arXiv subjects

Sertac Karaman

Publications and source records attributed to Sertac Karaman.

At least 73 records · Page 4Linked to original sources

arXiv2019

Shared Linear Quadratic Regulation Control: A Reinforcement Learning Approach

We propose controller synthesis for state regulation problems in which a human operator shares control with an autonomy system, running in parallel. The autonomy system continuously improves over human action, with minimal intervention, and can take over full-control. It additively combines user input with an adaptive optimal corrective signal. It is adaptive in that it neither estimates nor requires a model of the human's action policy, or the internal dynamics of the plant, and can adjust to changes in both. Our contribution is twofold; first, a new synthesis for shared control which we formulate as an adaptive optimal control problem for continuous-time linear systems and solve it online as a human-in-the-loop reinforcement learning. The result is an architecture that we call shared linear quadratic regulator (sLQR). Second, we provide new analysis of reinforcement learning for continuous-time linear systems in two parts. In the first analysis part, we avoid learning along a single state-space trajectory which we show leads to data collinearity under certain conditions. We make a clear separation between exploitation of learned policies and exploration of the state-space, and propose an exploration scheme that requires switching to new state-space trajectories rather than injecting noise continuously while learning. This avoidance of continuous noise injection minimizes interference with human action, and avoids bias in the convergence to the stabilizing solution of the underlying algebraic Riccati equation. We show that exploring a minimum number of pairwise distinct state-space trajectories is necessary to avoid collinearity in the learning data. In the second analysis part, we show conditions under which existence and uniqueness of solutions can be established for off-policy reinforcement learning in continuous-time linear systems; namely, prior knowledge of the input matrix.

eess.SY↗

arXiv2019

Optimal orthogonal approximations to symmetric tensors cannot always be chosen symmetric

We study the problem of finding orthogonal low-rank approximations of symmetric tensors. In the case of matrices, the approximation is a truncated singular value decomposition which is then symmetric. Moreover, for rank-one approximations of tensors of any dimension, a classical result proven by Banach in 1938 shows that the optimal approximation can always be chosen to be symmetric. In contrast to these results, this article shows that the corresponding statement is no longer true for orthogonal approximations of higher rank. Specifically, for any of the four common notions of tensor orthogonality used in the literature, we show that optimal orthogonal approximations of rank greater than one cannot always be chosen to be symmetric.

math.NA↗

arXiv2019

Variational End-to-End Navigation and Localization

Deep learning has revolutionized the ability to learn "end-to-end" autonomous vehicle control directly from raw sensory data. While there have been recent extensions to handle forms of navigation instruction, these works are unable to capture the full distribution of possible actions that could be taken and to reason about localization of the robot within the environment. In this paper, we extend end-to-end driving networks with the ability to perform point-to-point navigation as well as probabilistic localization using only noisy GPS data. We define a novel variational network capable of learning from raw camera data of the environment as well as higher level roadmaps to predict (1) a full probability distribution over the possible control commands; and (2) a deterministic control command capable of navigating on the route specified within the map. Additionally, we formulate how our model can be used to localize the robot according to correspondences between the map and the observed visual road topology, inspired by the rough localization that human drivers can perform. We test our algorithms on real-world driving data that the vehicle has never driven through before, and integrate our point-to-point navigation algorithms onboard a full-scale autonomous vehicle for real-time performance. Our localization algorithm is also evaluated over a new set of roads and intersections to demonstrates rough pose localization even in situations without any GPS prior.

cs.LG↗

arXiv2019

Spatial Uncertainty Sampling for End-to-End Control

End-to-end trained neural networks (NNs) are a compelling approach to autonomous vehicle control because of their ability to learn complex tasks without manual engineering of rule-based decisions. However, challenging road conditions, ambiguous navigation situations, and safety considerations require reliable uncertainty estimation for the eventual adoption of full-scale autonomous vehicles. Bayesian deep learning approaches provide a way to estimate uncertainty by approximating the posterior distribution of weights given a set of training data. Dropout training in deep NNs approximates Bayesian inference in a deep Gaussian process and can thus be used to estimate model uncertainty. In this paper, we propose a Bayesian NN for end-to-end control that estimates uncertainty by exploiting feature map correlation during training. This approach achieves improved model fits, as well as tighter uncertainty estimates, than traditional element-wise dropout. We evaluate our algorithms on a challenging dataset collected over many different road types, times of day, and weather conditions, and demonstrate how uncertainties can be used in conjunction with a human controller in a parallel autonomous setting.

cs.AI↗

arXiv2019

FSMI: Fast computation of Shannon Mutual Information for information-theoretic mapping

