Searcharxiv⌕ Search

arXiv subjects

Lorenzo Lamberti

Publications and source records attributed to Lorenzo Lamberti.

At least 19 recordsLinked to original sources
arXiv2026

Good access to the crack and integrability of the full gradient for Griffith almost-minimizers in the plane

We show that, for almost-minimizers of the Griffith energy in the plane, the complement of the crack is locally covered by a finite number of John domains where the displacement satisfies H\"older-type estimates. As a consequence, we derive the integrability of the full gradient and the finiteness of the traces along the crack. In particular, we show that any Griffith almost-minimizer in dimension two locally belongs to the space SBV^2.

math.AP↗
arXiv2026

Thinking Fast, Thinking Slow: Adaptive Multimodal Transformer-based Sensor Fusion for Depth Estimation on Ultra-low-power MCUs

Artificial intelligence (AI)-based multimodal sensor fusion is a relevant topic gaining ever more traction across ultra-low-power (ULP) embedded and cyber-physical systems, as it improves reliability, accuracy, and robustness under real-world constraints. However, adding more and more sensors to ultra-constrained sub-100 mW platforms requires balancing energy consumption against prediction accuracy. To achieve this ambitious goal, we present a novel adaptive AI methodology that combines multimodal sensor fusion (camera, ultrasound, and Time-of-Flight sensors) with a lightweight recurrent Transformer-based architecture (688 k parameters). We address the depth map estimation task with a mechanism that combines token propagation across iterations with incremental sensor utilization. At each iteration, a confidence-based gating mechanism dynamically decides whether to continue the computation by adding progressively richer but more power-demanding sensors as input. Token propagation ensures temporal consistency by forwarding context features across time. To deploy our algorithm and test a first real-world prototype, we design a novel printed circuit board featuring all three sensors, coupled with an ULP GWT GAP9 multicore System-on-Chip. When comparing our adaptive system against the same pipeline using all sensors and iterations on the NYUv2 dataset, we lose only 4.8% of the {\delta}1 accuracy in exchange for 90% energy saving (2.44 mJ/frame). Finally, our adaptive method marks only 5.6% lower {\delta}1 accuracy than MobileDepth despite using 9x fewer parameters. Compared with a state-of-the-art model also running on GAP9, our method improves {\delta}1 accuracy by 31.8% thanks to our adaptive sensor fusion while operating within the same average power budget (~400 mW).

eess.IV↗
arXiv2026

Improving Autonomous Nano-drones Performance via Automated End-to-End Optimization and Deployment of DNNs

The evolution of energy-efficient ultra-low-power (ULP) parallel processors and the diffusion of convolutional neural networks (CNNs) are fueling the advent of autonomous driving nano-sized unmanned aerial vehicles (UAVs). These sub-10 cm robotic platforms are envisioned as next-generation ubiquitous smart-sensors and unobtrusive robotic-helpers. However, the limited computational/memory resources available aboard nano-UAVs introduce the challenge of minimizing and optimizing vision-based CNNs -- which to date require error-prone, labor-intensive iterative development flows. This work explores methodologies and software tools to streamline and automate all the deployment of vision-based CNN navigation on a ULP multicore system-on-chip acting as a mission computer on a Crazyflie 2.1 nano-UAV. We focus on the deployment of PULP-Dronet, a state-of-the-art CNN for autonomous navigation of nano-UAVs, from the initial training to the final closed-loop evaluation. Compared to the original hand-crafted CNN, our results show a 2x reduction of memory footprint and a speedup of 1.6x in inference time while guaranteeing the same prediction accuracy and significantly improving the behavior in the field, achieving: i) obstacle avoidance with a peak braking-speed of 1.65 m/s and improving the speed/braking-space ratio of the baseline, ii) free flight in a familiar environment up to 1.96 m/s (0.5 m/s for the baseline), and iii) lane following on a path featuring a 90 deg turn -- all while using for computation less than 1.6% of the drone's power budget. To foster new applications and future research, we open-source all the software design in a ready-to-run project compatible with the Crazyflie 2.1

eess.IV↗
arXiv2026

Low-Power License Plate Detection and Recognition on a RISC-V Multi-Core MCU-Based Vision System

