State Estimation for Robotics

Barfoot, Timothy D.

doi:10.1017/9781316671528

Cited by 608 publications

(460 citation statements)

References 50 publications

Supporting

Mentioning

457

Contrasting

Order By: Relevance

“…Furthermore, the number of optimisation variables reduces from four to three. Our approach draws inspiration from the multiplicative extended Kalman filter (MEKF) [12,15,16] and from approaches within the field of robotics [17][18][19][20][21]. Inspired by [5,6], instead of solving (10) for each time step, we perform only a single gradient descent iteration.…”

Section: Orientation From Accelerometer and Magnetometermentioning

confidence: 99%

A Fast and Robust Algorithm for Orientation Estimation Using Inertial Sensors

Kok

Schön

2019

IEEE Signal Process. Lett.

View full text Add to dashboard Cite

We present a novel algorithm for online, real-time orientation estimation. Our algorithm integrates gyroscope data and corrects the resulting orientation estimate for integration drift using accelerometer and magnetometer data. This correction is computed, at each time instance, using a single gradient descent step with fixed step length. This fixed step length results in robustness against model errors, e.g. caused by large accelerations or by short-term magnetic field disturbances, which we numerically illustrate using Monte Carlo simulations. Our algorithm estimates a three-dimensional update to the orientation rather than the entire orientation itself. This reduces the computational complexity by approximately 1/3 with respect to the state of the art. It also improves the quality of the resulting estimates, specifically when the orientation corrections are large. We illustrate the efficacy of the algorithm using experimental data.

show abstract

Section: Orientation From Accelerometer and Magnetometermentioning

confidence: 99%

A Fast and Robust Algorithm for Orientation Estimation Using Inertial Sensors

Kok

Schön

2019

IEEE Signal Process. Lett.

View full text Add to dashboard Cite

show abstract

“…Among them, we can easily determine the derivative with respect to the translation from . Moreover, the derivative with respect to the rotation vector

bold-italicω goodbreakinfix= [ω_{1}, ω_{2}, ω_{3}] goodbreakinfix\in frakturso (3)

can be derived according to Barfoot () as follows:

\begin{matrix} true \\ right \frac{\partial {bold-italicp}_{i}^{c}}{\partial ω} & center = & left \frac{\partial (R \cdot {bold-italicp}_{i} + t)}{\partial ω} \\ right & center = & left - {(bold-italicR \cdot p_{i})}^{\land} J, \end{matrix}

where the

i

‐th column indicates the derivative with respect to the rotation parameter

ω_{i}

and

bold-italicJ

represents the left Jacobian of

S O (3)

bold-italicJ goodbreakinfix= \frac{\sin (\bar{ω})}{\bar{ω}} bold-italicI goodbreakinfix+ ((), 1 - \frac{\sin (\bar{ω})}{\bar{ω}}) bold-italica a^{T} goodbreakinfix+ \frac{1 - \cos (\bar{ω})}{\bar{ω}} a^{\land},

where

\overset{ω}{true} goodbreakinfix= ∣ bold-italicω ∣

and

bold-italica goodbreakinfix= bold-italicω ∕ \overset{ω}{true}

.…”

Section: Optimizationmentioning

confidence: 99%

Automatic targetless camera–LIDAR calibration by aligning edge with Gaussian mixture model

Kang

Doh

2019

Journal of Field Robotics

View full text Add to dashboard Cite

This paper presents a calibration algorithm that does not require an artificial target object to precisely estimate a rigid‐body transformation between a camera and a light detection and ranging (LIDAR) sensor. The proposed algorithm estimates calibration parameters by minimizing a cost function that evaluates the edge alignment between two sensor measurements. In particular, the proposed cost function is constructed using a projection model‐based many‐to‐many correspondence of the edges to fully exploit measurements with different densities (dense photometry and sparse geometry). The alignment of the many‐to‐many correspondence is represented using the Gaussian mixture model (GMM) framework. Here, each component of the GMM, including weight, displacement, and standard deviation, is derived to suitably capture the intensity, location, and influential range of the edge measurements, respectively. The derived cost function is optimized by the gradient descent method with an analytical derivative. A coarse‐to‐fine scheme is also applied by gradually decreasing the standard deviation of the GMM to enhance the robustness of the algorithm. Extensive indoor and outdoor experiments validate the claim that the proposed GMM strategy improves the performance of the proposed algorithm. The experimental results also show that the proposed algorithm outperforms previous methods in terms of precision and accuracy by providing calibration parameters of standard deviations less than 0.6° and 2.1 cm with a reprojection error of 1.78 for a 2.1‐megapixel image (2,048 × 1,024) in the best case.

show abstract

“…And we define the operator ⊞ that maps the disturbance Δx in tangent space to a disturbance on the manifold around the estimate X ̅ , X * = X ̅ ⊞ Δx. A detailed introduction of SE(3) Lie-manifold can be found in [10,15]. By replacing the operator + with ⊞, the framework of conventional optimization algorithm can be applied to the optimization problem on manifold.…”

Section: Problem Formulationmentioning

confidence: 99%

Visual-UWB Navigation System for Unknown Environments

Shi¹,

Cui²,

Li³

et al. 2018

Proceedings of the 31st International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 201

View full text Add to dashboard Cite

Navigation applications relying on the Global Navigation Satellite System (GNSS) are limited in indoor environments and GNSS-denied outdoor terrains such as dense urban or forests. In this paper, we present a novel accurate, robust and low-cost GNSS-independent navigation system, which is composed of a monocular camera and Ultra-wideband (UWB) transceivers. Visual techniques have gained excellent results when computing the incremental motion of the sensor, and UWB methods have proved to provide promising localization accuracy due to the high time resolution of the UWB ranging signals. However, the monocular visual techniques with scale ambiguity are not suitable for applications requiring metric results, and UWB methods assume that the positions of the UWB transceiver anchor are pre-calibrated and known, thus precluding their application in unknown and challenging environments. To this end, we advocate leveraging the monocular camera and UWB to create a map of visual features and UWB anchors. We propose a visual-UWB Simultaneous Localization and Mapping (SLAM) algorithm which tightly combines visual and UWB measurements to form a joint non-linear optimization problem on Lie-Manifold. The 6 Degrees of Freedom (DoF) state of the vehicles and the map are estimated by minimizing the UWB ranging errors and landmark reprojection errors. Our navigation system starts with an exploratory task which performs the real-time visual-UWB SLAM to obtain the global map, then the navigation task by reusing this global map. The tasks can be performed by different vehicles in terms of equipped sensors and payload capability in a heterogeneous team. We validate our system on the public datasets, achieving typical centimeter accuracy and 0.1% scale error.

show abstract

State Estimation for Robotics

Cited by 608 publications

References 50 publications

A Fast and Robust Algorithm for Orientation Estimation Using Inertial Sensors

A Fast and Robust Algorithm for Orientation Estimation Using Inertial Sensors

Automatic targetless camera–LIDAR calibration by aligning edge with Gaussian mixture model

Visual-UWB Navigation System for Unknown Environments

Contact Info

Product

Resources

About