Exploration tasks are embedded in many robotics applications, such as search and rescue and space exploration. Information-based exploration algorithms aim to find the most informative trajectories by maximizing an information-theoretic metric, such as the mutual information between the map and potential future measurements. Unfortunately, most existing information-based exploration algorithms are plagued by the computational difficulty of evaluating the Shannon mutual information metric. In this paper, we consider the fundamental problem of evaluating Shannon mutual information between the map and a range measurement. First, we consider 2D environments. We propose a novel algorithm, called the Fast Shannon Mutual Information (FSMI). The key insight behind the algorithm is that a certain integral can be computed analytically, leading to substantial computational savings. Second, we consider 3D environments, represented by efficient data structures, e.g., an OctoMap, such that the measurements are compressed by Run-Length Encoding (RLE). We propose a novel algorithm, called FSMI-RLE, that efficiently evaluates the Shannon mutual information when the measurements are compressed using RLE. For both the FSMI and the FSMI-RLE, we also propose variants that make different assumptions on the sensor noise distribution for the purpose of further computational savings. We evaluate the proposed algorithms in extensive experiments. In particular, we show that the proposed algorithms outperform existing algorithms that compute Shannon mutual information as well as other algorithms that compute the Cauchy-Schwarz Quadratic mutual information (CSQMI). In addition, we demonstrate the computation of Shannon mutual information on a 3D map for the first time.

cs.RO↗

arXiv2019

Asymptotic Optimality of a Time Optimal Path Parametrization Algorithm

Time Optimal Path Parametrization is the problem of minimizing the time interval during which an actuation constrained agent can traverse a given path. Recently, an efficient linear-time algorithm for solving this problem was proposed. However, its optimality was proved for only a strict subclass of problems solved optimally by more computationally intensive approaches based on convex programming. In this paper, we prove that the same linear-time algorithm is asymptotically optimal for all problems solved optimally by convex optimization approaches. We also characterize the optimum of the Time Optimal Path Parametrization Problem, which may be of independent interest.

cs.RO↗

arXiv2019

FastDepth: Fast Monocular Depth Estimation on Embedded Systems

Depth sensing is a critical function for robotic tasks such as localization, mapping and obstacle detection. There has been a significant and growing interest in depth estimation from a single RGB image, due to the relatively low cost and size of monocular cameras. However, state-of-the-art single-view depth estimation algorithms are based on fairly complex deep neural networks that are too slow for real-time inference on an embedded platform, for instance, mounted on a micro aerial vehicle. In this paper, we address the problem of fast depth estimation on embedded systems. We propose an efficient and lightweight encoder-decoder network architecture and apply network pruning to further reduce computational complexity and latency. In particular, we focus on the design of a low-latency decoder. Our methodology demonstrates that it is possible to achieve similar accuracy as prior work on depth estimation, but at inference speeds that are an order of magnitude faster. Our proposed network, FastDepth, runs at 178 fps on an NVIDIA Jetson TX2 GPU and at 27 fps when using only the TX2 CPU, with active power consumption under 10 W. FastDepth achieves close to state-of-the-art accuracy on the NYU Depth v2 dataset. To the best of the authors' knowledge, this paper demonstrates real-time monocular depth estimation using a deep neural network with the lowest latency and highest throughput on an embedded platform that can be carried by a micro aerial vehicle.

cs.CV↗

arXiv2019

Can Determinacy Minimize Age of Information?

Age-of-information (AoI) is a newly proposed performance metric of information freshness. It differs from the traditional delay metric, because it is destination centric and measures the time that elapsed since the last received fresh information update was generated at the source. AoI has been analyzed for several queueing models, and the problem of optimizing AoI over arrival and service rates has been studied in the literature. We consider the problem of minimizing AoI over the space of update generation and service time distributions. In particular, we ask whether determinacy, i.e. periodic generation of update packets and/or deterministic service, optimizes AoI. By considering several queueing systems, we show that in certain settings, deterministic service can in fact result in the worst case AoI, while a heavy-tailed distributed service can yield the minimum AoI. This leads to an interesting conclusion that, in some queueing systems, the service time distribution that minimizes expected packet delay, or variance in packet delay can, in fact, result in the worst case AoI. This exposes a fundamental difference between AoI metrics and packet delay.

