Observer design on the Special Euclidean group SE(3)

Hua, Minh‐Duc; Zamani, Morteza Saheb; Trumpf, Jochen; Mahony, Robert; Hamel, Tarek

doi:10.1109/cdc.2011.6160453

Cited by 61 publications

(63 citation statements)

References 10 publications

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“…In several robotics applications where the considered Lie group is SO(3) and where the outputs live in copies of S 2 , as well as in the case where the considered Lie group is SE(3) and the homogeneous output spaces are copies of R 3 , it has been shown that the reductivity condition imposed by part (d) of Proposition 4 holds and hence the resulting observer is implementable based on sensor measurements [15], [11].…”

Section: Constructing a Cost Function On The Lie Groupmentioning

confidence: 99%

“…Specifically, when the output manifold is a reductive homogeneous space of the Lie group, the authors in [14], [15] propose an observer design on the output manifold and then lift the designed observer to obtain a corresponding observer on the Lie group. The approach can be applied to many interesting real world scenarios such as attitude estimator design on the Lie group SO (3) or pose estimation on the Lie group SE(3) [3], [7], [11], [18], [20], [26]. For the specific cases of attitude estimation on SO(3) and pose estimation on SE(3), some methods have been proposed for the concurrent estimation of an unknown constant bias corrupting the velocity measurement [18], [26], [27].…”

Section: Introductionmentioning

confidence: 99%

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Bias estimation for invariant systems on Lie groups with homogeneous outputs

Khosravian

Trumpf

Mahony

et al. 2013

52nd IEEE Conference on Decision and Control

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In this paper, we provide a general method of state estimation for a class of invariant systems on connected matrix Lie groups where the group velocity measurement is corrupted by an unknown constant bias. The output measurements are given by a collection of actions of a single Lie group on several homogeneous output spaces, a model that applies to a wide range of practical scenarios. The proposed observer consists of a group estimator part, providing an estimate of a bounded state evolving on the Lie group, and a bias estimator part, providing an estimate of the bias in the associated Lie algebra. We employ the gradient of a suitable invariant cost function on the Lie group as an innovation term in the group estimator. We design the bias estimator such that it guarantees uniform local exponential stability of the estimation error dynamics around the zero error state. We propose a systematic methodology for the design of suitable cost functions on Lie groups by lifting invariant cost functions from the homogeneous output spaces. We show that the resulting observer is implementable based on available sensor measurements if the homogeneous output spaces are reductive. As an example, we derive an observer for rigid body attitude using vector and gyro measurements with unknown constant gyro bias.

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Section: Constructing a Cost Function On The Lie Groupmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bias estimation for invariant systems on Lie groups with homogeneous outputs

Khosravian

Trumpf

Mahony

et al. 2013

52nd IEEE Conference on Decision and Control

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“…An example is shown by Vasconcelos et al [15] in which estimation is done by using known landmarks. Similar work is done by Hua [16] and Bras et al [17], where the latter is for range-only measurements. These methods require prior knowledge of the landmarks position which makes them fall short on the SLAM problem.…”

Section: Introductionmentioning

confidence: 62%

“…In simulations the observer has been tested with initializationθ li = π without any convergence problem. The bias estimated can then be used in cascade with the simplified complimentary filter from [16] …”

Section: E Slam Attitude Problem Formulationmentioning

confidence: 99%

Cascade attitude observer for the SLAM filtering problem

Bjørne

Brekke

Johansen

2017

2017 IEEE Conference on Control Technology and Applications (CCTA)

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Abstract-This article presents an attitude observer that exploits both bearing and range measurements from landmarks, in addition to reference vectors such as magnetometer and accelerometer. It is a gyro bias observer in cascade with a simplified complementary filter, driven by a gyro measurement, in which the gyro bias is estimated by comparing the bearing dynamics with the gyro measurements. The observer is compared to a full complimentary filter, and it is shown that it is more robust to initial gyro bias estimation error compared to the complimentary filter. The article also reveals how this new observer handles magnetometer failure and can use landmarks as reference vectors.

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“…In [10] an exponentially convergent nonlinear observer on SE(3) was presented with almost global stability for attitude, position and bias estimation, using landmark measurements and non-ideal velocity readings. A gradient-based observer on SE(3) using position measurements, was designed in [11], however, the effect of bias was not considered. In [12], using strapdown inertial measurements, GPS, and vector observations, discrete-time complementary filters for estimating the attitude and position with compensating for rate gyro bias was proposed.…”

Section: Introductionmentioning

confidence: 99%

Global estimation of rigid-body attitude/position using a single landmark and biased velocity measurements

Moeini

Namvar

2014

53rd IEEE Conference on Decision and Control

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In this paper we propose an observer for attitude and position estimation of a rigid body using data provided by rate gyros, Doppler sensors and a single landmark measurement. Under an observability condition which depends on landmark position, asymptotic convergence of the observer is proved. The initial attitude and position estimates can assume any values and hence the convergence is in global sense. We extend the observer for the case of non-ideal translational and angular velocity measurements. Simulation examples demonstrate position and attitude estimation in two cases: a single moving landmark, and three fixed landmarks.

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Observer design on the Special Euclidean group SE(3)

Cited by 61 publications

References 10 publications

Bias estimation for invariant systems on Lie groups with homogeneous outputs

Bias estimation for invariant systems on Lie groups with homogeneous outputs

Cascade attitude observer for the SLAM filtering problem

Global estimation of rigid-body attitude/position using a single landmark and biased velocity measurements

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