximate correctly the physical phenomenon of the sensor/transducer, resulting in inaccurate F/T measurements for specific applications such as thrust estimation of a jet-powered humanoid robot. This paper proposes and validates nonlinear polynomial models for F/T calibration, increasing the number of model coefficients to minimize the estimation residuals. The analysis of several models, based on the data collected from experiments with the iCub3 robot, shows a significant improvement in minimizing the force/torque estimation error when using higher-degree polynomials. In particular, when using a 4th-degree polynomial model, the Root Mean Square error (RMSE) decreased to 2.28N from the 4.58N obtained with an affine model, and the absolute error in the forces remained under 6N while it was reaching up to 16N with the affine model.

cs.RO↗

Vehicle State Estimation through Modular Factor Graph-based Fusion of Multiple Sensors

This study focuses on the critical aspect of robust state estimation for the safe navigation of an Autonomous Vehicle (AV). Existing literature primarily employs two prevalent techniques for state estimation, namely filtering-based and graph-based approaches. Factor Graph (FG) is a graph-based approach, constructed using Values and Factors for Maximum Aposteriori (MAP) estimation, that offers a modular architecture that facilitates the integration of inputs from diverse sensors. However, most FG-based architectures in current use require explicit knowledge of sensor parameters and are designed for single setups. To address these limitations, this research introduces a novel plug-and-play FG-based state estimator capable of operating without predefined sensor parameters. This estimator is suitable for deployment in multiple sensor setups, offering convenience and providing comprehensive state estimation at a high frequency, including mean and covariances. The proposed algorithm undergoes rigorous validation using various sensor setups on two different vehicles: a quadricycle and a shuttle bus. The algorithm provides accurate and robust state estimation across diverse scenarios, even when faced with degraded Global Navigation Satellite System (GNSS) measurements or complete outages. These findings highlight the efficacy and reliability of the algorithm in real-world AV applications.

cs.RO↗

Predicting human motion intention for pHRI assistive control

This work addresses human intention identification during physical Human-Robot Interaction (pHRI) tasks to include this information in an assistive controller. To this purpose, human intention is defined as the desired trajectory that the human wants to follow over a finite rolling prediction horizon so that the robot can assist in pursuing it. This work investigates a Recurrent Neural Network (RNN), specifically, Long-Short Term Memory (LSTM) cascaded with a Fully Connected layer. In particular, we propose an iterative training procedure to adapt the model. Such an iterative procedure is powerful in reducing the prediction error. Still, it has the drawback that it is time-consuming and does not generalize to different users or different co-manipulated objects. To overcome this issue, Transfer Learning (TL) adapts the pre-trained model to new trajectories, users, and co-manipulated objects by freezing the LSTM layer and fine-tuning the last FC layer, which makes the procedure faster. Experiments show that the iterative procedure adapts the model and reduces prediction error. Experiments also show that TL adapts to different users and to the co-manipulation of a large object. Finally, to check the utility of adopting the proposed method, we compare the proposed controller enhanced by the intention prediction with the other two standard controllers of pHRI.

cs.RO↗

Optimal Control of Short-Time Attractors in Active Fluid Flows

Objective Eulerian Coherent Structures (OECSs) and instantaneous Lyapunov exponents (iLEs) govern short-term material transport in fluid flows as Lagrangian Coherent Structures and the Finite-Time Lyapunov Exponent do over longer times. Attracting OECSs and iLEs reveal short-time attractors and are computable from the Eulerian rate-of-strain tensor. Here we devise an optimal control strategy to create short-time attractors in viscosity-dominated active fluids. By modulating the active stress intensity, our framework achieves a target profile of the minimum eigenvalue of the rate-of-strain tensor, controlling the location and shape of short-time attractors. We use numerical simulations to show that our optimal control strategy effectively achieves desired short-time attractors while rejecting disturbances. Combining optimal control and recent advances on coherent structures, our work offers a new perspective to steer material transport in unsteady flows, with applications in synthetic active nematics and multicellular systems.

