Expensive ultrasonic anemometers are usually required to measure wind speed accurately. The aim of this work is to overcome the loss of accuracy of a low cost hot-wire anemometer caused by the changes of air temperature, by means of a probabilistic calibration using Gaussian Process Regression. Gaussian Process Regression is a non-parametric, Bayesian, and supervised learning method designed to make predictions of an unknown target variable as a function of one or more known input variables. Our approach is validated against real datasets, obtaining a good performance in inferring the actual wind speed values. By performing, before its real use in the field, a calibration of the hot-wire anemometer taking into account air temperature, permits that the wind speed can be estimated for the typical range of ambient temperatures, including a grounded uncertainty estimation for each speed measure.
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Structured state-space models (SSMs) such as S4, stemming from the seminal work of Gu et al., are gaining popularity as effective approaches for modeling sequential data. Deep SSMs demonstrate outstanding performance across a diverse set of domains, at a reduced training and inference cost compared to attention-based transformers. Recent developments show that if the linear recurrence powering SSMs allows for multiplicative interactions between inputs and hidden states (e.g. GateLoop, Mamba, GLA), then the resulting architecture can surpass in both in accuracy and efficiency attention-powered foundation models trained on text, at scales of billion parameters. In this paper, we give theoretical grounding to this recent finding using tools from Rough Path Theory: we show that when random linear recurrences are equipped with simple input-controlled transitions (selectivity mechanism), then the hidden state is provably a low-dimensional projection of a powerful mathematical object called the signature of the input -- capturing non-linear interactions between tokens at distinct timescales. Our theory not only motivates the success of modern selective state-space models such as Mamba but also provides a solid framework to understand the expressive power of future SSM variants.
We propose a new method for fine registering multiple point clouds simultaneously. The approach is characterized by being dense, therefore point clouds are not reduced to pre-selected features in advance. Furthermore, the approach is robust against small overlaps and dynamic objects, since no direct correspondences are assumed between point clouds. Instead, all points are merged into a global point cloud, whose scattering is then iteratively reduced. This is achieved by dividing the global point cloud into uniform grid cells whose contents are subsequently modeled by normal distributions. We show that the proposed approach can be used in a sliding window continuous trajectory optimization combined with IMU measurements to obtain a highly accurate and robust LiDAR inertial odometry estimation. Furthermore, we show that the proposed approach is also suitable for large scale keyframe optimization to increase accuracy. We provide the source code and some experimental data on //github.com/davidskdds/DMSA_LiDAR_SLAM.git.
Atmospheric turbulence poses a challenge for the interpretation and visual perception of visual imagery due to its distortion effects. Model-based approaches have been used to address this, but such methods often suffer from artefacts associated with moving content. Conversely, deep learning based methods are dependent on large and diverse datasets that may not effectively represent any specific content. In this paper, we address these problems with a self-supervised learning method that does not require ground truth. The proposed method is not dependent on any dataset outside of the single data sequence being processed but is also able to improve the quality of any input raw sequences or pre-processed sequences. Specifically, our method is based on an accelerated Deep Image Prior (DIP), but integrates temporal information using pixel shuffling and a temporal sliding window. This efficiently learns spatio-temporal priors leading to a system that effectively mitigates atmospheric turbulence distortions. The experiments show that our method improves visual quality results qualitatively and quantitatively.
Automated Layout Design and Control of Robust Cooperative Grasped-Load Aerial Transportation Systems
We present a novel approach to cooperative aerial transportation through a team of drones, using optimal control theory and a hierarchical control strategy. We assume the drones are connected to the payload through rigid attachments, essentially transforming the whole system into a larger flying object with "thrust modules" at the attachment locations of the drones. We investigate the optimal arrangement of the thrust modules around the payload, so that the resulting system is robust to disturbances. We choose the $\mathcal{H}_2$ norm as a measure of robustness, and propose an iterative optimization routine to compute the optimal layout of the vehicles around the object. We experimentally validate our approach using four drones and comparing the disturbance rejection performances achieved by two different layouts (the optimal one and a sub-optimal one), and observe that the results match our predictions.
Non-flat surfaces pose difficulties for robots operating in unstructured environments. Reconstructions of uneven surfaces may only be partially possible due to non-compliant end-effectors and limitations on vision systems such as transparency, reflections, and occlusions. This study achieves blind surface reconstruction by harnessing the robotic manipulator's kinematic data and a compliant tactile sensing module, which incorporates inertial, magnetic, and pressure sensors. The module's flexibility enables us to estimate contact positions and surface normals by analyzing its deformation during interactions with unknown objects. While previous works collect only positional information, we include the local normals in a geometrical approach to estimate curvatures between adjacent contact points. These parameters then guide a spline-based patch generation, which allows us to recreate larger surfaces without an increase in complexity while reducing the time-consuming step of probing the surface. Experimental validation demonstrates that this approach outperforms an off-the-shelf vision system in estimation accuracy. Moreover, this compliant haptic method works effectively even when the manipulator's approach angle is not aligned with the surface normals, which is ideal for unknown non-flat surfaces.
