We address the theoretical and practical problems related to the trajectory generation and tracking control of tail-sitter UAVs. Theoretically, we focus on the differential flatness property with full exploitation of actual UAV aerodynamic models, which lays a foundation for generating dynamically feasible trajectory and achieving high-performance tracking control. We have found that a tail-sitter is differentially flat with accurate aerodynamic models within the entire flight envelope, by specifying coordinate flight condition and choosing the vehicle position as the flat output. This fundamental property allows us to fully exploit the high-fidelity aerodynamic models in the trajectory planning and tracking control to achieve accurate tail-sitter flights. Particularly, an optimization-based trajectory planner for tail-sitters is proposed to design high-quality, smooth trajectories with consideration of kinodynamic constraints, singularity-free constraints and actuator saturation. The planned trajectory of flat output is transformed to state trajectory in real-time with consideration of wind in environments. To track the state trajectory, a global, singularity-free, and minimally-parameterized on-manifold MPC is developed, which fully leverages the accurate aerodynamic model to achieve high-accuracy trajectory tracking within the whole flight envelope. The effectiveness of the proposed framework is demonstrated through extensive real-world experiments in both indoor and outdoor field tests, including agile SE(3) flight through consecutive narrow windows requiring specific attitude and with speed up to 10m/s, typical tail-sitter maneuvers (transition, level flight and loiter) with speed up to 20m/s, and extremely aggressive aerobatic maneuvers (Wingover, Loop, Vertical Eight and Cuban Eight) with acceleration up to 2.5g.
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We consider the problem of signal estimation in a generalized linear model (GLM). GLMs include many canonical problems in statistical estimation, such as linear regression, phase retrieval, and 1-bit compressed sensing. Recent work has precisely characterized the asymptotic minimum mean-squared error (MMSE) for GLMs with i.i.d. Gaussian sensing matrices. However, in many models there is a significant gap between the MMSE and the performance of the best known feasible estimators. In this work, we address this issue by considering GLMs defined via spatially coupled sensing matrices. We propose an efficient approximate message passing (AMP) algorithm for estimation and prove that with a simple choice of spatially coupled design, the MSE of a carefully tuned AMP estimator approaches the asymptotic MMSE in the high-dimensional limit. To prove the result, we first rigorously characterize the asymptotic performance of AMP for a GLM with a generic spatially coupled design. This characterization is in terms of a deterministic recursion (`state evolution') that depends on the parameters defining the spatial coupling. Then, using a simple spatially coupled design and judicious choice of functions defining the AMP, we analyze the fixed points of the resulting state evolution and show that it achieves the asymptotic MMSE. Numerical results for phase retrieval and rectified linear regression show that spatially coupled designs can yield substantially lower MSE than i.i.d. Gaussian designs at finite dimensions when used with AMP algorithms.
We propose an upwind finite volume method for a system of two kinetic equations in one dimension that are coupled through nonlocal interaction terms. These cross-interaction systems were recently obtained as the mean-field limit of a second-order system of ordinary differential equations for two interacting species. Models of this kind are encountered in a myriad of contexts, for instance, to describe large systems of indistinguishable agents such as cell colonies, flocks of birds, schools of fish, herds of sheep. The finite volume method we propose is constructed to conserve mass and preserve positivity. Moreover, convex functionals of the discrete solution are controlled, which we use to show the convergence of the scheme. Finally, we investigate the scheme numerically.
To plan the trajectories of a large and heterogeneous swarm, sequential or synchronous distributed methods usually become intractable, due to the lack of global connectivity and clock synchronization, Moreover, the existing asynchronously distributed schemes usually require recheck-like mechanisms instead of inherently considering the other' moving tendency. To this end, we propose a novel asynchronous protocol to allocate the agents' derivable space in a distributed way, by which each agent can replan trajectory depending on its own timetable. Properties such as collision avoidance and recursive feasibility are theoretically shown and a lower bound of protocol updating is provided. Comprehensive simulations and comparisons with five state-of-the-art methods validate the effectiveness of our method and illustrate the improvement in both the completion time and the moving distance. Finally, hardware experiments are carried out, where 8 heterogeneous unmanned ground vehicles with onboard computation navigate in cluttered scenarios at a high agility.
We consider a decentralized formulation of the active hypothesis testing (AHT) problem, where multiple agents gather noisy observations from the environment with the purpose of identifying the correct hypothesis. At each time step, agents have the option to select a sampling action. These different actions result in observations drawn from various distributions, each associated with a specific hypothesis. The agents collaborate to accomplish the task, where message exchanges between agents are allowed over a rate-limited communications channel. The objective is to devise a multi-agent policy that minimizes the Bayes risk. This risk comprises both the cost of sampling and the joint terminal cost incurred by the agents upon making a hypothesis declaration. Deriving optimal structured policies for AHT problems is generally mathematically intractable, even in the context of a single agent. As a result, recent efforts have turned to deep learning methodologies to address these problems, which have exhibited significant success in single-agent learning scenarios. In this paper, we tackle the multi-agent AHT formulation by introducing a novel algorithm rooted in the framework of deep multi-agent reinforcement learning. This algorithm, named Multi-Agent Reinforcement Learning for AHT (MARLA), operates at each time step by having each agent map its state to an action (sampling rule or stopping rule) using a trained deep neural network with the goal of minimizing the Bayes risk. We present a comprehensive set of experimental results that effectively showcase the agents' ability to learn collaborative strategies and enhance performance using MARLA. Furthermore, we demonstrate the superiority of MARLA over single-agent learning approaches. Finally, we provide an open-source implementation of the MARLA framework, for the benefit of researchers and developers in related domains.
