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This work proposes a discretization of the acoustic wave equation with possibly oscillatory coefficients based on a superposition of discrete solutions to spatially localized subproblems computed with an implicit time discretization. Based on exponentially decaying entries of the global system matrices and an appropriate partition of unity, it is proved that the superposition of localized solutions is appropriately close to the solution of the (global) implicit scheme. It is thereby justified that the localized (and especially parallel) computation on multiple overlapping subdomains is reasonable. Moreover, a re-start is introduced after a certain amount of time steps to maintain a moderate overlap of the subdomains. Overall, the approach may be understood as a domain decomposition strategy (in space and time) that completely avoids inner iterations. Numerical examples are presented.

Autonomous vehicles rely on LiDAR sensors to perceive the environment. Adverse weather conditions like rain, snow, and fog negatively affect these sensors, reducing their reliability by introducing unwanted noise in the measurements. In this work, we tackle this problem by proposing a novel approach for detecting adverse weather effects in LiDAR data. We reformulate this problem as an outlier detection task and use an energy-based framework to detect outliers in point clouds. More specifically, our method learns to associate low energy scores with inlier points and high energy scores with outliers allowing for robust detection of adverse weather effects. In extensive experiments, we show that our method performs better in adverse weather detection and has higher robustness to unseen weather effects than previous state-of-the-art methods. Furthermore, we show how our method can be used to perform simultaneous outlier detection and semantic segmentation. Finally, to help expand the research field of LiDAR perception in adverse weather, we release the SemanticSpray dataset, which contains labeled vehicle spray data in highway-like scenarios. The dataset is available at //semantic-spray-dataset.github.io .

Perception algorithms that provide estimates of their uncertainty are crucial to the development of autonomous robots that can operate in challenging and uncontrolled environments. Such perception algorithms provide the means for having risk-aware robots that reason about the probability of successfully completing a task when planning. There exist perception algorithms that come with models of their uncertainty; however, these models are often developed with assumptions, such as perfect data associations, that do not hold in the real world. Hence the resultant estimated uncertainty is a weak lower bound. To tackle this problem we present introspective perception - a novel approach for predicting accurate estimates of the uncertainty of perception algorithms deployed on mobile robots. By exploiting sensing redundancy and consistency constraints naturally present in the data collected by a mobile robot, introspective perception learns an empirical model of the error distribution of perception algorithms in the deployment environment and in an autonomously supervised manner. In this paper, we present the general theory of introspective perception and demonstrate successful implementations for two different perception tasks. We provide empirical results on challenging real-robot data for introspective stereo depth estimation and introspective visual simultaneous localization and mapping and show that they learn to predict their uncertainty with high accuracy and leverage this information to significantly reduce state estimation errors for an autonomous mobile robot.

Continuum robots are promising candidates for interactive tasks in medical and industrial applications due to their unique shape, compliance, and miniaturization capability. Accurate and real-time shape sensing is essential for such tasks yet remains a challenge. Embedded shape sensing has high hardware complexity and cost, while vision-based methods require stereo setup and struggle to achieve real-time performance. This paper proposes the first eye-to-hand monocular approach to continuum robot shape sensing. Utilizing a deep encoder-decoder network, our method, MoSSNet, eliminates the computation cost of stereo matching and reduces requirements on sensing hardware. In particular, MoSSNet comprises an encoder and three parallel decoders to uncover spatial, length, and contour information from a single RGB image, and then obtains the 3D shape through curve fitting. A two-segment tendon-driven continuum robot is used for data collection and testing, demonstrating accurate (mean shape error of 0.91 mm, or 0.36% of robot length) and real-time (70 fps) shape sensing on real-world data. Additionally, the method is optimized end-to-end and does not require fiducial markers, manual segmentation, or camera calibration. Code and datasets will be made available at //github.com/ContinuumRoboticsLab/MoSSNet.

Offloading high-demanding applications to the edge provides better quality of experience (QoE) for users with limited hardware devices. However, to maintain a competitive QoE, infrastructure, and service providers must adapt to users' different mobility patterns, which can be challenging, especially for location-based services (LBS). Another issue that needs to be tackled is the increasing demand for user privacy protection. With less (accurate) information regarding user location, preferences, and usage patterns, forecasting the performance of offloading mechanisms becomes even more challenging. This work discusses the impacts of users' privacy and mobility when offloading to the edge. Different privacy and mobility scenarios are simulated and discussed to shed light on the trade-offs (e.g., privacy protection at the cost of increased latency) among privacy protection, mobility, and offloading performance.

We present a finite element scheme for fractional diffusion problems with varying diffusivity and fractional order. We consider a symmetric integral form of these nonlocal equations defined on general geometries and in arbitrary bounded domains. A number of challenges are encountered when discretizing these equations. The first comes from the heterogeneous kernel singularity in the fractional integral operator. The second comes from the dense discrete operator with its quadratic growth in memory footprint and arithmetic operations. An additional challenge comes from the need to handle volume conditions-the generalization of classical local boundary conditions to the nonlocal setting. Satisfying these conditions requires that the effect of the whole domain, including both the interior and exterior regions, can be computed on every interior point in the discretization. Performed directly, this would result in quadratic complexity. To address these challenges, we propose a strategy that decomposes the stiffness matrix into three components. The first is a sparse matrix that handles the singular near-field separately and is computed by adapting singular quadrature techniques available for the homogeneous case to the case of spatially variable order. The second component handles the remaining smooth part of the near-field as well as the far field and is approximated by a hierarchical $\mathcal{H}^{2}$ matrix that maintains linear complexity in storage and operations. The third component handles the effect of the global mesh at every node and is written as a weighted mass matrix whose density is computed by a fast-multipole type method. The resulting algorithm has therefore overall linear space and time complexity. Analysis of the consistency of the stiffness matrix is provided and numerical experiments are conducted to illustrate the convergence and performance of the proposed algorithm.