In this paper, we present the first (to the best of our knowledge) demonstration of a low-power MCU-based edge device for Automatic License Plate Recognition (ALPR). The design leverages on a 9-core RISC-V processor, GAP8, coupled with a QVGA ultra-low-power greyscale imager. The proposed visual processing pipeline uses a multi-model inference approach based on SSDlite-MobilenetV2 for license plate detection and LPRNet for optical character recognition, reaching a 38.9% mAP score for the first task and a recognition rate of >99.13% for the latter on public datasets. On real-world data, the pipeline recognizes registration numbers when the size of LP crops is as small as 30x5 pixels. Thanks to the applied compression and optimization strategies, the multi-model inference (687 MMAC) achieves a throughput of 1.09 FPS at a power cost of 117 mW when running on GAP8. Our solution is the first MCU-class device embedding such a level of network complexity, resulting to be 73x more energy-efficient w.r.t. precedent mobile-class ALPR system featuring a Raspberry Pi3. The proposed design does not resort to any hardwired acceleration engines, thus retaining full flexibility for future algorithmic improvements.

cs.CV↗
arXiv2026

TinyDEVO: Deep Event-based Visual Odometry on Ultra-low-power Multi-core Microcontrollers

A key task in embedded vision is visual odometry (VO), which estimates camera motion from visual sensors, and it is a core component in many embedded power-constrained systems, from autonomous robots to augmented and virtual reality wearable devices. The newest class of VO systems combines deep learning models with bio-inspired event-based cameras, which are robust to motion blur and lighting conditions. However, state-of-the-art (SoA) event-based VO algorithms require significant memory and computation. For example, the leading approach DEVO requires 733 MB of memory and 155 billion multiply-accumulate (MAC) operations per frame. We present TinyDEVO, an event-based VO deep learning model designed for resource-constrained microcontroller units (MCUs). We deploy TinyDEVO on an ultra-low-power (ULP) 9-core RISC-V-based MCU, achieving a throughput of approximately 1.2 frames per second with an average power consumption of only 86 mW. Thanks to our neural network architectural optimizations and hyperparameter tuning, TinyDEVO reduces the memory footprint by 11.5x (to 63.8 MB) and the number of operations per frame by 29.7x (to 5.2 billion MACs per frame) compared to DEVO, while maintaining an average trajectory error of 27 cm, i.e., only 19 cm higher than DEVO, on three state-of-the-art datasets. Our work demonstrates, for the first time, the feasibility of an event-based VO pipeline on ultra-low-power devices.

eess.IV↗
arXiv2026

Tiny-DroNeRF: Tiny Neural Radiance Fields aboard Federated Learning-enabled Nano-drones

Sub-30g nano-sized aerial robots can leverage their agility and form factor to autonomously explore cluttered and narrow environments, like in industrial inspection and search and rescue missions. However, the price for their tiny size is a strong limit in their resources, i.e., sub-100 mW microcontroller units (MCUs) delivering $\sim$100 GOps/s at best, and memory budgets well below 100 MB. Despite these strict constraints, we aim to enable complex vision-based tasks aboard nano-drones, such as dense 3D scene reconstruction: a key robotic task underlying fundamental capabilities like spatial awareness and motion planning. Top-performing 3D reconstruction methods leverage neural radiance fields (NeRF) models, which require GBs of memory and massive computation, usually delivered by high-end GPUs consuming 100s of Watts. Our work introduces Tiny-DroNeRF, a lightweight NeRF model, based on Instant-NGP, and optimized for running on a GAP9 ultra-low-power (ULP) MCU aboard our nano-drones. Then, we further empower our Tiny-DroNeRF by leveraging a collaborative federated learning scheme, which distributes the model training among multiple nano-drones. Our experimental results show a 96% reduction in Tiny-DroNeRF's memory footprint compared to Instant-NGP, with only a 5.7 dB drop in reconstruction accuracy. Finally, our federated learning scheme allows Tiny-DroNeRF to train with an amount of data otherwise impossible to keep in a single drone's memory, increasing the overall reconstruction accuracy. Ultimately, our work combines, for the first time, NeRF training on an ULP MCU with federated learning on nano-drones.

cs.RO↗
arXiv2026

Morrey estimates for the gradient in non-linear variational transmission problems

We study a class of variational transmission problems driven by nonlinear energies with discontinuous coefficients across a prescribed interface. The model setting consists of integral functionals of the form \[ \mathcal{F}(u;E)=\int_{\Omega}\sigma_E(x)\,F(\nabla u)\,dx, \] where the coefficient $\sigma_E$ takes two constant values on complementary regions separated by a $C^1$ hypersurface, and the integrand $F$ satisfies standard $p$-growth and monotonicity conditions with $p>2$. In this nonlinear variational framework, we establish local Morrey-space regularity for the gradient of local minimizers, proving that $\nabla u\in L^{2,\lambda}_{\mathrm{loc}}(\Omega)$ for every $0\leq\lambda<n$, provided $2<p<\frac{2n}{n-2}$. The proof is based on quantitative decay estimates for the energy near the interface, first obtained in a flat configuration and then extended to the general case by a suitable approximation argument.

