15,376 research outputs found
Dynamic Estimation of Rigid Motion from Perspective Views via Recursive Identification of Exterior Differential Systems with Parameters on a Topological Manifold
We formulate the problem of estimating the motion of a rigid object viewed under perspective projection as the identification of a dynamic model in Exterior Differential form with parameters on a topological manifold.
We first describe a general method for recursive identification of nonlinear implicit systems using prediction error criteria. The parameters are allowed to move slowly on some topological (not necessarily smooth) manifold. The basic recursion is solved in two different ways: one is based on a simple extension of the traditional Kalman Filter to nonlinear and implicit measurement constraints, the other may be regarded as a generalized "Gauss-Newton" iteration, akin to traditional Recursive Prediction Error Method techniques in linear identification. A derivation of the "Implicit Extended Kalman Filter" (IEKF) is reported in the appendix.
The ID framework is then applied to solving the visual motion problem: it indeed is possible to characterize it in terms of identification of an Exterior Differential System with parameters living on a C0 topological manifold, called the "essential manifold". We consider two alternative estimation paradigms. The first is in the local coordinates of the essential manifold: we estimate the state of a nonlinear implicit model on a linear space. The second is obtained by a linear update on the (linear) embedding space followed by a projection onto the essential manifold. These schemes proved successful in performing the motion estimation task, as we show in experiments on real and noisy synthetic image sequences
Nonlinear Model Predictive Control for Multi-Micro Aerial Vehicle Robust Collision Avoidance
Multiple multirotor Micro Aerial Vehicles sharing the same airspace require a
reliable and robust collision avoidance technique. In this paper we address the
problem of multi-MAV reactive collision avoidance. A model-based controller is
employed to achieve simultaneously reference trajectory tracking and collision
avoidance. Moreover, we also account for the uncertainty of the state estimator
and the other agents position and velocity uncertainties to achieve a higher
degree of robustness. The proposed approach is decentralized, does not require
collision-free reference trajectory and accounts for the full MAV dynamics. We
validated our approach in simulation and experimentally.Comment: Video available on: https://www.youtube.com/watch?v=Ot76i9p2ZZo&t=40
Extended Kalman Filter on SE(3) for Geometric Control of a Quadrotor UAV
An extended Kalman filter (EKF) is developed on the special Euclidean group,
SE(3) for geometric control of a quadrotor UAV. It is obtained by performing an
extensive linearization on SE(3) to estimate the state of the quadrotor from
noisy measurements. Proposed estimator considers all the coupling effects
between rotational and translational dynamics, and it is developed in a
coordinate-free fashion. The desirable features of the proposed EKF are
illustrated by numerical examples and experimental results for several
scenarios. The proposed estimation scheme on SE(3) has been unprecedented and
these results can be particularly useful for aggressive maneuvers in GPS denied
environments or in situations where parts of onboard sensors fail.Comment: arXiv admin note: text overlap with arXiv:1304.6765, arXiv:1411.298
Invariant EKF Design for Scan Matching-aided Localization
Localization in indoor environments is a technique which estimates the
robot's pose by fusing data from onboard motion sensors with readings of the
environment, in our case obtained by scan matching point clouds captured by a
low-cost Kinect depth camera. We develop both an Invariant Extended Kalman
Filter (IEKF)-based and a Multiplicative Extended Kalman Filter (MEKF)-based
solution to this problem. The two designs are successfully validated in
experiments and demonstrate the advantage of the IEKF design
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