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Optimal control of general nonlinear systems is a central challenge in automation. Data-driven approaches to control, enabled by powerful function approximators, have recently had great success in tackling challenging robotic applications. However, such methods often obscure the structure of dynamics and control behind black-box over-parameterized representations, thus limiting our ability to understand the closed-loop behavior. This paper adopts a hybrid-system view of nonlinear modeling and control that lends an explicit hierarchical structure to the problem and breaks down complex dynamics into simpler localized units. Therefore, we consider a sequence modeling paradigm that captures the temporal structure of the data and derive an expecation-maximization (EM) algorithm that automatically decomposes nonlinear dynamics into stochastic piecewise affine dynamical systems with nonlinear boundaries. Furthermore, we show that these time-series models naturally admit a closed-loop extension that we use to extract locally linear or polynomial feedback controllers from nonlinear experts via imitation learning. Finally, we introduce a novel hybrid realtive entropy policy search (Hb-REPS) technique that incorporates the hierarchical nature of hybrid systems and optimizes a set of time-invariant local feedback controllers derived from a locally polynomial approximation of a global value function.

With the unprecedented shift towards automated urban environments in recent years, a new paradigm is required to study pedestrian behaviour. Studying pedestrian behaviour in futuristic scenarios requires modern data sources that consider both the Automated Vehicle (AV) and pedestrian perspectives. Current open datasets on AVs predominantly fail to account for the latter, as they do not include an adequate number of events and associated details that involve pedestrian and vehicle interactions. To address this issue, we propose using Virtual Reality (VR) data as a complementary resource to current datasets, which can be designed to measure pedestrian behaviour under specific conditions. In this research, we focus on the context-aware pedestrian trajectory prediction framework for automated vehicles at mid-block unsignalized crossings. For this purpose, we develop a novel multi-input network of Long Short-Term Memory (LSTM) and fully connected dense layers. In addition to past trajectories, the proposed framework incorporates pedestrian head orientations and distance to the upcoming vehicles as sequential input data. By merging the sequential data with contextual information of the environment, we train a model to predict the future pedestrian trajectory. Our results show that the prediction error and overfitting to the training data are reduced by considering contextual information in the model. To analyze the application of the methods to real AV data, the proposed framework is trained and applied to pedestrian trajectory extracted from an open-access video dataset. Finally, by implementing a game theory-based model interpretability method, we provide detailed insights and propose recommendations to improve the current automated vehicle sensing systems from a pedestrian-oriented point of view.

This paper studies a new variant of the stochastic multi-armed bandits problem where auxiliary information about the arm rewards is available in the form of control variates. In many applications like queuing and wireless networks, the arm rewards are functions of some exogenous variables. The mean values of these variables are known a priori from historical data and can be used as control variates. Leveraging the theory of control variates, we obtain mean estimates with smaller variance and tighter confidence bounds. We develop an improved upper confidence bound based algorithm named UCB-CV and characterize the regret bounds in terms of the correlation between rewards and control variates when they follow a multivariate normal distribution. We also extend UCB-CV to other distributions using resampling methods like Jackknifing and Splitting. Experiments on synthetic problem instances validate performance guarantees of the proposed algorithms.

We consider non-convex stochastic optimization using first-order algorithms for which the gradient estimates may have heavy tails. We show that a combination of gradient clipping, momentum, and normalized gradient descent yields convergence to critical points in high-probability with best-known rates for smooth losses when the gradients only have bounded $\mathfrak{p}$th moments for some $\mathfrak{p}\in(1,2]$. We then consider the case of second-order smooth losses, which to our knowledge have not been studied in this setting, and again obtain high-probability bounds for any $\mathfrak{p}$. Moreover, our results hold for arbitrary smooth norms, in contrast to the typical SGD analysis which requires a Hilbert space norm. Further, we show that after a suitable "burn-in" period, the objective value will monotonically decrease for every iteration until a critical point is identified, which provides intuition behind the popular practice of learning rate "warm-up" and also yields a last-iterate guarantee.

We study the optimal batch-regret tradeoff for batch linear contextual bandits. For any batch number $M$, number of actions $K$, time horizon $T$, and dimension $d$, we provide an algorithm and prove its regret guarantee, which, due to technical reasons, features a two-phase expression as the time horizon $T$ grows. We also prove a lower bound theorem that surprisingly shows the optimality of our two-phase regret upper bound (up to logarithmic factors) in the \emph{full range} of the problem parameters, therefore establishing the exact batch-regret tradeoff. Compared to the recent work \citep{ruan2020linear} which showed that $M = O(\log \log T)$ batches suffice to achieve the asymptotically minimax-optimal regret without the batch constraints, our algorithm is simpler and easier for practical implementation. Furthermore, our algorithm achieves the optimal regret for all $T \geq d$, while \citep{ruan2020linear} requires that $T$ greater than an unrealistically large polynomial of $d$. Along our analysis, we also prove a new matrix concentration inequality with dependence on their dynamic upper bounds, which, to the best of our knowledge, is the first of its kind in literature and maybe of independent interest.

