arXiv subjects

Sertac Karaman

Publications and source records attributed to Sertac Karaman.

89 records · Page 5Linked to original sources

arXiv2018

CDDT: Fast Approximate 2D Ray Casting for Accelerated Localization

Localization is an essential component for autonomous robots. A well-established localization approach combines ray casting with a particle filter, leading to a computationally expensive algorithm that is difficult to run on resource-constrained mobile robots. We present a novel data structure called the Compressed Directional Distance Transform for accelerating ray casting in two dimensional occupancy grid maps. Our approach allows online map updates, and near constant time ray casting performance for a fixed size map, in contrast with other methods which exhibit poor worst case performance. Our experimental results show that the proposed algorithm approximates the performance characteristics of reading from a three dimensional lookup table of ray cast solutions while requiring two orders of magnitude less memory and precomputation. This results in a particle filter algorithm which can maintain 2500 particles with 61 ray casts per particle at 40Hz, using a single CPU thread onboard a mobile robot.

cs.DS↗

arXiv2018

Sparse-to-Dense: Depth Prediction from Sparse Depth Samples and a Single Image

We consider the problem of dense depth prediction from a sparse set of depth measurements and a single RGB image. Since depth estimation from monocular images alone is inherently ambiguous and unreliable, to attain a higher level of robustness and accuracy, we introduce additional sparse depth samples, which are either acquired with a low-resolution depth sensor or computed via visual Simultaneous Localization and Mapping (SLAM) algorithms. We propose the use of a single deep regression network to learn directly from the RGB-D raw data, and explore the impact of number of depth samples on prediction accuracy. Our experiments show that, compared to using only RGB images, the addition of 100 spatially random depth samples reduces the prediction root-mean-square error by 50% on the NYU-Depth-v2 indoor dataset. It also boosts the percentage of reliable prediction from 59% to 92% on the KITTI dataset. We demonstrate two applications of the proposed algorithm: a plug-in module in SLAM to convert sparse maps to dense maps, and super-resolution for LiDARs. Software and video demonstration are publicly available.

cs.RO↗

arXiv2018

A General Pipeline for 3D Detection of Vehicles

Autonomous driving requires 3D perception of vehicles and other objects in the in environment. Much of the current methods support 2D vehicle detection. This paper proposes a flexible pipeline to adopt any 2D detection network and fuse it with a 3D point cloud to generate 3D information with minimum changes of the 2D detection networks. To identify the 3D box, an effective model fitting algorithm is developed based on generalised car models and score maps. A two-stage convolutional neural network (CNN) is proposed to refine the detected 3D box. This pipeline is tested on the KITTI dataset using two different 2D detection networks. The 3D detection results based on these two networks are similar, demonstrating the flexibility of the proposed pipeline. The results rank second among the 3D detection algorithms, indicating its competencies in 3D detection.

cs.CV↗

arXiv2018

High-Dimensional Stochastic Optimal Control using Continuous Tensor Decompositions

Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately, most existing algorithms that guarantee convergence to optimal solutions suffer from the curse of dimensionality: the run time of the algorithm grows exponentially with the dimension of the state space of the system. We propose novel dynamic programming algorithms that alleviate the curse of dimensionality in problems that exhibit certain low-rank structure. The proposed algorithms are based on continuous tensor decompositions recently developed by the authors. Essentially, the algorithms represent high-dimensional functions (e.g., the value function) in a compressed format, and directly perform dynamic programming computations (e.g., value iteration, policy iteration) in this format. Under certain technical assumptions, the new algorithms guarantee convergence towards optimal solutions with arbitrary precision. Furthermore, the run times of the new algorithms scale polynomially with the state dimension and polynomially with the ranks of the value function. This approach realizes substantial computational savings in "compressible" problem instances, where value functions admit low-rank approximations. We demonstrate the new algorithms in a wide range of problems, including a simulated six-dimensional agile quadcopter maneuvering example and a seven-dimensional aircraft perching example. In some of these examples, we estimate computational savings of up to ten orders of magnitude over standard value iteration algorithms. We further demonstrate the algorithms running in real time on board a quadcopter during a flight experiment under motion capture.