cs.NI↗

arXiv2018

A continuous analogue of the tensor-train decomposition

We develop new approximation algorithms and data structures for representing and computing with multivariate functions using the functional tensor-train (FT), a continuous extension of the tensor-train (TT) decomposition. The FT represents functions using a tensor-train ansatz by replacing the three-dimensional TT cores with univariate matrix-valued functions. The main contribution of this paper is a framework to compute the FT that employs adaptive approximations of univariate fibers, and that is not tied to any tensorized discretization. The algorithm can be coupled with any univariate linear or nonlinear approximation procedure. We demonstrate that this approach can generate multivariate function approximations that are several orders of magnitude more accurate, for the same cost, than those based on the conventional approach of compressing the coefficient tensor of a tensor-product basis. Our approach is in the spirit of other continuous computation packages such as Chebfun, and yields an algorithm which requires the computation of "continuous" matrix factorizations such as the LU and QR decompositions of vector-valued functions. To support these developments, we describe continuous versions of an approximate maximum-volume cross approximation algorithm and of a rounding algorithm that re-approximates an FT by one of lower ranks. We demonstrate that our technique improves accuracy and robustness, compared to TT and quantics-TT approaches with fixed parameterizations, of high-dimensional integration, differentiation, and approximation of functions with local features such as discontinuities and other nonlinearities.

math.NA↗

arXiv2018

The Blackbird Dataset: A large-scale dataset for UAV perception in aggressive flight

The Blackbird unmanned aerial vehicle (UAV) dataset is a large-scale, aggressive indoor flight dataset collected using a custom-built quadrotor platform for use in evaluation of agile perception.Inspired by the potential of future high-speed fully-autonomous drone racing, the Blackbird dataset contains over 10 hours of flight data from 168 flights over 17 flight trajectories and 5 environments at velocities up to $7.0ms^-1$. Each flight includes sensor data from 120Hz stereo and downward-facing photorealistic virtual cameras, 100Hz IMU, $\sim190Hz$ motor speed sensors, and 360Hz millimeter-accurate motion capture ground truth. Camera images for each flight were photorealistically rendered using FlightGoggles across a variety of environments to facilitate easy experimentation of high performance perception algorithms. The dataset is available for download at http://blackbird-dataset.mit.edu/

cs.CV↗

arXiv2018

Navion: A 2mW Fully Integrated Real-Time Visual-Inertial Odometry Accelerator for Autonomous Navigation of Nano Drones

This paper presents Navion, an energy-efficient accelerator for visual-inertial odometry (VIO) that enables autonomous navigation of miniaturized robots (e.g., nano drones), and virtual/augmented reality on portable devices. The chip uses inertial measurements and mono/stereo images to estimate the drone's trajectory and a 3D map of the environment. This estimate is obtained by running a state-of-the-art VIO algorithm based on non-linear factor graph optimization, which requires large irregularly structured memories and heterogeneous computation flow. To reduce the energy consumption and footprint, the entire VIO system is fully integrated on chip to eliminate costly off-chip processing and storage. This work uses compression and exploits both structured and unstructured sparsity to reduce on-chip memory size by 4.1$\times$. Parallelism is used under tight area constraints to increase throughput by 43%. The chip is fabricated in 65nm CMOS, and can process 752$\times$480 stereo images from EuRoC dataset in real-time at 20 frames per second (fps) consuming only an average power of 2mW. At its peak performance, Navion can process stereo images at up to 171 fps and inertial measurements at up to 52 kHz, while consuming an average of 24mW. The chip is configurable to maximize accuracy, throughput and energy-efficiency trade-offs and to adapt to different environments. To the best of our knowledge, this is the first fully integrated VIO system in an ASIC.

cs.RO↗

arXiv2018

Capacity and Delay Scaling for Broadcast Transmission in Highly Mobile Wireless Networks

We study broadcast capacity and minimum delay scaling laws for highly mobile wireless networks, in which each node has to disseminate or broadcast packets to all other nodes in the network. In particular, we consider a cell partitioned network under the simplified independent and identically distributed (IID) mobility model, in which each node chooses a new cell at random every time slot. We derive scaling laws for broadcast capacity and minimum delay as a function of the cell size. We propose a simple first-come-first-serve (FCFS) flooding scheme that nearly achieves both capacity and minimum delay scaling. Our results show that high mobility does not improve broadcast capacity, and that both capacity and delay improve with increasing cell sizes. In contrast to what has been speculated in the literature we show that there is (nearly) no tradeoff between capacity and delay. Our analysis makes use of the theory of Markov Evolving Graphs (MEGs) and develops two new bounds on flooding time in MEGs by relaxing the previously required expander property assumption.

