Francesco Braghin

Ugo Rosolia, Francesco Braghin, Andrew G. Alleyne et al.

In this paper a decentralized control algorithm for systems composed of $N$ dynamically decoupled agents, coupled by feasibility constraints, is presented. The control problem is divided into $N$ optimal control sub-problems and a communication scheme is proposed to decouple computations. The derivative of the solution of each sub-problem is used to approximate the evolution of the system allowing the algorithm to decentralize and parallelize computations. The effectiveness of the proposed algorithm is shown through simulations in a cooperative driving scenario.

Mohammed Irshadh Ismaaeel Sathyamangalam Imran, Lasse Peters, Michael Khayyat et al.

We address the multi-agent motion planning problem where interactions, collisions, and congestion co-exist. Conventional game-theoretic planners capture interactions among agents but often converge to conservative, congested equilibria. Homotopy planners, on the other hand, can explore topologically distinct paths, but lack mechanisms to account for the interdependence of agents' future actions. We propose a unified framework that leverages homotopy classes as structured strategy sets within a receding-horizon setup. At each planning stage, a deterministic homotopy planner generates topologically distinct paths for each agent, conditioned on the joint configuration. To avoid intractable growth of candidate paths, we propose a simple heuristic filtering step that selects a top-$K$ subset of the most suitable congestion-free joint strategies to ensure computational tractability. These serve as initializations for a potential game that enforces homotopy-consistent constraints and yields a generalized open-loop Nash equilibrium (OLNE), with penalties discouraging abrupt strategy shifts in a receding-horizon setting. Simulations with three agents demonstrate improved efficiency (faster completion) and enhanced safety (greater inter-agent clearance, leading to reduced congestion) compared to a local baseline and NH-ORCA that do not reason about homotopies. Hardware trials with two robots and one human demonstrate robustness to irrational behaviors, where our method adapts by switching to alternative feasible equilibria while the baseline game fails.

Matteo Tomasetto, Andrea Manzoni, Francesco Braghin

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.

Hafeez Husain Cholakkal, Stefano Arrigoni, Francesco Braghin

Accurate extrinsic calibration of LiDAR, RADAR, and camera sensors is essential for reliable perception in autonomous vehicles. Still, it remains challenging due to factors such as mechanical vibrations and cumulative sensor drift in dynamic environments. This paper presents RLCNet, a novel end-to-end trainable deep learning framework for the simultaneous online calibration of these multimodal sensors. Validated on real-world datasets, RLCNet is designed for practical deployment and demonstrates robust performance under diverse conditions. To support real-time operation, an online calibration framework is introduced that incorporates a weighted moving average and outlier rejection, enabling dynamic adjustment of calibration parameters with reduced prediction noise and improved resilience to drift. An ablation study highlights the significance of architectural choices, while comparisons with existing methods demonstrate the superior accuracy and robustness of the proposed approach.

Matteo Tomasetto, Jan P. Williams, Francesco Braghin et al.

Reduced Order Modeling is of paramount importance for efficiently inferring high-dimensional spatio-temporal fields in parametric contexts, enabling computationally tractable parametric analyses, uncertainty quantification and control. However, conventional dimensionality reduction techniques are typically limited to known and constant parameters, inefficient for nonlinear and chaotic dynamics, and uninformed to the actual system behavior. In this work, we propose sensor-driven SHallow REcurrent Decoder networks for Reduced Order Modeling (SHRED-ROM). Specifically, we consider the composition of a long short-term memory network, which encodes the temporal dynamics of limited sensor data in multiple scenarios, and a shallow decoder, which reconstructs the corresponding high-dimensional states. SHRED-ROM is a robust decoding-only strategy that circumvents the numerically unstable approximation of an inverse which is required by encoding-decoding schemes. To enhance computational efficiency and memory usage, the full-order state snapshots are reduced by, e.g., proper orthogonal decomposition, allowing for compressive training of the networks with minimal hyperparameter tuning. Through applications on chaotic and nonlinear fluid dynamics, we show that SHRED-ROM (i) accurately reconstructs the state dynamics for new parameter values starting from limited fixed or mobile sensors, independently on sensor placement, (ii) can cope with both physical, geometrical and time-dependent parametric dependencies, while being agnostic to their actual values, (iii) can accurately estimate unknown parameters, and (iv) can deal with different data sources, such as high-fidelity simulations, coupled fields and videos.