cs.RO↗

arXiv2017

Sparse Depth Sensing for Resource-Constrained Robots

We consider the case in which a robot has to navigate in an unknown environment but does not have enough on-board power or payload to carry a traditional depth sensor (e.g., a 3D lidar) and thus can only acquire a few (point-wise) depth measurements. We address the following question: is it possible to reconstruct the geometry of an unknown environment using sparse and incomplete depth measurements? Reconstruction from incomplete data is not possible in general, but when the robot operates in man-made environments, the depth exhibits some regularity (e.g., many planar surfaces with only a few edges); we leverage this regularity to infer depth from a small number of measurements. Our first contribution is a formulation of the depth reconstruction problem that bridges robot perception with the compressive sensing literature in signal processing. The second contribution includes a set of formal results that ascertain the exactness and stability of the depth reconstruction in 2D and 3D problems, and completely characterize the geometry of the profiles that we can reconstruct. Our third contribution is a set of practical algorithms for depth reconstruction: our formulation directly translates into algorithms for depth estimation based on convex programming. In real-world problems, these convex programs are very large and general-purpose solvers are relatively slow. For this reason, we discuss ad-hoc solvers that enable fast depth reconstruction in real problems. The last contribution is an extensive experimental evaluation in 2D and 3D problems, including Monte Carlo runs on simulated instances and testing on multiple real datasets. Empirical results confirm that the proposed approach ensures accurate depth reconstruction, outperforms interpolation-based strategies, and performs well even when the assumption of structured environment is violated.

cs.RO↗

arXiv2017

On Sensing, Agility, and Computation Requirements for a Data-gathering Agile Robotic Vehicle

We consider a robotic vehicle tasked with gathering information by visiting a set of spatially-distributed data sources, the locations of which are not known a priori, but are discovered on the fly. We assume a first-order robot dynamics involving drift and that the locations of the data sources are Poisson-distributed. In this setting, we characterize the performance of the robot in terms of its sensing, agility, and computation capabilities. More specifically, the robot's performance is characterized in terms of its ability to sense the target locations from a distance, to maneuver quickly, and to perform computations for inference and planning. We also characterize the performance of the robot in terms of the amount and distribution of information that can be acquired at each data source. The following are among our theoretical results: the distribution of the amount of information among the target locations immensely impacts the requirements for sensing targets from a distance; performance increases with increasing maneuvering capability, but with diminishing returns; and the computation requirements increase more rapidly for planning as opposed to inference, with both increasing sensing range and maneuvering ability. We provide computational experiments to validate our theoretical results. Finally, we demonstrate that these results can be utilized in the co-design of sensing, actuation, and computation capabilities of mobile robotic systems for an information-gathering mission. Our proof techniques establish novel connections between the fundamental problems of robotic information-gathering and the last-passage percolation problem of statistical mechanics, which may be of interest on its own right.

cs.RO↗

arXiv2016

Polling-systems-based Autonomous Vehicle Coordination in Traffic Intersections with No Traffic Signals

The rapid development of autonomous vehicles spurred a careful investigation of the potential benefits of all-autonomous transportation networks. Most studies conclude that autonomous systems can enable drastic improvements in performance. A widely studied concept is all-autonomous, collision-free intersections, where vehicles arriving in a traffic intersection with no traffic light adjust their speeds to cross safely through the intersection as quickly as possible. In this paper, we propose a coordination control algorithm for this problem, assuming stochastic models for the arrival times of the vehicles. The proposed algorithm provides provable guarantees on safety and performance. More precisely, it is shown that no collisions occur surely, and moreover a rigorous upper bound is provided for the expected wait time. The algorithm is also demonstrated in simulations. The proposed algorithms are inspired by polling systems. In fact, the problem studied in this paper leads to a new polling system where customers are subject to differential constraints, which may be interesting in its own right.

eess.SY↗

arXiv2014

Optimal Tourist Problem and Anytime Planning of Trip Itineraries

We introduce and study the problem in which a mobile sensing robot (our tourist) is tasked to travel among and gather intelligence at a set of spatially distributed point-of-interests (POIs). The quality of the information collected at each POI is characterized by some non-decreasing reward function over the time spent at the POI. With limited time budget, the robot must balance between spending time traveling to POIs and spending time at POIs for information collection (sensing) so as to maximize the total reward. Alternatively, the robot may be required to acquire a minimum mount of reward and hopes to do so with the least amount of time. We propose a mixed integer programming (MIP) based anytime algorithm for solving these two NP-hard optimization problems to arbitrary precision. The effectiveness of our algorithm is demonstrated using an extensive set of computational experiments including the planning of a realistic itinerary for a first-time tourist in Istanbul.

