In many unmanned aerial vehicle (UAV) applications for surveillance and data collection, it is not possible to reach all requested locations due to the given maximum flight time. Hence, the requested locations must be prioritized and the problem of selecting the most important locations is modeled as an Orienteering Problem (OP). To fully exploit the kinematic properties of the UAV in such scenarios, we combine the OP with the generation of time-optimal trajectories with bounds on velocity and acceleration. We define the resulting problem as the Kinematic Orienteering Problem (KOP) and propose an exact mixed-integer formulation together with a Large Neighborhood Search (LNS) as a heuristic solution method. We demonstrate the effectiveness of our approach based on Orienteering instances from the literature and benchmark against optimal solutions of the Dubins Orienteering Problem (DOP) as the state-of-the-art. Additionally, we show by simulation \color{black} that the resulting solutions can be tracked precisely by a modern MPC-based flight controller. Since we demonstrate that the state-of-the-art in generating time-optimal trajectories in multiple dimensions is not generally correct, we further present an improved analytical method for time-optimal trajectory generation.
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The problem to compute the vertices of a polytope given by affine inequalities is called vertex enumeration. The inverse problem, which is equivalent by polarity, is called the convex hull problem. We introduce `approximate vertex enumeration' as the problem to compute the vertices of a polytope which is close to the original polytope given by affine inequalities. In contrast to exact vertex enumerations, both polytopes are not required to be combinatorially equivalent. Two algorithms for this problem are introduced. The first one is an approximate variant of Motzkin's double description method. Only under certain strong conditions, which are not acceptable for practical reasons, we were able to prove correctness of this method for polytopes of arbitrary dimension. The second method, called shortcut algorithm, is based on constructing a plane graph and is restricted to polytopes of dimension 2 and 3. We prove correctness of the shortcut algorithm. As a consequence, we also obtain correctness of the approximate double description method, only for dimension 2 and 3 but without any restricting conditions as still required for higher dimensions. We show that for dimension 2 and 3 both algorithm remain correct if imprecise arithmetic is used and the computational error caused by imprecision is not too high. Both algorithms were implemented. The numerical examples motivate the approximate vertex enumeration problem by showing that the approximate problem is often easier to solve than the exact vertex enumeration problem. It remains open whether or not the approximate double description method (without any restricting condition) is correct for polytopes of dimension 4 and higher.
We propose a new class of models for variable clustering called Asymptotic Independent block (AI-block) models, which defines population-level clusters based on the independence of the maxima of a multivariate stationary mixing random process among clusters. This class of models is identifiable, meaning that there exists a maximal element with a partial order between partitions, allowing for statistical inference. We also present an algorithm for recovering the clusters of variables without specifying the number of clusters \emph{a priori}. Our work provides some theoritical insights into the consistency of our algorithm, demonstrating that under certain conditions it can effectively identify clusters in the data with a computational complexity that is polynomial in the dimension. This implies that groups can be learned nonparametrically in which block maxima of a dependent process are only sub-asymptotic.
We propose a spatio-temporal mixing kinematic data estimation method to estimate the shape of the colon with deformations caused by colonoscope insertion. Endoscope tracking or a navigation system that navigates physicians to target positions is needed to reduce such complications as organ perforations. Although many previous methods focused to track bronchoscopes and surgical endoscopes, few number of colonoscope tracking methods were proposed. This is because the colon largely deforms during colonoscope insertion. The deformation causes significant tracking errors. Colon deformation should be taken into account in the tracking process. We propose a colon shape estimation method using a Kinematic Spatio-Temporal data Mixer (KST-Mixer) that can be used during colonoscope insertions to the colon. Kinematic data of a colonoscope and the colon, including positions and directions of their centerlines, are obtained using electromagnetic and depth sensors. The proposed method separates the data into sub-groups along the spatial and temporal axes. The KST-Mixer extracts kinematic features and mix them along the spatial and temporal axes multiple times. We evaluated colon shape estimation accuracies in phantom studies. The proposed method achieved 11.92 mm mean Euclidean distance error, the smallest of the previous methods. Statistical analysis indicated that the proposed method significantly reduced the error compared to the previous methods.
To enable space mission sets like on-orbit servicing and manufacturing, agents in close proximity maybe operating too close to yield resolved localization solutions to operators from ground sensors. This leads to a requirement on the systems need to maintain a catalog of their local neighborhood, however, this may impose a large burden on each agent by requiring updating and maintenance of this catalog at each node. To alleviate this burden, this paper considers the case of a single satellite agent (a chief) updating a single catalog. More specifically, we consider the case of numerous satellite deputy agents in a local neighborhood of a chief, the goal of the chief satellite is to maintain and update a catalog of all agents within this neighborhood through onboard measurements. We consider the agents having relative translational and attitude motion dynamics between the chief and deputy, with the chief centered at the origin of the frame. We provide an end-to-end solution of the this problem through providing both a supervisory control method coupled with a Bayesian Filter that propagates the belief state and provides the catalog solutions to the supervisor. The goal of the supervisory controller is to determine which agent to look at and at which times while adhering to constraints of the chief satellite. We provide a numerical validation to this problem with three agents.