Matteo Tomasetto, Francesco Braghin, Andrea Manzoni

Continuous monitoring and real-time control of high-dimensional distributed systems are often crucial in applications to ensure a desired physical behavior, without degrading stability and system performances. Traditional feedback control design that relies on full-order models, such as high-dimensional state-space representations or partial differential equations, fails to meet these requirements due to the delay in the control computation, which requires multiple expensive simulations of the physical system. The computational bottleneck is even more severe when considering parametrized systems, as new strategies have to be determined for every new scenario. To address these challenges, we propose a real-time closed-loop control strategy enhanced by nonlinear non-intrusive Deep Learning-based Reduced Order Models (DL-ROMs). Specifically, in the offline phase, (i) full-order state-control pairs are generated for different scenarios through the adjoint method, (ii) the essential features relevant for control design are extracted from the snapshots through a combination of Proper Orthogonal Decomposition (POD) and deep autoencoders, and (iii) the low-dimensional policy bridging latent control and state spaces is approximated with a feedforward neural network. After data generation and neural networks training, the optimal control actions are retrieved in real-time for any observed state and scenario. In addition, the dynamics may be approximated through a cheap surrogate model in order to close the loop at the latent level, thus continuously controlling the system in real-time even when full-order state measurements are missing. The effectiveness of the proposed method, in terms of computational speed, accuracy, and robustness against noisy data, is finally assessed on two different high-dimensional optimal transport problems, one of which also involving an underlying fluid flow.

Nicolò Botteghi, Matteo Tomasetto, Urban Fasel et al.

Deep reinforcement learning has recently emerged as a promising feedback control strategy for complex dynamical systems governed by partial differential equations (PDEs). When dealing with distributed, high-dimensional problems in state and control variables, multi-agent reinforcement learning (MARL) has been proposed as a scalable approach for breaking the curse of dimensionality. In particular, through decentralized training and execution, multiple agents cooperate to steer the system towards a target configuration, relying solely on local state and reward information. However, the principle of locality may become a limiting factor whenever a collective, nonlocal behavior of the agents is crucial to maximize the reward function, as typically happens in PDE-constrained optimal control problems. In this work, we propose HypeMARL: a decentralized MARL algorithm tailored to the control of high-dimensional, parametric, and distributed systems. HypeMARL employs hypernetworks to effectively parametrize the agents' policies and value functions with respect to the system parameters and the agents' relative positions, encoded by sinusoidal positional encoding. Through the application on challenging control problems, such as density and flow control, we show that HypeMARL (i) can effectively control systems through a collective behavior of the agents, outperforming state-of-the-art decentralized MARL, (ii) can efficiently deal with parametric dependencies, (iii) requires minimal hyperparameter tuning and (iv) can reduce the amount of expensive environment interactions by a factor of ~10 thanks to its model-based extension, MB-HypeMARL, which relies on computationally efficient deep learning-based surrogate models approximating the dynamics locally, with minimal deterioration of the policy performance.

Francesco Braghin, Luca Paparusso, Manuel Riani et al.

World Endurance Championship (WEC) racing events are characterised by a relevant performance gap among competitors. The fastest vehicles category, consisting in hybrid vehicles, has to respect energy usage constraints set by the technical regulation. Considering absence of competitors, i.e. traffic conditions, the optimal energy usage strategy for lap time minimisation is typically computed through a constrained optimisation problem. To the best of our knowledge, the majority of state-of-the-art works neglects competitors. This leads to a mismatch with the real world, where traffic generates considerable time losses. To bridge this gap, we propose a new framework to offline compute optimal strategies for the powertrain energy management considering competitors. Through analysis of the available data from previous events, statistics on the sector times and overtaking probabilities are extracted to encode the competitors' behaviour. Adopting a multi-agent model, the statistics are then used to generate realistic Monte Carlo (MC) simulation of their position along the track. The simulator is then adopted to identify the optimal strategy as follows. We develop a longitudinal vehicle model for the ego-vehicle and implement an optimisation problem for lap time minimisation in absence of traffic, based on Genetic Algorithms. Solving the optimisation problem for a variety of constraints generates a set of candidate optimal strategies. Stochastic Dynamic Programming is finally implemented to choose the best strategy considering competitors, whose motion is generated by the MC simulator. Our approach, validated on data from a real stint of race, allows to significantly reduce the lap time.

