The state-of-the-art (SoTA) surface normal estimators (SNEs) generally translate depth images into surface normal maps in an end-to-end fashion. Although such SNEs have greatly minimized the trade-off between efficiency and accuracy, their performance on spatial discontinuities, e.g., edges and ridges, is still unsatisfactory. To address this issue, this paper first introduces a novel multi-directional dynamic programming strategy to adaptively determine inliers (co-planar 3D points) by minimizing a (path) smoothness energy. The depth gradients can then be refined iteratively using a novel recursive polynomial interpolation algorithm, which helps yield more reasonable surface normals. Our introduced spatial discontinuity-aware (SDA) depth gradient refinement strategy is compatible with any depth-to-normal SNEs. Our proposed SDA-SNE achieves much greater performance than all other SoTA approaches, especially near/on spatial discontinuities. We further evaluate the performance of SDA-SNE with respect to different iterations, and the results suggest that it converges fast after only a few iterations. This ensures its high efficiency in various robotics and computer vision applications requiring real-time performance. Additional experiments on the datasets with different extents of random noise further validate our SDA-SNE's robustness and environmental adaptability. Our source code, demo video, and supplementary material are publicly available at mias.group/SDA-SNE.

A fundamental problem in science and engineering is designing optimal control policies that steer a given system towards a desired outcome. This work proposes Control Physics-Informed Neural Networks (Control PINNs) that simultaneously solve for a given system state, and for the optimal control signal, in a one-stage framework that conforms to the underlying physical laws. Prior approaches use a two-stage framework that first models and then controls a system in sequential order. In contrast, a Control PINN incorporates the required optimality conditions in its architecture and in its loss function. The success of Control PINNs is demonstrated by solving the following open-loop optimal control problems: (i) an analytical problem, (ii) a one-dimensional heat equation, and (iii) a two-dimensional predator-prey problem.

In semi-supervised graph-based binary classifier learning, a subset of known labels $\hat{x}_i$ are used to infer unknown labels, assuming that the label signal $\mathbf{x}$ is smooth with respect to a similarity graph specified by a Laplacian matrix. When restricting labels $x_i$ to binary values, the problem is NP-hard. While a conventional semi-definite programming relaxation (SDR) can be solved in polynomial time using, for example, the alternating direction method of multipliers (ADMM), the complexity of projecting a candidate matrix $\mathbf{M}$ onto the positive semi-definite (PSD) cone ($\mathbf{M} \succeq 0$) per iteration remains high. In this paper, leveraging a recent linear algebraic theory called Gershgorin disc perfect alignment (GDPA), we propose a fast projection-free method by solving a sequence of linear programs (LP) instead. Specifically, we first recast the SDR to its dual, where a feasible solution $\mathbf{H} \succeq 0$ is interpreted as a Laplacian matrix corresponding to a balanced signed graph minus the last node. To achieve graph balance, we split the last node into two, each retains the original positive / negative edges, resulting in a new Laplacian $\bar{\mathbf{H}}$. We repose the SDR dual for solution $\bar{\mathbf{H}}$, then replace the PSD cone constraint $\bar{\mathbf{H}} \succeq 0$ with linear constraints derived from GDPA -- sufficient conditions to ensure $\bar{\mathbf{H}}$ is PSD -- so that the optimization becomes an LP per iteration. Finally, we extract predicted labels from converged solution $\bar{\mathbf{H}}$. Experiments show that our algorithm enjoyed a $28\times$ speedup over the next fastest scheme while achieving comparable label prediction performance.

After a pandemic-driven cloud adoption boom in the enterprise, costs are finally coming under a microscope. More than a third of businesses report having cloud budget overruns of up to 40%, according to a recent poll by observability software vendor Pepperdata. A separate survey from Flexera found that optimizing the existing use of cloud services is a top initiative at 59% of companies -- cost being the main motivation. An entire cottage industry of startups has sprung up around optimizing cloud compute. But one in the race, Sync Computing, claims to uniquely tie business objectives like cost and runtime reduction directly to low-level infrastructure configurations.

Abstract--Dynamic locomotion in rough terrain requires accurate foot placement, collision avoidance, and planning of the underactuated dynamics of the system. Reliably optimizing for such motions and interactions in the presence of imperfect and often incomplete perceptive information is challenging. We present a complete perception, planning, and control pipeline, that can optimize motions for all degrees of freedom of the robot in real-time. To mitigate the numerical challenges posed by the terrain a sequence of convex inequality constraints is extracted as local approximations of foothold feasibility and embedded into an online model predictive controller. Steppability classification, plane segmentation, and a signed distance field are precomputed per elevation map to minimize the computational effort during the optimization. In the shown configuration, the top foothold is 60 cm above the lowest foothold. These approaches build on a strict hierarchy of first selecting footholds and optimizing torso motion afterward. Still, complex terrains that jointly optimized has shown impressive results in simulation require precise foot placements, e.g., negative obstacles and [18]-[20] and removes the need for engineered torsofoot stepping stones as shown in Figure 1, remain difficult. Complex motions can be automatically A key challenge lies in the fact that both the terrain and discovered by including the entire terrain in the optimization. Additionally, due to the non-convexity, nonlinearity, mature methods exist for perceptive locomotion with a slow, and discontinuity introduced by optimizing over static gait [4]-[8] and for blind, dynamic locomotion that arbitrary terrain, these methods can get stuck in poor local assumes flat terrain [9]-[11]. Dedicated work on providing an initial guess is recently shown the ability to generalize blind locomotion needed to find feasible motions reliably [21]. Still, tightly integrating perception to achieve coordinated and This work presents a planning and control framework precise foot placement remains an active research problem.