We introduce a decentralized mechanism for pricing and exchanging alternatives constrained by transaction costs. We characterize the time-invariant solutions of a heat equation involving a (weighted) Tarski Laplacian operator, defined for max-plus matrix-weighted graphs, as approximate equilibria of the trading system. We study algebraic properties of the solution sets as well as convergence behavior of the dynamical system. We apply these tools to the "economic problem" of allocating scarce resources among competing uses. Our theory suggests differences in competitive equilibrium, bargaining, or cost-benefit analysis, depending on the context, are largely due to differences in the way that transaction costs are incorporated into the decision-making process. We present numerical simulations of the synchronization algorithm (RRAggU), demonstrating our theoretical findings.
Several recent contributions in the field of iterative STFT phase retrieval have demonstrated that the performance of the classical Griffin-Lim method can be considerably improved upon. By using the same projection operators as Griffin-Lim, but combining them in innovative ways, these approaches achieve better results in terms of both reconstruction quality and required number of iterations, while retaining a similar computational complexity per iteration. However, like Griffin-Lim, these algorithms operate in an offline manner and thus require an entire spectrogram as input, which is an unrealistic requirement for many real-world speech communication applications. We propose to extend RTISI -- an existing online (frame-by-frame) variant of the Griffin-Lim algorithm -- into a flexible framework that enables straightforward online implementation of any algorithm based on iterative projections. We further employ this framework to implement online variants of the fast Griffin-Lim algorithm, the accelerated Griffin-Lim algorithm, and two algorithms from the optics domain. Evaluation results on speech signals show that, similarly to the offline case, these algorithms can achieve a considerable performance gain compared to RTISI.
Motivated by the proliferation of observational datasets and the need to integrate non-randomized evidence with randomized controlled trials, causal inference researchers have recently proposed several new methodologies for combining biased and unbiased estimators. We contribute to this growing literature by developing a new class of estimators for the data-combination problem: double-shrinkage estimators. Double-shrinkers first compute a data-driven convex combination of the the biased and unbiased estimators, and then apply a final, Stein-like shrinkage toward zero. Such estimators do not require hyperparameter tuning, and are targeted at multidimensional causal estimands, such as vectors of conditional average treatment effects (CATEs). We derive several workable versions of double-shrinkage estimators and propose a method for constructing valid Empirical Bayes confidence intervals. We also demonstrate the utility of our estimators using simulations on data from the Women's Health Initiative.
Graph Convolutional Networks (GCNs) have been widely applied in various fields due to their significant power on processing graph-structured data. Typical GCN and its variants work under a homophily assumption (i.e., nodes with same class are prone to connect to each other), while ignoring the heterophily which exists in many real-world networks (i.e., nodes with different classes tend to form edges). Existing methods deal with heterophily by mainly aggregating higher-order neighborhoods or combing the immediate representations, which leads to noise and irrelevant information in the result. But these methods did not change the propagation mechanism which works under homophily assumption (that is a fundamental part of GCNs). This makes it difficult to distinguish the representation of nodes from different classes. To address this problem, in this paper we design a novel propagation mechanism, which can automatically change the propagation and aggregation process according to homophily or heterophily between node pairs. To adaptively learn the propagation process, we introduce two measurements of homophily degree between node pairs, which is learned based on topological and attribute information, respectively. Then we incorporate the learnable homophily degree into the graph convolution framework, which is trained in an end-to-end schema, enabling it to go beyond the assumption of homophily. More importantly, we theoretically prove that our model can constrain the similarity of representations between nodes according to their homophily degree. Experiments on seven real-world datasets demonstrate that this new approach outperforms the state-of-the-art methods under heterophily or low homophily, and gains competitive performance under homophily.
Knowledge graph completion aims to predict missing relations between entities in a knowledge graph. While many different methods have been proposed, there is a lack of a unifying framework that would lead to state-of-the-art results. Here we develop PathCon, a knowledge graph completion method that harnesses four novel insights to outperform existing methods. PathCon predicts relations between a pair of entities by: (1) Considering the Relational Context of each entity by capturing the relation types adjacent to the entity and modeled through a novel edge-based message passing scheme; (2) Considering the Relational Paths capturing all paths between the two entities; And, (3) adaptively integrating the Relational Context and Relational Path through a learnable attention mechanism. Importantly, (4) in contrast to conventional node-based representations, PathCon represents context and path only using the relation types, which makes it applicable in an inductive setting. Experimental results on knowledge graph benchmarks as well as our newly proposed dataset show that PathCon outperforms state-of-the-art knowledge graph completion methods by a large margin. Finally, PathCon is able to provide interpretable explanations by identifying relations that provide the context and paths that are important for a given predicted relation.
Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis.
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