Pragyan Dahal, Simone Mentasti, Stefano Arrigoni et al.

In literature, Extended Object Tracking (EOT) algorithms developed for autonomous driving predominantly provide obstacles state estimation in cartesian coordinates in the Vehicle Reference Frame. However, in many scenarios, state representation in road-aligned curvilinear coordinates is preferred when implementing autonomous driving subsystems like cruise control, lane-keeping assist, platooning, etc. This paper proposes a Gaussian Mixture Probability Hypothesis Density~(GM-PHD) filter with an Unscented Kalman Filter~(UKF) estimator that provides obstacle state estimates in curvilinear road coordinates. We employ a hybrid sensor fusion architecture between Lidar and Radar sensors to obtain rich measurement point representations for EOT. The measurement model for the UKF estimator is developed with the integration of coordinate conversion from curvilinear road coordinates to cartesian coordinates by using cubic hermit spline road model. The proposed algorithm is validated through Matlab Driving Scenario Designer simulation and experimental data collected at Monza Eni Circuit.

Marco Zangrandi, Stefano Arrigoni, Francesco Braghin

Bio-inspired walking hexapod robots are a relatively young branch in robotics in both state of the art and applications. Despite their high degree of flexibility and adaptability derived by their redundant design, the research field that compliments their abilities is still very lacking. In this paper will be proposed state-of-the-art hexapod robot specific control architecture that allows for full control over robot speed, body orientation and walk gait type to employ. Furthermore terrain interaction will be deeply investigated, leading to the development of a terrain-adapting control algorithm that will allow the robot to react swiftly to terrain shape and asperities such as non-linearities and non-continuity within the workspace. It will be presented a dynamic model derived from the interpretation of the hexapod movement to be comparable to these of the base-platform PKM machines, and said model will be validated through Matlab SimMechanicsTM physics simulation. A feed-back control system able to recognize leg-terrain touch and react accordingly to assure movement stability will then be developed. Finally results coming from an experimental campaign based of the PhantomX AX Metal Hexapod Mark II robotic platform by Trossen RoboticsTM is reported.

Stefano Arrigoni, Simone Mentasti, Federico Cheli et al.

Self-driving technology is expected to revolutionize different sectors and is seen as the natural evolution of road vehicles. In the last years, real-world validation of designed and virtually tested solutions is growing in importance since simulated environments will never fully replicate all the aspects that can affect results in the real world. To this end, this paper presents our prototype platform for experimental research on connected and autonomous driving projects. In detail, the paper presents the overall architecture of the vehicle focusing both on mechanical aspects related to remote actuation and sensors set-up and software aspects by means of a comprehensive description of the main algorithms required for autonomous driving as ego-localization, environment perception, motion planning, and actuation. Finally, experimental tests conducted in an urban-like environment are reported to validate and assess the performances of the overall system.

Francesco Micheli, Mattia Bersani, Stefano Arrigoni et al.

This paper presents a trajectory planner for autonomous driving based on a Nonlinear Model Predictive Control (NMPC) algorithm that accounts for Pacejka's nonlinear lateral tyre dynamics as well as for zero speed conditions through a novel slip angles calculation. In the NMPC framework, road boundaries and obstacles (both static and moving) are taken into account thanks to soft and hard constraints implementation. The numerical solution of the NMPC problem is carried out using ACADO toolkit coupled with the quadratic programming solver qpOASES. The effectiveness of the proposed NMPC trajectory planner has been tested using CarMaker multibody models. Time analysis results provided by the simulations shown, state that the proposed algorithm can be implemented on the real-time control framework of an autonomous vehicle under the assumption of data coming from an upstream estimation block.