cs.RO↗

arXiv2014

Persistent Monitoring of Events with Stochastic Arrivals at Multiple Stations

This paper introduces a new mobile sensor scheduling problem, involving a single robot tasked with monitoring several events of interest that occur at different locations. Of particular interest is the monitoring of transient events that can not be easily forecast. Application areas range from natural phenomena ({\em e.g.}, monitoring abnormal seismic activity around a volcano using a ground robot) to urban activities ({\em e.g.}, monitoring early formations of traffic congestion using an aerial robot). Motivated by those and many other examples, this paper focuses on problems in which the precise occurrence times of the events are unknown {\em a priori}, but statistics for their inter-arrival times are available. The robot's task is to monitor the events to optimize the following two objectives: {\em (i)} maximize the number of events observed and {\em (ii)} minimize the delay between two consecutive observations of events occurring at the same location. The paper considers the case when a robot is tasked with optimizing the event observations in a balanced manner, following a cyclic patrolling route. First, assuming the cyclic ordering of stations is known, we prove the existence and uniqueness of the optimal solution, and show that the optimal solution has desirable convergence and robustness properties. Our constructive proof also produces an efficient algorithm for computing the unique optimal solution with $O(n)$ time complexity, in which $n$ is the number of stations, with $O(\log n)$ time complexity for incrementally adding or removing stations. Except for the algorithm, most of the analysis remains valid when the cyclic order is unknown. We then provide a polynomial-time approximation scheme that gives a $(1+ε)$-optimal solution for this more general, NP-hard problem.

cs.RO↗

arXiv2013

Incremental Sampling-based Algorithm for Minimum-violation Motion Planning

This paper studies the problem of control strategy synthesis for dynamical systems with differential constraints to fulfill a given reachability goal while satisfying a set of safety rules. Particular attention is devoted to goals that become feasible only if a subset of the safety rules are violated. The proposed algorithm computes a control law, that minimizes the level of unsafety while the desired goal is guaranteed to be reached. This problem is motivated by an autonomous car navigating an urban environment while following rules of the road such as "always travel in right lane'' and "do not change lanes frequently''. Ideas behind sampling based motion-planning algorithms, such as Probabilistic Road Maps (PRMs) and Rapidly-exploring Random Trees (RRTs), are employed to incrementally construct a finite concretization of the dynamics as a durational Kripke structure. In conjunction with this, a weighted finite automaton that captures the safety rules is used in order to find an optimal trajectory that minimizes the violation of safety rules. We prove that the proposed algorithm guarantees asymptotic optimality, i.e., almost-sure convergence to optimal solutions. We present results of simulation experiments and an implementation on an autonomous urban mobility-on-demand system.

cs.RO↗

arXiv2013

Anytime computation algorithms for approach-evasion differential games

This paper studies a class of approach-evasion differential games, in which one player aims to steer the state of a dynamic system to the given target set in minimum time, while avoiding some set of disallowed states, and the other player desires to achieve the opposite. We propose a class of novel anytime computation algorithms, analyze their convergence properties and verify their performance via a number of numerical simulations. Our algorithms significantly outperform the multi-grid method for the approach-evasion differential games both theoretically and numerically. Our technical approach leverages incremental sampling in robotic motion planning and viability theory.

math.OC↗

arXiv2013

Minimum-violation LTL Planning with Conflicting Specifications

We consider the problem of automatic generation of control strategies for robotic vehicles given a set of high-level mission specifications, such as "Vehicle x must eventually visit a target region and then return to a base," "Regions A and B must be periodically surveyed," or "None of the vehicles can enter an unsafe region." We focus on instances when all of the given specifications cannot be reached simultaneously due to their incompatibility and/or environmental constraints. We aim to find the least-violating control strategy while considering different priorities of satisfying different parts of the mission. Formally, we consider the missions given in the form of linear temporal logic formulas, each of which is assigned a reward that is earned when the formula is satisfied. Leveraging ideas from the automata-based model checking, we propose an algorithm for finding an optimal control strategy that maximizes the sum of rewards earned if this control strategy is applied. We demonstrate the proposed algorithm on an illustrative case study.

cs.RO↗

arXiv2012

Adaptive Q control for Tapping-mode Nano-scanning Using a Piezo-actuated Bimorph Probe

A new approach, called Adaptive Q-control, for tapping-mode Atomic Force Microscopy (AFM) is introduced and implemented on a home-made AFM set-up utilizing a Laser Doppler Vibrometer (LDV) and a piezo-actuated bimorph probe. In the standard Q-control, the effective Q-factor of the scanning probe is adjusted prior to the scanning depending on the application. However, there is a trade-off in setting the effective Q-factor of an AFM probe. The Q-factor is either increased to reduce the tapping forces or decreased to increase the maximum achievable scan speed. Realizing these two benefits simultaneously using the standard Q-control is not possible. In adaptive Q-control, the Q-factor of the probe is set to an initial value as in standard Q-control, but then modified on the fly during scanning when necessary to achieve this goal. In this paper, we present the basic theory behind the adaptive Q-control, the electronics enabling the on-line modification of the probe's effective Q-factor, and the results of the experiments comparing three different methods: scanning a) without Q-control, b) with the standard Q-control, and c) with the adaptive Q-control. The results show that the performance of the adaptive Q-control is superior to the other two methods.