We consider a Gathering problem for n autonomous mobile robots with persistent memory called light in an asynchronous scheduler (ASYNC). It is well known that Gathering is impossible when robots have no lights in basic common models, if the system is semi-synchronous (SSYNC) or even centralized (only one robot is active in each time). It is known that Gathering can be solved by robots with 10 colors of lights in ASYNC. This result is obtained by combining the following results. (1) The simulation of SSYNC robots with k colors by ASYNC robots with 5k colors, and (2) Gathering is solved by SSYNC robots with 2 colors. In this paper, we improve the result by reducing the number of colors and show that Gathering can be solved by ASYNC robots with 3 colors of lights. We also show that we can construct a simulation algorithm of any unfair SSYNC algorithm using k colors by ASYNC robots with 3k colors, where unfairness does not guarantee that every robot is activated infinitely often. Combining this simulation and the Gathering algorithm by SSYNC robots with 2 colors, we obtain a Gathering algorithm by ASYNC robots with 6 colors. Our main result can be obtained by reducing the number of colors from 6 to 3.

The use of object detection algorithms is becoming increasingly important in autonomous vehicles, and object detection at high accuracy and a fast inference speed is essential for safe autonomous driving. A false positive (FP) from a false localization during autonomous driving can lead to fatal accidents and hinder safe and efficient driving. Therefore, a detection algorithm that can cope with mislocalizations is required in autonomous driving applications. This paper proposes a method for improving the detection accuracy while supporting a real-time operation by modeling the bounding box (bbox) of YOLOv3, which is the most representative of one-stage detectors, with a Gaussian parameter and redesigning the loss function. In addition, this paper proposes a method for predicting the localization uncertainty that indicates the reliability of bbox. By using the predicted localization uncertainty during the detection process, the proposed schemes can significantly reduce the FP and increase the true positive (TP), thereby improving the accuracy. Compared to a conventional YOLOv3, the proposed algorithm, Gaussian YOLOv3, improves the mean average precision (mAP) by 3.09 and 3.5 on the KITTI and Berkeley deep drive (BDD) datasets, respectively. In addition, on the same datasets, the proposed algorithm can reduce the FP by 41.40% and 40.62%, and increase the TP by 7.26% and 4.3%, respectively. Nevertheless, the proposed algorithm is capable of real-time detection at faster than 42 frames per second (fps).

Latest deep learning methods for object detection provide remarkable performance, but have limits when used in robotic applications. One of the most relevant issues is the long training time, which is due to the large size and imbalance of the associated training sets, characterized by few positive and a large number of negative examples (i.e. background). Proposed approaches are based on end-to-end learning by back-propagation [22] or kernel methods trained with Hard Negatives Mining on top of deep features [8]. These solutions are effective, but prohibitively slow for on-line applications. In this paper we propose a novel pipeline for object detection that overcomes this problem and provides comparable performance, with a 60x training speedup. Our pipeline combines (i) the Region Proposal Network and the deep feature extractor from [22] to efficiently select candidate RoIs and encode them into powerful representations, with (ii) the FALKON [23] algorithm, a novel kernel-based method that allows fast training on large scale problems (millions of points). We address the size and imbalance of training data by exploiting the stochastic subsampling intrinsic into the method and a novel, fast, bootstrapping approach. We assess the effectiveness of the approach on a standard Computer Vision dataset (PASCAL VOC 2007 [5]) and demonstrate its applicability to a real robotic scenario with the iCubWorld Transformations [18] dataset.

We propose accelerated randomized coordinate descent algorithms for stochastic optimization and online learning. Our algorithms have significantly less per-iteration complexity than the known accelerated gradient algorithms. The proposed algorithms for online learning have better regret performance than the known randomized online coordinate descent algorithms. Furthermore, the proposed algorithms for stochastic optimization exhibit as good convergence rates as the best known randomized coordinate descent algorithms. We also show simulation results to demonstrate performance of the proposed algorithms.

TraQuad is an autonomous tracking quadcopter capable of tracking any moving (or static) object like cars, humans, other drones or any other object on-the-go. This article describes the applications and advantages of TraQuad and the reduction in cost (to about 250$) that has been achieved so far using the hardware and software capabilities and our custom algorithms wherever needed. This description is backed by strong data and the research analyses which have been drawn out of extant information or conducted on own when necessary. This also describes the development of completely autonomous (even GPS is optional) low-cost drone which can act as a major platform for further developments in automation, transportation, reconnaissance and more. We describe our ROS Gazebo simulator and our STATUS algorithms which form the core of our development of our object tracking drone for generic purposes.