Luca Paparusso, Stefano Melzi, Francesco Braghin

Most state-of-the-art works in trajectory forecasting for automotive target predicting the pose and orientation of the agents in the scene. This represents a particularly useful problem, for instance in autonomous driving, but it does not cover a spectrum of applications in control and simulation that require information on vehicle dynamics features other than pose and orientation. Also, multi-step dynamic simulation of complex multibody models does not seem to be a viable solution for real-time long-term prediction, due to the high computational time required. To bridge this gap, we present a deep-learning framework to model and predict the evolution of the coupled driver-vehicle system dynamics jointly on a complex road geometry. It consists of two components. The first, a neural network predictor, is based on Long Short-Term Memory autoencoders and fuses the information on the road geometry and the past driver-vehicle system dynamics to produce context-aware predictions. The second, a Bayesian optimiser, is proposed to tune some significant hyperparameters of the network. These govern the network complexity, as well as the features importance. The result is a self-tunable framework with real-time applicability, which allows the user to specify the features of interest. The approach has been validated with a case study centered on motion cueing algorithms, using a dataset collected during test sessions of a non-professional driver on a dynamic driving simulator. A 3D track with complex geometry has been employed as driving environment to render the prediction task challenging. Finally, the robustness of the neural network to changes in the driver and track was investigated to set guidelines for future works.

Stefano Arrigoni, Francesco Braghin, Federico Cheli

Autonomous vehicle's technology is expected to be disruptive for automotive industry in next years. This paper proposes a novel real-time trajectory planner based on a Nonlinear Model Predictive Control (NMPC) algorithm. A nonlinear single track vehicle model with Pacejka's lateral tyre formulas has been implemented. The numerical solution of the NMPC problem is obtained by means of the implementation of a novel genetic algorithm strategy. Numerical results are discussed through simulations that shown a reasonable behavior of the proposed strategy in presence of static or moving obstacles as well as in a wide rage of road friction conditions. Moreover a real-time implementation is made possible by the reported computational time analysis.

Guidong Yang, Simone Mentasti, Mattia Bersani et al.

An accurate and rapid-response perception system is fundamental for autonomous vehicles to operate safely. 3D object detection methods handle point clouds given by LiDAR sensors to provide accurate depth and position information for each detection, together with its dimensions and classification. The information is then used to track vehicles and other obstacles in the surroundings of the autonomous vehicle, and also to feed control units that guarantee collision avoidance and motion planning. Nowadays, object detection systems can be divided into two main categories. The first ones are the geometric based, which retrieve the obstacles using geometric and morphological operations on the 3D points. The seconds are the deep learning-based, which process the 3D points, or an elaboration of the 3D point-cloud, with deep learning techniques to retrieve a set of obstacles. This paper presents a comparison between those two approaches, presenting one implementation of each class on a real autonomous vehicle. Accuracy of the estimates of the algorithms has been evaluated with experimental tests carried in the Monza ENI circuit. The position of the ego vehicle and the obstacle is given by GPS sensors with RTK correction, which guarantees an accurate ground truth for the comparison. Both algorithms have been implemented on ROS and run on a consumer laptop.

Wenhui Huang, Francesco Braghin, Zhuo Wang

With the implementation of reinforcement learning (RL) algorithms, current state-of-art autonomous vehicle technology have the potential to get closer to full automation. However, most of the applications have been limited to game domains or discrete action space which are far from the real world driving. Moreover, it is very tough to tune the parameters of reward mechanism since the driving styles vary a lot among the different users. For instance, an aggressive driver may prefer driving with high acceleration whereas some conservative drivers prefer a safer driving style. Therefore, we propose an apprenticeship learning in combination with deep reinforcement learning approach that allows the agent to learn the driving and stopping behaviors with continuous actions. We use gradient inverse reinforcement learning (GIRL) algorithm to recover the unknown reward function and employ REINFORCE as well as Deep Deterministic Policy Gradient algorithm (DDPG) to learn the optimal policy. The performance of our method is evaluated in simulation-based scenario and the results demonstrate that the agent performs human like driving and even better in some aspects after training.