Federated learning (FL) has received a surge of interest in recent years thanks to its benefits in data privacy protection, efficient communication, and parallel data processing. Also, with appropriate algorithmic designs, one could achieve the desirable linear speedup for convergence effect in FL. However, most existing works on FL are limited to systems with i.i.d. data and centralized parameter servers and results on decentralized FL with heterogeneous datasets remains limited. Moreover, whether or not the linear speedup for convergence is achievable under fully decentralized FL with data heterogeneity remains an open question. In this paper, we address these challenges by proposing a new algorithm, called NET-FLEET, for fully decentralized FL systems with data heterogeneity. The key idea of our algorithm is to enhance the local update scheme in FL (originally intended for communication efficiency) by incorporating a recursive gradient correction technique to handle heterogeneous datasets. We show that, under appropriate parameter settings, the proposed NET-FLEET algorithm achieves a linear speedup for convergence. We further conduct extensive numerical experiments to evaluate the performance of the proposed NET-FLEET algorithm and verify our theoretical findings.

This paper introduces the correlated arc orienteering problem (CAOP), where the task is to find routes for a team of robots to maximize the collection of rewards associated with features in the environment. These features can be one-dimensional or points in the environment, and can have spatial correlation, i.e., visiting a feature in the environment may provide a portion of the reward associated with a correlated feature. A robot incurs costs as it traverses the environment, and the total cost for its route is limited by a resource constraint such as battery life or operation time. As environments are often large, we permit multiple depots where the robots must start and end their routes. The CAOP generalizes the correlated orienteering problem (COP), where the rewards are only associated with point features, and the arc orienteering problem (AOP), where the rewards are not spatially correlated. We formulate a mixed integer quadratic program (MIQP) that formalizes the problem and gives optimal solutions. However, the problem is NP-hard, and therefore we develop an efficient greedy constructive algorithm. We illustrate the problem with two different applications: informative path planning for methane gas leak detection and coverage of road networks.

GANs generate new designs from an existing dataset utilizing a generator and a discriminator which are usually Deep Generative design has been growing across the Neural Networks (DNNs). The objective function of GANs design community as a viable method for design should be differentiable to utilize gradient-based optimization space exploration. Thermal design is more complex while reward of a deep RL can be defined based on the than mechanical or aerodynamic design because design requirements (Chen & Ahmed, 2021b). of the additional convection-diffusion equation and its pertinent boundary interaction. We Shape and Topology Optimization (TO) play a major role in present a generative thermal design using cooperative Generative models in engineering design (Chen & Ahmed, multi-agent deep reinforcement learning 2021a). Engineering design often require Finite Element and continuous geometric representation of the Analysis (FEA) or Computational Fluid Dynamics (CFD) fluid and solid domain. The proposed framework to assess the performance of the output design (Hoyer et al., consists of a pre-trained neural network surrogate 2019). These numerical approaches are computationally model as an environment to predict heat transfer expensive and require human expertise (Regenwetter et al., and pressure drop of the generated geometries.

Terahertz (THz) wireless networks are expected to catalyze the beyond fifth generation (B5G) era. However, due to the directional nature and the line-of-sight demand of THz links, as well as the ultra-dense deployment of THz networks, a number of challenges that the medium access control (MAC) layer needs to face are created. In more detail, the need of rethinking user association and resource allocation strategies by incorporating artificial intelligence (AI) capable of providing "real-time" solutions in complex and frequently changing environments becomes evident. Moreover, to satisfy the ultra-reliability and low-latency demands of several B5G applications, novel mobility management approaches are required. Motivated by this, this article presents a holistic MAC layer approach that enables intelligent user association and resource allocation, as well as flexible and adaptive mobility management, while maximizing systems' reliability through blockage minimization. In more detail, a fast and centralized joint user association, radio resource allocation, and blockage avoidance by means of a novel metaheuristic-machine learning framework is documented, that maximizes the THz networks performance, while minimizing the association latency by approximately three orders of magnitude. To support, within the access point (AP) coverage area, mobility management and blockage avoidance, a deep reinforcement learning (DRL) approach for beam-selection is discussed. Finally, to support user mobility between coverage areas of neighbor APs, a proactive hand-over mechanism based on AI-assisted fast channel prediction is~reported.

Multiple mobile manipulators show superiority in the tasks requiring mobility and dexterity compared with a single robot, especially when manipulating/transporting bulky objects. When the object and the manipulators are rigidly connected, closed-chain will form and the motion of the whole system will be restricted onto a lower-dimensional manifold. However, current research on multi-robot motion planning did not fully consider the formation of the whole system, the redundancy of the mobile manipulator and obstacles in the environment, which make the tasks challenging. Therefore, this paper proposes a hierarchical framework to efficiently solve the above challenges, where the centralized layer plans the object's motion offline and the decentralized layer independently explores the redundancy of each robot in real-time. In addition, closed-chain, obstacle-avoidance and the lower bound of the formation constraints are guaranteed in the centralized layer, which cannot be achieved simultaneously by other planners. Moreover, capability map, which represents the distribution of the formation constraint, is applied to speed up the two layers. Both simulation and experimental results show that the proposed framework outperforms the benchmark planners significantly. The system could bypass or cross obstacles in cluttered environments, and the framework can be applied to different numbers of heterogeneous mobile manipulators.