math.AP↗
arXiv2025

Ahlfors-regularity for minimizers of a multiphase optimal design problem

We establish an Alhfors-regularity result for minimizers of a multiphase optimal design problem. It is a variant of the classical variational problem which involves a finite number of chambers $\mathcal{E}(i)$ of prescribed volume that partition a given domain $Ω\subset\mathbb{R}^n$. The cost functional associated with a configuration $\left(\{\mathcal{E}(i)\}_i,u\right)$ is made up of the perimeter of the partition interfaces and a Dirichlet energy term, which is discontinuous across the interfaces. We prove that the union of the optimal interfaces is $(n-1)$-Alhfors-regular via a penalization method and decay estimates of the energy.

math.OC↗
arXiv2025

Finsler $p$-Laplacian in domains becoming unbounded

We study the asymptotic behavior of sequences of solutions, energies functionals, and the first eigenvalues associated with the Finsler $p$-Laplace operator, also known as the anisotropic $p$-Laplace operator on a sequence of bounded cylinders whose length tends to infinity. We prove that the solutions on the bounded cylinders converge to the solution on the cross-section, with a polynomial rate of convergence in the general case and exponential convergence in some special cases. We show that energies on finite cylinders, with the multiplication of a scaling factor, converge to the energy on the cross-section. Finally, we investigate the convergence of the first eigenvalue and, for a specific subclass, we provide the optimal convergence rate.

math.AP↗
arXiv2025

Quantitative regularity properties for the optimal design problem

In this paper we slightly improve the regularity theory for the so called optimal design problem. We first establish the uniform rectifiability of the boundary of the optimal set, for a larger class of minimizers, in any dimension. As an application, we improve the bound obtained by Larsen in dimension~2 about the mutual distance between two connected components. Finally we also prove that the full regularity in dimension 2 holds true provided that the ratio between the two constants in front of the Dirichlet energy is not larger than 4, which partially answers to a question raised by Larsen.

math.OC↗
arXiv2025

Quasiconvex Bulk and Surface Energies with subquadratic growth

We establish partial Hölder continuity of the gradient for equilibrium configurations of vectorial multidimensional variational problems, involving bulk and surface energies. The bulk energy densities are uniformly strictly quasiconvex functions with $p$-growth, $1<p< 2$, without any further structure conditions. The anisotropic surface energy is defined by means of an elliptic integrand $Φ$ not necessarily regular.

math.OC↗
arXiv2024

Circuits and Systems for Embodied AI: Exploring uJ Multi-Modal Perception for Nano-UAVs on the Kraken Shield

Embodied artificial intelligence (AI) requires pushing complex multi-modal models to the extreme edge for time-constrained tasks such as autonomous navigation of robots and vehicles. On small form-factor devices, e.g., nano-sized unmanned aerial vehicles (UAVs), such challenges are exacerbated by stringent constraints on energy efficiency and weight. In this paper, we explore embodied multi-modal AI-based perception for Nano-UAVs with the Kraken shield, a 7g multi-sensor (frame-based and event-based imagers) board based on Kraken, a 22 nm SoC featuring multiple acceleration engines for multi-modal event and frame-based inference based on spiking (SNN) and ternary (TNN) neural networks, respectively. Kraken can execute SNN real-time inference for depth estimation at 1.02k inf/s, 18 μJ/inf, TNN real-time inference for object classification at 10k inf/s, 6 μJ/inf, and real-time inference for obstacle avoidance at 221 frame/s, 750 μJ/inf.

cs.AR↗
arXiv2024

Distilling Tiny and Ultra-fast Deep Neural Networks for Autonomous Navigation on Nano-UAVs

Nano-sized unmanned aerial vehicles (UAVs) are ideal candidates for flying Internet-of-Things smart sensors to collect information in narrow spaces. This requires ultra-fast navigation under very tight memory/computation constraints. The PULP-Dronet convolutional neural network (CNN) enables autonomous navigation running aboard a nano-UAV at 19 frame/s, at the cost of a large memory footprint of 320 kB -- and with drone control in complex scenarios hindered by the disjoint training of collision avoidance and steering capabilities. In this work, we distill a novel family of CNNs with better capabilities than PULP-Dronet, but memory footprint reduced by up to 168x (down to 2.9 kB), achieving an inference rate of up to 139 frame/s; we collect a new open-source unified collision/steering 66 k images dataset for more robust navigation; and we perform a thorough in-field analysis of both PULP-Dronet and our tiny CNNs running on a commercially available nano-UAV. Our tiniest CNN, called Tiny-PULP-Dronet v3, navigates with a 100% success rate a challenging and never-seen-before path, composed of a narrow obstacle-populated corridor and a 180° turn, at a maximum target speed of 0.5 m/s. In the same scenario, the SoA PULP-Dronet consistently fails despite having 168x more parameters.

