A factorization approach to inertial affine structure from motion

We consider the problem of reconstructing a 3-D scene from a moving camera with high frame rate using the affine projection model. This problem is traditionally known as Affine Structure from Motion (Affine SfM), and can be solved using an elegant low-rank factorization formulation. In this paper, we assume that an accelerometer and gyro are rigidly mounted with the camera, so that synchronized linear acceleration and angular velocity measurements are available together with the image measurements. We extend the standard Affine SfM algorithm to integrate these measurements through the use of image derivatives

Bearing-based formation control with second-order agent dynamics

We consider the distributed formation control problem for a network of agents using visual measurements. We propose solutions that are based on bearing (and optionally distance) measurements, and agents with double integrator dynamics. We assume that a subset of the agents can track, in addition to their neighbors, a set of static features in the environment. These features are not considered to be part of the formation, but they are used to asymptotically control the velocity of the agents. We analyze the convergence properties of the proposed protocols analytically and through simulations.Published versionSupporting documentatio

A factorization approach to inertial affine structure from motion

We consider the problem of reconstructing a 3-D scene from a moving camera with high frame rate using the affine projection model. This problem is traditionally known as Affine Structure from Motion (Affine SfM), and can be solved using an elegant low-rank factorization formulation. In this paper, we assume that an accelerometer and gyro are rigidly mounted with the camera, so that synchronized linear acceleration and angular velocity measurements are available together with the image measurements. We extend the standard Affine SfM algorithm to integrate these measurements through the use of image derivatives

The space of essential matrices as a Riemannian quotient manifold

The essential matrix, which encodes the epipolar constraint between points in two projective views, is a cornerstone of modern computer vision. Previous works have proposed different characterizations of the space of essential matrices as a Riemannian manifold. However, they either do not consider the symmetric role played by the two views, or do not fully take into account the geometric peculiarities of the epipolar constraint. We address these limitations with a characterization as a quotient manifold which can be easily interpreted in terms of camera poses. While our main focus in on theoretical aspects, we include applications to optimization problems in computer vision.This work was supported by grants NSF-IIP-0742304, NSF-OIA-1028009, ARL MAST-CTA W911NF-08-2-0004, and ARL RCTA W911NF-10-2-0016, NSF-DGE-0966142, and NSF-IIS-1317788

Non-natural metrics on the tangent bundle

Natural metrics provide a way to induce a metric on the tangent bundle from the metric on its base manifold. The most studied type is the Sasaki metric, which applies the base metric separately to the vertical and horizontal components. We study a more general class of metrics which introduces interactions between the vertical and horizontal components, with scalar weights. Additionally, we explicitly clarify how to apply our and other induced metrics on the tangent bundle to vector fields where the vertical component is not constant along the fibers. We give application to the Special Orthogonal Group SO(3) as an example.Published versio

Technical report on Optimization-Based Bearing-Only Visual Homing with Applications to a 2-D Unicycle Model

We consider the problem of bearing-based visual homing: Given a mobile robot which can measure bearing directions with respect to known landmarks, the goal is to guide the robot toward a desired "home" location. We propose a control law based on the gradient field of a Lyapunov function, and give sufficient conditions for global convergence. We show that the well-known Average Landmark Vector method (for which no convergence proof was known) can be obtained as a particular case of our framework. We then derive a sliding mode control law for a unicycle model which follows this gradient field. Both controllers do not depend on range information. Finally, we also show how our framework can be used to characterize the sensitivity of a home location with respect to noise in the specified bearings. This is an extended version of the conference paper [1].Comment: This is an extender version of R. Tron and K. Daniilidis, "An optimization approach to bearing-only visual homing with applications to a 2-D unicycle model," in IEEE International Conference on Robotics and Automation, 2014, containing additional proof

Riemannian consensus for manifolds with bounded curvature

Consensus algorithms are popular distributed algorithms for computing aggregate quantities, such as averages, in ad-hoc wireless networks. However, existing algorithms mostly address the case where the measurements lie in Euclidean space. In this work we propose Riemannian consensus, a natural extension of existing averaging consensus algorithms to the case of Riemannian manifolds. Unlike previous generalizations, our algorithm is intrinsic and, in principle, can be applied to any complete Riemannian manifold. We give sufficient convergence conditions on Riemannian manifolds with bounded curvature and we analyze the differences with respect to the Euclidean case. We test the proposed algorithms on synthetic data sampled from the space of rotations, the sphere and the Grassmann manifold.This work was supported by the grant NSF CNS-0834470. Recommended by Associate Editor L. Schenato. (CNS-0834470 - NSF

Resilience of multi-robot systems to physical masquerade attacks

The advent of autonomous mobile multi-robot systems has driven innovation in both the industrial and defense sectors. The integration of such systems in safety-and security-critical applications has raised concern over their resilience to attack. In this work, we investigate the security problem of a stealthy adversary masquerading as a properly functioning agent. We show that conventional multi-agent pathfinding solutions are vulnerable to these physical masquerade attacks. Furthermore, we provide a constraint-based formulation of multi-agent pathfinding that yields multi-agent plans that are provably resilient to physical masquerade attacks. This formalization leverages inter-agent observations to facilitate introspective monitoring to guarantee resilience.Accepted manuscrip