physics.flu-dyn↗

Optimal Strategies to Steer and Control Water Waves

In this paper, we propose a novel approach for controlling surface water waves and their interaction with floating bodies. We consider a floating target rigid body surrounded by a control region where we design three control strategies of increasing complexity: an active strategy based on controlling the pressure at the air-water interface and two passive strategies where an additional controlled floating device is designed. We model such device both as a membrane and as a thin plate and study the effect of this modelling choice on the performance of the overall controlled system. We frame this problem as an optimal control problem where the underlying state dynamics is represented by a system of coupled partial differential equations describing the interaction between the surface water waves and the floating target body in the frequency domain. An additional intermediate coupling is then added when considering the control floating device. The optimal control problem then aims at minimizing a cost functional which weights the unwanted motions of the floating body. A system of first-order necessary optimality conditions is derived and numerically solved using the finite element method. Numerical simulations then show the efficacy of this method in reducing hydrodynamic loads on floating objects.

math.OC↗

Design and Simulation-Based Testing of Connected Traffic Light Guidance Systems

The establishment of fast and reliable communication technologies, such as 5G, is enabling the evolution of a new generation of connected ADAS. This work aims to develop a traffic light advisory system, Multiple Traffic Light Advisor (MTLA), to improve driving efficiency and intersection viability, and reduce urban pollution. The developed system guides the driver on how to modify the vehicle speed to efficiently utilize the current and future states of the traffic lights ahead. Starting from a non-optimal implementation of the overall architecture, MTLA is further improved through a non-linear MPC approach. The developed system is tested in a virtual environment in IPG CarMaker and results show good performances with a high potential and space for future developments.

eess.SY↗

Robust optimal density control of robotic swarms

In this paper, we propose a computationally efficient, robust density control strategy for the mean-field model of a robotic swarm. We formulate a static optimal control problem (OCP) that computes a robot velocity field which drives the swarm to a target equilibrium density, and we prove the stability of the controlled system in the presence of transient perturbations and uncertainties in the initial conditions. The density dynamics are described by a linear elliptic advection-diffusion equation in which the control enters bilinearly into the advection term. The well-posedness of the state problem is ensured by an integral constraint. We prove the existence of optimal controls by embedding the state constraint into the weak formulation of the state dynamics. The resulting control field is space-dependent and does not require any communication between robots or costly density estimation algorithms. Based on the properties of the primal and dual systems, we first propose a method to accommodate the state constraint. Exploiting the properties of the state dynamics and associated controls, we then construct a modified dynamic OCP to speed up the convergence to the target equilibrium density of the associated static problem. We then show that the finite-element discretization of the static and dynamic OCPs inherits the structure and several useful properties of their infinite-dimensional formulations. Finally, we demonstrate the effectiveness of our control approach through numerical simulations of scenarios with obstacles and an external velocity field.

math.OC↗

Centroidal Aerodynamic Modeling and Control of Flying Multibody Robots

This paper presents a modeling and control framework for multibody flying robots subject to non-negligible aerodynamic forces acting on the centroidal dynamics. First, aerodynamic forces are calculated during robot flight in different operating conditions by means of Computational Fluid Dynamics (CFD) analysis. Then, analytical models of the aerodynamics coefficients are generated from the dataset collected with CFD analysis. The obtained simplified aerodynamic model is also used to improve the flying robot control design. We present two control strategies: compensating for the aerodynamic effects via feedback linearization and enforcing the controller robustness with gain-scheduling. Simulation results on the jet-powered humanoid robot iRonCub validate the proposed approach.

cs.RO↗

Nonlinear Model Identification and Observer Design for Thrust Estimation of Small-scale Turbojet Engines

Jet-powered vertical takeoff and landing (VTOL) drones require precise thrust estimation to ensure adequate stability margins and robust maneuvering. Small-scale turbojets have become good candidates for powering heavy aerial drones. However, due to limited instrumentation available in these turbojets, estimating the precise thrust using classical techniques is not straightforward. In this paper, we present a methodology to accurately estimate the online thrust for the small-scale turbojets used on the iRonCub - an aerial humanoid robot. We use a grey-box method to capture the turbojet system dynamics with a nonlinear state-space model based on the data acquired from a custom engine test bench. This model is then used to design an extended Kalman filter that estimates the turbojet thrust only from the angular speed measurements. We exploited the parameter estimation algorithm to ensure that the EKF gives smooth and accurate estimates even at engine failures. The designed EKF was validated on the test bench where the mean absolute error in estimated thrust was found to be within 2% of rated peak thrust.

cs.RO↗