In science we are interested in finding the governing equations, the dynamical rules, underlying empirical phenomena. While traditionally scientific models are derived through cycles of human insight and experimentation, recently deep learning (DL) techniques have been advanced to reconstruct dynamical systems (DS) directly from time series data. State-of-the-art dynamical systems reconstruction (DSR) methods show promise in capturing invariant and long-term properties of observed DS, but their ability to generalize to unobserved domains remains an open challenge. Yet, this is a crucial property we would expect from any viable scientific theory. In this work, we provide a formal framework that addresses generalization in DSR. We explain why and how out-of-domain (OOD) generalization (OODG) in DSR profoundly differs from OODG considered elsewhere in machine learning. We introduce mathematical notions based on topological concepts and ergodic theory to formalize the idea of learnability of a DSR model. We formally prove that black-box DL techniques, without adequate structural priors, generally will not be able to learn a generalizing DSR model. We also show this empirically, considering major classes of DSR algorithms proposed so far, and illustrate where and why they fail to generalize across the whole phase space. Our study provides the first comprehensive mathematical treatment of OODG in DSR, and gives a deeper conceptual understanding of where the fundamental problems in OODG lie and how they could possibly be addressed in practice.
The autonomous quadrotor's flying speed has kept increasing in the past 5 years, especially in the field of autonomous drone racing. However, the majority of the research mainly focuses on the aggressive flight of a single quadrotor. In this letter, we propose a novel method called Pairwise Model Predictive Control (PMPC) that can guide two quadrotors online to fly through the waypoints with minimum time without collisions. The flight task is first modeled as a nonlinear optimization problem and then an efficient two-step mass point velocity search method is used to provide initial values and references to improve the solving efficiency so that the method can run online with a frequency of 50 Hz and can handle dynamic waypoints. The simulation and real-world experiments validate the feasibility of the proposed method and in the real-world experiments, the two quadrotors can achieve a top speed of 8.1m/s in a 6-waypoint racing track in a compact flying arena of 6m*4m*2m.
When is heterogeneity in the composition of an autonomous robotic team beneficial and when is it detrimental? We investigate and answer this question in the context of a minimally viable model that examines the role of heterogeneous speeds in perimeter defense problems, where defenders share a total allocated speed budget. We consider two distinct problem settings and develop strategies based on dynamic programming and on local interaction rules. We present a theoretical analysis of both approaches and our results are extensively validated using simulations. Interestingly, our results demonstrate that the viability of heterogeneous teams depends on the amount of information available to the defenders. Moreover, our results suggest a universality property: across a wide range of problem parameters the optimal ratio of the speeds of the defenders remains nearly constant.
The development of unmanned aerial vehicles (UAVs) has been gaining momentum in recent years owing to technological advances and a significant reduction in their cost. UAV technology can be used in a wide range of domains, including communication, agriculture, security, and transportation. It may be useful to group the UAVs into clusters/flocks in certain domains, and various challenges associated with UAV usage can be alleviated by clustering. Several computational challenges arise in UAV flock management, which can be solved by using machine learning (ML) methods. In this survey, we describe the basic terms relating to UAVS and modern ML methods, and we provide an overview of related tutorials and surveys. We subsequently consider the different challenges that appear in UAV flocks. For each issue, we survey several machine learning-based methods that have been suggested in the literature to handle the associated challenges. Thereafter, we describe various open issues in which ML can be applied to solve the different challenges of flocks, and we suggest means of using ML methods for this purpose. This comprehensive review may be useful for both researchers and developers in providing a wide view of various aspects of state-of-the-art ML technologies that are applicable to flock management.
We consider the problem of explaining the predictions of graph neural networks (GNNs), which otherwise are considered as black boxes. Existing methods invariably focus on explaining the importance of graph nodes or edges but ignore the substructures of graphs, which are more intuitive and human-intelligible. In this work, we propose a novel method, known as SubgraphX, to explain GNNs by identifying important subgraphs. Given a trained GNN model and an input graph, our SubgraphX explains its predictions by efficiently exploring different subgraphs with Monte Carlo tree search. To make the tree search more effective, we propose to use Shapley values as a measure of subgraph importance, which can also capture the interactions among different subgraphs. To expedite computations, we propose efficient approximation schemes to compute Shapley values for graph data. Our work represents the first attempt to explain GNNs via identifying subgraphs explicitly and directly. Experimental results show that our SubgraphX achieves significantly improved explanations, while keeping computations at a reasonable level.
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