physics.atom-ph↗

arXiv2012

An Incremental Sampling-based Algorithm for Stochastic Optimal Control

In this paper, we consider a class of continuous-time, continuous-space stochastic optimal control problems. Building upon recent advances in Markov chain approximation methods and sampling-based algorithms for deterministic path planning, we propose a novel algorithm called the incremental Markov Decision Process (iMDP) to compute incrementally control policies that approximate arbitrarily well an optimal policy in terms of the expected cost. The main idea behind the algorithm is to generate a sequence of finite discretizations of the original problem through random sampling of the state space. At each iteration, the discretized problem is a Markov Decision Process that serves as an incrementally refined model of the original problem. We show that with probability one, (i) the sequence of the optimal value functions for each of the discretized problems converges uniformly to the optimal value function of the original stochastic optimal control problem, and (ii) the original optimal value function can be computed efficiently in an incremental manner using asynchronous value iterations. Thus, the proposed algorithm provides an anytime approach to the computation of optimal control policies of the continuous problem. The effectiveness of the proposed approach is demonstrated on motion planning and control problems in cluttered environments in the presence of process noise.

cs.RO↗

arXiv2012

High-speed Flight in an Ergodic Forest

Inspired by birds flying through cluttered environments such as dense forests, this paper studies the theoretical foundations of a novel motion planning problem: high-speed navigation through a randomly-generated obstacle field when only the statistics of the obstacle generating process are known a priori. Resembling a planar forest environment, the obstacle generating process is assumed to determine the locations and sizes of disk-shaped obstacles. When this process is ergodic, and under mild technical conditions on the dynamics of the bird, it is shown that the existence of an infinite collision-free trajectory through the forest exhibits a phase transition. On one hand, if the bird flies faster than a certain critical speed, then, with probability one, there is no infinite collision-free trajectory, i.e., the bird will eventually collide with some tree, almost surely, regardless of the planning algorithm governing the bird's motion. On the other hand, if the bird flies slower than this critical speed, then there exists at least one infinite collision-free trajectory, almost surely. Lower and upper bounds on the critical speed are derived for the special case of a homogeneous Poisson forest considering a simple model for the bird's dynamics. For the same case, an equivalent percolation model is provided. Using this model, the phase diagram is approximated in Monte-Carlo simulations. This paper also establishes novel connections between robot motion planning and statistical physics through ergodic theory and percolation theory, which may be of independent interest.

cs.RO↗

arXiv2011

Sampling-based Algorithms for Optimal Motion Planning

During the last decade, sampling-based path planning algorithms, such as Probabilistic RoadMaps (PRM) and Rapidly-exploring Random Trees (RRT), have been shown to work well in practice and possess theoretical guarantees such as probabilistic completeness. However, little effort has been devoted to the formal analysis of the quality of the solution returned by such algorithms, e.g., as a function of the number of samples. The purpose of this paper is to fill this gap, by rigorously analyzing the asymptotic behavior of the cost of the solution returned by stochastic sampling-based algorithms as the number of samples increases. A number of negative results are provided, characterizing existing algorithms, e.g., showing that, under mild technical conditions, the cost of the solution returned by broadly used sampling-based algorithms converges almost surely to a non-optimal value. The main contribution of the paper is the introduction of new algorithms, namely, PRM* and RRT*, which are provably asymptotically optimal, i.e., such that the cost of the returned solution converges almost surely to the optimum. Moreover, it is shown that the computational complexity of the new algorithms is within a constant factor of that of their probabilistically complete (but not asymptotically optimal) counterparts. The analysis in this paper hinges on novel connections between stochastic sampling-based path planning algorithms and the theory of random geometric graphs.

cs.RO↗

arXiv2010

Incremental Sampling-based Algorithms for Optimal Motion Planning

During the last decade, incremental sampling-based motion planning algorithms, such as the Rapidly-exploring Random Trees (RRTs) have been shown to work well in practice and to possess theoretical guarantees such as probabilistic completeness. However, no theoretical bounds on the quality of the solution obtained by these algorithms have been established so far. The first contribution of this paper is a negative result: it is proven that, under mild technical conditions, the cost of the best path in the RRT converges almost surely to a non-optimal value. Second, a new algorithm is considered, called the Rapidly-exploring Random Graph (RRG), and it is shown that the cost of the best path in the RRG converges to the optimum almost surely. Third, a tree version of RRG is introduced, called the RRT$^*$ algorithm, which preserves the asymptotic optimality of RRG while maintaining a tree structure like RRT. The analysis of the new algorithms hinges on novel connections between sampling-based motion planning algorithms and the theory of random geometric graphs. In terms of computational complexity, it is shown that the number of simple operations required by both the RRG and RRT$^*$ algorithms is asymptotically within a constant factor of that required by RRT.

cs.RO↗