Maximum Inner Product Search (MIPS) is a ubiquitous task in machine learning applications such as recommendation systems. Given a query vector and $n$ atom vectors in $d$-dimensional space, the goal of MIPS is to find the atom that has the highest inner product with the query vector. Existing MIPS algorithms scale at least as $O(\sqrt{d})$, which becomes computationally prohibitive in high-dimensional settings. In this work, we present BanditMIPS, a novel randomized MIPS algorithm whose complexity is independent of $d$. BanditMIPS estimates the inner product for each atom by subsampling coordinates and adaptively evaluates more coordinates for more promising atoms. The specific adaptive sampling strategy is motivated by multi-armed bandits. We provide theoretical guarantees that BanditMIPS returns the correct answer with high probability, while improving the complexity in $d$ from $O(\sqrt{d})$ to $O(1)$. We also perform experiments on four synthetic and real-world datasets and demonstrate that BanditMIPS outperforms prior state-of-the-art algorithms. For example, in the Movie Lens dataset ($n$=4,000, $d$=6,000), BanditMIPS is 20$\times$ faster than the next best algorithm while returning the same answer. BanditMIPS requires no preprocessing of the data and includes a hyperparameter that practitioners may use to trade off accuracy and runtime. We also propose a variant of our algorithm, named BanditMIPS-$\alpha$, which achieves further speedups by employing non-uniform sampling across coordinates. Finally, we demonstrate how known preprocessing techniques can be used to further accelerate BanditMIPS, and discuss applications to Matching Pursuit and Fourier analysis.

Autonomous racing control is a challenging research problem as vehicles are pushed to their limits of handling to achieve an optimal lap time; therefore, vehicles exhibit highly nonlinear and complex dynamics. Difficult-to-model effects, such as drifting, aerodynamics, chassis weight transfer, and suspension can lead to infeasible and suboptimal trajectories. While offline planning allows optimizing a full reference trajectory for the minimum lap time objective, such modeling discrepancies are particularly detrimental when using offline planning, as planning model errors compound with controller modeling errors. Gaussian Process Regression (GPR) can compensate for modeling errors. However, previous works primarily focus on modeling error in real-time control without consideration for how the model used in offline planning can affect the overall performance. In this work, we propose a double-GPR error compensation algorithm to reduce model uncertainties; specifically, we compensate both the planner's model and controller's model with two respective GPR-based error compensation functions. Furthermore, we design an iterative framework to re-collect error-rich data using the racing control system. We test our method in the high-fidelity racing simulator Gran Turismo Sport (GTS); we find that our iterative, double-GPR compensation functions improve racing performance and iteration stability in comparison to a single compensation function applied merely for real-time control.

Real-time learning is crucial for robotic agents adapting to ever-changing, non-stationary environments. A common setup for a robotic agent is to have two different computers simultaneously: a resource-limited local computer tethered to the robot and a powerful remote computer connected wirelessly. Given such a setup, it is unclear to what extent the performance of a learning system can be affected by resource limitations and how to efficiently use the wirelessly connected powerful computer to compensate for any performance loss. In this paper, we implement a real-time learning system called the Remote-Local Distributed (ReLoD) system to distribute computations of two deep reinforcement learning (RL) algorithms, Soft Actor-Critic (SAC) and Proximal Policy Optimization (PPO), between a local and a remote computer. The performance of the system is evaluated on two vision-based control tasks developed using a robotic arm and a mobile robot. Our results show that SAC's performance degrades heavily on a resource-limited local computer. Strikingly, when all computations of the learning system are deployed on a remote workstation, SAC fails to compensate for the performance loss, indicating that, without careful consideration, using a powerful remote computer may not result in performance improvement. However, a carefully chosen distribution of computations of SAC consistently and substantially improves its performance on both tasks. On the other hand, the performance of PPO remains largely unaffected by the distribution of computations. In addition, when all computations happen solely on a powerful tethered computer, the performance of our system remains on par with an existing system that is well-tuned for using a single machine. ReLoD is the only publicly available system for real-time RL that applies to multiple robots for vision-based tasks.

The ongoing discussion regarding the utilization of individual research performance for academic hiring, funding allocation, and resource distribution has prompted the need for improved metrics. While traditional measures such as total publications, citations count, and the h-index provide a general overview of research impact, they fall short of capturing the continuous contribution of researchers over time. To address this limitation, we propose the implementation of the Kz index, which takes into account both publication impact and age. In this study, we calculated Kz scores for 376 research profiles. Kz reveals that the researchers with the same h-index can exhibit different Kz scores, and vice versa. Furthermore, we observed instances where researchers with lower citation counts obtained higher Kz scores, and vice versa. Interestingly, the Kz metric follows a log-normal distribution. It highlights its potential as a valuable tool for ranking researchers and facilitating informed decision-making processes. By measuring the continuous research impact, we enable fair evaluations, enhance decision-making processes, and provide focused career advancement support and funding opportunities.