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Rotation equivariance is a desirable property in many practical applications such as motion forecasting and 3D perception, where it can offer benefits like sample efficiency, better generalization, and robustness to input perturbations. Vector Neurons (VN) is a recently developed framework offering a simple yet effective approach for deriving rotation-equivariant analogs of standard machine learning operations by extending one-dimensional scalar neurons to three-dimensional "vector neurons." We introduce a novel "VN-Transformer" architecture to address several shortcomings of the current VN models. Our contributions are: $(i)$ we derive a rotation-equivariant attention mechanism which eliminates the need for the heavy feature preprocessing required by the original Vector Neurons models; $(ii)$ we extend the VN framework to support non-spatial attributes, expanding the applicability of these models to real-world datasets; $(iii)$ we derive a rotation-equivariant mechanism for multi-scale reduction of point-cloud resolution, greatly speeding up inference and training; $(iv)$ we show that small tradeoffs in equivariance ($\epsilon$-approximate equivariance) can be used to obtain large improvements in numerical stability and training robustness on accelerated hardware, and we bound the propagation of equivariance violations in our models. Finally, we apply our VN-Transformer to 3D shape classification and motion forecasting with compelling results.

We present a novel approach to path planning for robotic manipulators, in which paths are produced via iterative optimisation in the latent space of a generative model of robot poses. Constraints are incorporated through the use of constraint satisfaction classifiers operating on the same space. Optimisation leverages gradients through our learned models that provide a simple way to combine goal reaching objectives with constraint satisfaction, even in the presence of otherwise non-differentiable constraints. Our models are trained in a task-agnostic manner on randomly sampled robot poses. In baseline comparisons against a number of widely used planners, we achieve commensurate performance in terms of task success, planning time and path length, performing successful path planning with obstacle avoidance on a real 7-DoF robot arm.

The automatic synthesis of a policy through reinforcement learning (RL) from a given set of formal requirements depends on the construction of a reward signal and consists of the iterative application of many policy-improvement steps. The synthesis algorithm has to balance target, safety, and comfort requirements in a single objective and to guarantee that the policy improvement does not increase the number of safety-requirements violations, especially for safety-critical applications. In this work, we present a solution to the synthesis problem by solving its two main challenges: reward-shaping from a set of formal requirements and safe policy update. For the former, we propose an automatic reward-shaping procedure, defining a scalar reward signal compliant with the task specification. For the latter, we introduce an algorithm ensuring that the policy is improved in a safe fashion with high-confidence guarantees. We also discuss the adoption of a model-based RL algorithm to efficiently use the collected data and train a model-free agent on the predicted trajectories, where the safety violation does not have the same impact as in the real world. Finally, we demonstrate in standard control benchmarks that the resulting learning procedure is effective and robust even under heavy perturbations of the hyperparameters.

A network (CC-Net) based on complementary consistency training is proposed for semi-supervised left atrial image segmentation in this paper. From the perspective of complementary information, CC-Net efficiently utilizes unlabeled data and resolves the problem that semi-supervised segmentation algorithms currently in use have limited capacity to extract information from unlabeled data. A primary model and two complementary auxiliary models are part of the complementary symmetric structure of the CC-Net. The inter-model perturbation is formed between the main model and the auxiliary model to form complementary consistency training. The complementary information between the two auxiliary models helps the main model to focus on the fuzzy region effectively. Additionally, forcing consistency between the main model and the auxiliary models makes it easier to obtain decision boundaries with low uncertainty. CC-Net was validated in the benchmark dataset of the 2018 Atrial Segmentation Challenge. The Dice reached of 89.82% with 10% labeled data training and 91.27% with 20% labeled data training. By comparing with current state-of-the-art algorithms, CC-Net has the best segmentation performance and robustness. Our code is publicly available at //github.com/Cuthbert-Huang/CC-Net.

In this paper, we study unmanned aerial vehicles (UAVs) assisted wireless data aggregation (WDA) in multicluster networks, where multiple UAVs simultaneously perform different WDA tasks via over-the-air computation (AirComp) without terrestrial base stations. This work focuses on maximizing the minimum amount of WDA tasks performed among all clusters by optimizing the UAV's trajectory and transceiver design as well as cluster scheduling and association, while considering the WDA accuracy requirement. Such a joint design is critical for interference management in multi-cluster AirComp networks, via enhancing the signal quality between each UAV and its associated cluster for signal alignment and meanwhile reducing the inter-cluster interference between each UAV and its nonassociated clusters. Although it is generally challenging to optimally solve the formulated non-convex mixed-integer nonlinear programming, an efficient iterative algorithm as a compromise approach is developed by exploiting bisection and block coordinate descent methods, yielding an optimal transceiver solution in each iteration. The optimal binary variables and a suboptimal trajectory are obtained by using the dual method and successive convex approximation, respectively. Simulations show the considerable performance gains of the proposed design over benchmarks and the superiority of deploying multiple UAVs in increasing the number of performed tasks while reducing access delays.