eess.IV↗
arXiv2024

Tiny-PULP-Dronets: Squeezing Neural Networks for Faster and Lighter Inference on Multi-Tasking Autonomous Nano-Drones

Pocket-sized autonomous nano-drones can revolutionize many robotic use cases, such as visual inspection in narrow, constrained spaces, and ensure safer human-robot interaction due to their tiny form factor and weight -- i.e., tens of grams. This compelling vision is challenged by the high level of intelligence needed aboard, which clashes against the limited computational and storage resources available on PULP (parallel-ultra-low-power) MCU class navigation and mission controllers that can be hosted aboard. This work moves from PULP-Dronet, a State-of-the-Art convolutional neural network for autonomous navigation on nano-drones. We introduce Tiny-PULP-Dronet: a novel methodology to squeeze by more than one order of magnitude model size (50x fewer parameters), and number of operations (27x less multiply-and-accumulate) required to run inference with similar flight performance as PULP-Dronet. This massive reduction paves the way towards affordable multi-tasking on nano-drones, a fundamental requirement for achieving high-level intelligence.

cs.RO↗
arXiv2024

Combining Local and Global Perception for Autonomous Navigation on Nano-UAVs

A critical challenge in deploying unmanned aerial vehicles (UAVs) for autonomous tasks is their ability to navigate in an unknown environment. This paper introduces a novel vision-depth fusion approach for autonomous navigation on nano-UAVs. We combine the visual-based PULP-Dronet convolutional neural network for semantic information extraction, i.e., serving as the global perception, with 8x8px depth maps for close-proximity maneuvers, i.e., the local perception. When tested in-field, our integration strategy highlights the complementary strengths of both visual and depth sensory information. We achieve a 100% success rate over 15 flights in a complex navigation scenario, encompassing straight pathways, static obstacle avoidance, and 90° turns.

cs.RO↗
arXiv2023

Multi-sensory Anti-collision Design for Autonomous Nano-swarm Exploration

This work presents a multi-sensory anti-collision system design to achieve robust autonomous exploration capabilities for a swarm of 10 cm-side nano-drones operating on object detection missions. We combine lightweight single-beam laser ranging to avoid proximity collisions with a long-range vision-based obstacle avoidance deep learning model (i.e., PULP-Dronet) and an ultra-wide-band (UWB) based ranging module to prevent intra-swarm collisions. An in-field study shows that our multisensory approach can prevent collisions with static obstacles, improving the mission success rate from 20% to 80% in cluttered environments w.r.t. a State-of-the-Art (SoA) baseline. At the same time, the UWB-based sub-system shows a 92.8% success rate in preventing collisions between drones of a four-agent fleet within a safety distance of 65 cm. On a SoA robotic platform extended by a GAP8 multi-core processor, the PULP-Dronet runs interleaved with an objected detection task, which constraints its execution at 1.6 frame/s. This throughput is sufficient for avoiding obstacles with a probability of about 40% but shows a need for more capable processors for the next-generation nano-drone swarms.

cs.RO↗
arXiv2023

A Sim-to-Real Deep Learning-based Framework for Autonomous Nano-drone Racing

Autonomous drone racing competitions are a proxy to improve unmanned aerial vehicles' perception, planning, and control skills. The recent emergence of autonomous nano-sized drone racing imposes new challenges, as their ~10cm form factor heavily restricts the resources available onboard, including memory, computation, and sensors. This paper describes the methodology and technical implementation of the system winning the first autonomous nano-drone racing international competition: the IMAV 2022 Nanocopter AI Challenge. We developed a fully onboard deep learning approach for visual navigation trained only on simulation images to achieve this goal. Our approach includes a convolutional neural network for obstacle avoidance, a sim-to-real dataset collection procedure, and a navigation policy that we selected, characterized, and adapted through simulation and actual in-field experiments. Our system ranked 1st among seven competing teams at the competition. In our best attempt, we scored 115m of traveled distance in the allotted 5-minute flight, never crashing while dodging static and dynamic obstacles. Sharing our knowledge with the research community, we aim to provide a solid groundwork to foster future development in this field.

cs.RO↗