Stochastic gradient descent plays a fundamental role in nearly all applications of deep learning. However its ability to converge to a global minimum remains shrouded in mystery. In this paper we propose to study the behavior of the loss function on fixed mini-batches along SGD trajectories. We show that the loss function on a fixed batch appears to be remarkably convex-like. In particular for ResNet the loss for any fixed mini-batch can be accurately modeled by a quadratic function and a very low loss value can be reached in just one step of gradient descent with sufficiently large learning rate. We propose a simple model that allows to analyze the relationship between the gradients of stochastic mini-batches and the full batch. Our analysis allows us to discover the equivalency between iterate aggregates and specific learning rate schedules. In particular, for Exponential Moving Average (EMA) and Stochastic Weight Averaging we show that our proposed model matches the observed training trajectories on ImageNet. Our theoretical model predicts that an even simpler averaging technique, averaging just two points a many steps apart, significantly improves accuracy compared to the baseline. We validated our findings on ImageNet and other datasets using ResNet architecture.
We initiate a study of supervised learning from many independent sequences ("trajectories") of non-independent covariates, reflecting tasks in sequence modeling, control, and reinforcement learning. Conceptually, our multi-trajectory setup sits between two traditional settings in statistical learning theory: learning from independent examples and learning from a single auto-correlated sequence. Our conditions for efficient learning generalize the former setting--trajectories must be non-degenerate in ways that extend standard requirements for independent examples. Notably, we do not require that trajectories be ergodic, long, nor strictly stable. For linear least-squares regression, given $n$-dimensional examples produced by $m$ trajectories, each of length $T$, we observe a notable change in statistical efficiency as the number of trajectories increases from a few (namely $m \lesssim n$) to many (namely $m \gtrsim n$). Specifically, we establish that the worst-case error rate of this problem is $\Theta(n / m T)$ whenever $m \gtrsim n$. Meanwhile, when $m \lesssim n$, we establish a (sharp) lower bound of $\Omega(n^2 / m^2 T)$ on the worst-case error rate, realized by a simple, marginally unstable linear dynamical system. A key upshot is that, in domains where trajectories regularly reset, the error rate eventually behaves as if all of the examples were independent, drawn from their marginals. As a corollary of our analysis, we also improve guarantees for the linear system identification problem.
Safety in the automotive domain is a well-known topic, which has been in constant development in the past years. The complexity of new systems that add more advanced components in each function has opened new trends that have to be covered from the safety perspective. In this case, not only specifications and requirements have to be covered but also scenarios, which cover all relevant information of the vehicle environment. Many of them are not yet still sufficient defined or considered. In this context, Safety of the Intended Functionality (SOTIF) appears to ensure the system when it might fail because of technological shortcomings or misuses by users. An identification of the plausibly insufficiencies of ADAS/ADS functions has to be done to discover the potential triggering conditions that can lead to these unknown scenarios, which might effect a hazardous behaviour. The main goal of this publication is the definition of an use case to identify these triggering conditions that have been applied to the collision avoidance function implemented in our self-developed mobile Hardware-in-Loop (HiL) platform.
In recent years, cloud and edge architectures have gained tremendous focus for offloading computationally heavy applications. From machine learning and Internet of Thing (IOT) to industrial procedures and robotics, cloud computing have been used extensively for data processing and storage purposes, thanks to its "infinite" resources. On the other hand, cloud computing is characterized by long time delays due to the long distance between the cloud servers and the machine requesting the resources. In contrast, edge computing provides almost real-time services since edge servers are located significantly closer to the source of data. This capability sets edge computing as an ideal option for real-time applications, like high level control, for resource-constrained platforms. In order to utilize the edge resources, several technologies, with basic ones as containers and orchestrators like Kubernetes, have been developed to provide an environment with many features, based on each application's requirements. In this context, this works presents the implementation and evaluation of a novel edge architecture based on Kubernetes orchestration for controlling the trajectory of a resource-constrained Unmanned Aerial Vehicle (UAV) by enabling Model Predictive Control (MPC).
Though denoising diffusion probabilistic models (DDPMs) have achieved remarkable generation results, the low sampling efficiency of DDPMs still limits further applications. Since DDPMs can be formulated as diffusion ordinary differential equations (ODEs), various fast sampling methods can be derived from solving diffusion ODEs. However, we notice that previous sampling methods with fixed analytical form are not robust with the error in the noise estimated from pretrained diffusion models. In this work, we construct an error-robust Adams solver (ERA-Solver), which utilizes the implicit Adams numerical method that consists of a predictor and a corrector. Different from the traditional predictor based on explicit Adams methods, we leverage a Lagrange interpolation function as the predictor, which is further enhanced with an error-robust strategy to adaptively select the Lagrange bases with lower error in the estimated noise. Experiments on Cifar10, LSUN-Church, and LSUN-Bedroom datasets demonstrate that our proposed ERA-Solver achieves 5.14, 9.42, and 9.69 Fenchel Inception Distance (FID) for image generation, with only 10 network evaluations.
The time and effort involved in hand-designing deep neural networks is immense. This has prompted the development of Neural Architecture Search (NAS) techniques to automate this design. However, NAS algorithms tend to be slow and expensive; they need to train vast numbers of candidate networks to inform the search process. This could be alleviated if we could partially predict a network's trained accuracy from its initial state. In this work, we examine the overlap of activations between datapoints in untrained networks and motivate how this can give a measure which is usefully indicative of a network's trained performance. We incorporate this measure into a simple algorithm that allows us to search for powerful networks without any training in a matter of seconds on a single GPU, and verify its effectiveness on NAS-Bench-101, NAS-Bench-201, NATS-Bench, and Network Design Spaces. Our approach can be readily combined with more expensive search methods; we examine a simple adaptation of regularised evolutionary search. Code for reproducing our experiments is available at //github.com/BayesWatch/nas-without-training.
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