The prospect of using autonomous robots to enhance the capabilities of physicians and enable novel procedures has led to considerable efforts in developing medical robots and incorporating autonomous capabilities. Motion planning is a core component for any such system working in an environment that demands near perfect levels of safety, reliability, and precision. Despite the extensive and promising work that has gone into developing motion planners for medical robots, a standardized and clinically-meaningful way to compare existing algorithms and evaluate novel planners and robots is not well established. We present the Medical Motion Planning Dataset (Med-MPD), a publicly-available dataset of real clinical scenarios in various organs for the purpose of evaluating motion planners for minimally-invasive medical robots. Our goal is that this dataset serve as a first step towards creating a larger robust medical motion planning benchmark framework, advance research into medical motion planners, and lift some of the burden of generating medical evaluation data.

This paper presents a novel physics-infused reduced-order modeling (PIROM) methodology for efficient and accurate modeling of non-linear dynamical systems. The PIROM consists of a physics-based analytical component that represents the known physical processes, and a data-driven dynamical component that represents the unknown physical processes. The PIROM is applied to the aerothermal load modeling for hypersonic aerothermoelastic (ATE) analysis and is found to accelerate the ATE simulations by two-three orders of magnitude while maintaining an accuracy comparable to high-fidelity solutions based on computational fluid dynamics (CFD). Moreover, the PIROM-based solver is benchmarked against the conventional POD-kriging surrogate model, and is found to significantly outperform the accuracy, generalizability and sampling efficiency of the latter in a wide range of operating conditions and in the presence of complex structural boundary conditions. Finally, the PIROM-based ATE solver is demonstrated by a parametric study on the effects of boundary conditions and rib-supports on the ATE response of a compliant and heat-conducting panel structure. The results not only reveal the dramatic snap-through behavior with respect to spring constraints of boundary conditions, but also demonstrates the potential of PIROM to facilitate the rapid and accurate design and optimization of multi-disciplinary systems such as hypersonic structures.

High-dimensional matrix-variate time series data are becoming widely available in many scientific fields, such as economics, biology, and meteorology. To achieve significant dimension reduction while preserving the intrinsic matrix structure and temporal dynamics in such data, Wang et al. (2017) proposed a matrix factor model that is shown to provide effective analysis. In this paper, we establish a general framework for incorporating domain or prior knowledge in the matrix factor model through linear constraints. The proposed framework is shown to be useful in achieving parsimonious parameterization, facilitating interpretation of the latent matrix factor, and identifying specific factors of interest. Fully utilizing the prior-knowledge-induced constraints results in more efficient and accurate modeling, inference, dimension reduction as well as a clear and better interpretation of the results. In this paper, constrained, multi-term, and partially constrained factor models for matrix-variate time series are developed, with efficient estimation procedures and their asymptotic properties. We show that the convergence rates of the constrained factor loading matrices are much faster than those of the conventional matrix factor analysis under many situations. Simulation studies are carried out to demonstrate the finite-sample performance of the proposed method and its associated asymptotic properties. We illustrate the proposed model with three applications, where the constrained matrix-factor models outperform their unconstrained counterparts in the power of variance explanation under the out-of-sample 10-fold cross-validation setting.

Imitation learning (IL) can generate computationally efficient sensorimotor policies from demonstrations provided by computationally expensive model-based sensing and control algorithms. However, commonly employed IL methods are often data-inefficient, requiring the collection of a large number of demonstrations and producing policies with limited robustness to uncertainties. In this work, we combine IL with an output feedback robust tube model predictive controller (RTMPC) to co-generate demonstrations and a data augmentation strategy to efficiently learn neural network-based sensorimotor policies. Thanks to the augmented data, we reduce the computation time and the number of demonstrations needed by IL, while providing robustness to sensing and process uncertainty. We tailor our approach to the task of learning a trajectory tracking visuomotor policy for an aerial robot, leveraging a 3D mesh of the environment as part of the data augmentation process. We numerically demonstrate that our method can learn a robust visuomotor policy from a single demonstration--a two-orders of magnitude improvement in demonstration efficiency compared to existing IL methods.

The massive increase of data traffic, the widespread proliferation of wireless applications and the full-scale deployment of 5G and the IoT, imply a steep increase in cellular networks energy use, resulting in a significant carbon footprint. This paper presents a comprehensive model to show the interaction between the networking and energy features of the problem and study the economical and technical viability of green networking. Solar equipment, cell zooming, energy management and dynamic user allocation are considered in the upgrading network planning process. We propose a mixed-integer optimization model to minimize long-term capital costs and operational energy expenditures in a heterogeneous on-grid cellular network with different types of base station, including solar. Based on eight scenarios where realistic costs of solar panels, batteries, and inverters were considered, we first found that solar base stations are currently not economically interesting for cellular operators. We next studied the impact of a significant and progressive carbon tax on reducing greenhouse gas emissions (GHG). We found that, at current energy and equipment prices, a carbon tax ten-fold the current value is the only element that could make green base stations economically viable.