265 research outputs found
Multi-resolution Low-rank Tensor Formats
We describe a simple, black-box compression format for tensors with a
multiscale structure. By representing the tensor as a sum of compressed tensors
defined on increasingly coarse grids, we capture low-rank structures on each
grid-scale, and we show how this leads to an increase in compression for a
fixed accuracy. We devise an alternating algorithm to represent a given tensor
in the multiresolution format and prove local convergence guarantees. In two
dimensions, we provide examples that show that this approach can beat the
Eckart-Young theorem, and for dimensions higher than two, we achieve higher
compression than the tensor-train format on six real-world datasets. We also
provide results on the closedness and stability of the tensor format and
discuss how to perform common linear algebra operations on the level of the
compressed tensors.Comment: 29 pages, 9 figure
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.Comment: 20 pages, 10 figures, this manuscript is submitted to the
International Journal of Robotics Research, a short version is to appear at
the 2010 Robotics: Science and Systems Conference
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.Comment: accepted to ICRA 2018. 8 pages, 8 figures, 3 tables. Video at
https://www.youtube.com/watch?v=vNIIT_M7x7Y. Code at
https://github.com/fangchangma/sparse-to-dens
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.Comment: 20 pages, 7 figures, 2 table
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.Comment: 8 pages, 14 figures, ICRA versio
Accurate Tracking of Aggressive Quadrotor Trajectories using Incremental Nonlinear Dynamic Inversion and Differential Flatness
Autonomous unmanned aerial vehicles (UAVs) that can execute aggressive (i.e.,
high-speed and high-acceleration) maneuvers have attracted significant
attention in the past few years. This paper focuses on accurate tracking of
aggressive quadcopter trajectories. We propose a novel control law for tracking
of position and yaw angle and their derivatives of up to fourth order,
specifically, velocity, acceleration, jerk, and snap along with yaw rate and
yaw acceleration. Jerk and snap are tracked using feedforward inputs for
angular rate and angular acceleration based on the differential flatness of the
quadcopter dynamics. Snap tracking requires direct control of body torque,
which we achieve using closed-loop motor speed control based on measurements
from optical encoders attached to the motors. The controller utilizes
incremental nonlinear dynamic inversion (INDI) for robust tracking of linear
and angular accelerations despite external disturbances, such as aerodynamic
drag forces. Hence, prior modeling of aerodynamic effects is not required. We
rigorously analyze the proposed control law through response analysis, and we
demonstrate it in experiments. The controller enables a quadcopter UAV to track
complex 3D trajectories, reaching speeds up to 12.9 m/s and accelerations up to
2.1g, while keeping the root-mean-square tracking error down to 6.6 cm, in a
flight volume that is roughly 18 m by 7 m and 3 m tall. We also demonstrate the
robustness of the controller by attaching a drag plate to the UAV in flight
tests and by pulling on the UAV with a rope during hover.Comment: To be published in IEEE Transactions on Control Systems Technology.
Revision: new set of experiments at increased speed (up to 12.9 m/s), updated
controller design using quaternion representation, new video available at
https://youtu.be/K15lNBAKDC
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 time
complexity, in which is the number of stations, with 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
-optimal solution for this more general, NP-hard problem
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
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