cs.IT↗

arXiv2018

Attention and Anticipation in Fast Visual-Inertial Navigation

We study a Visual-Inertial Navigation (VIN) problem in which a robot needs to estimate its state using an on-board camera and an inertial sensor, without any prior knowledge of the external environment. We consider the case in which the robot can allocate limited resources to VIN, due to tight computational constraints. Therefore, we answer the following question: under limited resources, what are the most relevant visual cues to maximize the performance of visual-inertial navigation? Our approach has four key ingredients. First, it is task-driven, in that the selection of the visual cues is guided by a metric quantifying the VIN performance. Second, it exploits the notion of anticipation, since it uses a simplified model for forward-simulation of robot dynamics, predicting the utility of a set of visual cues over a future time horizon. Third, it is efficient and easy to implement, since it leads to a greedy algorithm for the selection of the most relevant visual cues. Fourth, it provides formal performance guarantees: we leverage submodularity to prove that the greedy selection cannot be far from the optimal (combinatorial) selection. Simulations and real experiments on agile drones show that our approach ensures state-of-the-art VIN performance while maintaining a lean processing time. In the easy scenarios, our approach outperforms appearance-based feature selection in terms of localization errors. In the most challenging scenarios, it enables accurate visual-inertial navigation while appearance-based feature selection fails to track robot's motion during aggressive maneuvers.

cs.RO↗

arXiv2018

Perception-driven sparse graphs for optimal motion planning

Most existing motion planning algorithms assume that a map (of some quality) is fully determined prior to generating a motion plan. In many emerging applications of robotics, e.g., fast-moving agile aerial robots with constrained embedded computational platforms and visual sensors, dense maps of the world are not immediately available, and they are computationally expensive to construct. We propose a new algorithm for generating plan graphs which couples the perception and motion planning processes for computational efficiency. In a nutshell, the proposed algorithm iteratively switches between the planning sub-problem and the mapping sub-problem, each updating based on the other until a valid trajectory is found. The resulting trajectory retains a provable property of providing an optimal trajectory with respect to the full (unmapped) environment, while utilizing only a fraction of the sensing data in computational experiments.

cs.RO↗

arXiv2018

Self-supervised Sparse-to-Dense: Self-supervised Depth Completion from LiDAR and Monocular Camera

Depth completion, the technique of estimating a dense depth image from sparse depth measurements, has a variety of applications in robotics and autonomous driving. However, depth completion faces 3 main challenges: the irregularly spaced pattern in the sparse depth input, the difficulty in handling multiple sensor modalities (when color images are available), as well as the lack of dense, pixel-level ground truth depth labels. In this work, we address all these challenges. Specifically, we develop a deep regression model to learn a direct mapping from sparse depth (and color images) to dense depth. We also propose a self-supervised training framework that requires only sequences of color and sparse depth images, without the need for dense depth labels. Our experiments demonstrate that our network, when trained with semi-dense annotations, attains state-of-the- art accuracy and is the winning approach on the KITTI depth completion benchmark at the time of submission. Furthermore, the self-supervised framework outperforms a number of existing solutions trained with semi- dense annotations.

cs.CV↗

arXiv2018

Scheduling Policies for Age Minimization in Wireless Networks with Unknown Channel State

Age of information (AoI) is a recently proposed metric that measures the time elapsed since the generation of the last received information update. We consider the problem of AoI minimization for a network under general interference constraints, and time varying channel. We study the case where the channel statistics are known, but the current channel state is unknown. We propose two scheduling policies, namely, the virtual queue based policy and age-based policy. In the virtual queue based policy, the scheduler schedules links with maximum weighted sum of the virtual queue lengths, while in the age-based policy, the scheduler schedules links with maximum weighted sum of a function of link AoI. We prove that the virtual queue based policy is peak age optimal, up to an additive constant, while the age-based policy is at most factor 4 away from the optimal age. Numerical results suggest that both the proposed policies are, in fact, very close to the optimal.

cs.NI↗

arXiv2018

Distributed Scheduling Algorithms for Optimizing Information Freshness in Wireless Networks

Age of Information (AoI), measures the time elapsed since the last received information packet was generated at the source. We consider the problem of AoI minimization for single-hop flows in a wireless network, under pairwise interference constraints and time varying channel. We consider simple, yet broad, class of distributed scheduling policies, in which a transmission is attempted over each link with a certain attempt probability. We obtain an interesting relation between the optimal attempt probability and the optimal AoI of the link, and its neighboring links. We then show that the optimal attempt probabilities can be computed by solving a convex optimization problem, which can be done distributively.

cs.IT↗

arXiv2018

Optimizing Age of Information in Wireless Networks with Perfect Channel State Information

Age of information (AoI), defined as the time elapsed since the last received update was generated, is a newly proposed metric to measure the timeliness of information updates in a network. We consider AoI minimization problem for a network with general interference constraints, and time varying channels. We propose two policies, namely, virtual-queue based policy and age-based policy when the channel state is available to the network scheduler at each time step. We prove that the virtual-queue based policy is nearly optimal, up to a constant additive factor, and the age-based policy is at-most factor 4 away from optimality. Comparing with our previous work, which derived age optimal policies when channel state information is not available to the scheduler, we demonstrate a 4 fold improvement in age due to the availability of channel state information.

cs.IT↗