Orthogonal dual tensor method for solving the A X = X B sensor calibration problem

Condurache, Daniel; Burlacu, Adrian

doi:10.1016/j.mechmachtheory.2016.06.002

Cited by 77 publications

(33 citation statements)

References 23 publications

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“…In that framework, a MLE problem is formulated and solved with an iterative Levenberg-Marquardt solver. The closely related hand-eye calibration problem [6] has been extensively studied [7], [8], and we use a cost function formulation similar to the one in [9].…”

Section: Related Workmentioning

confidence: 99%

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Certifiably Globally Optimal Extrinsic Calibration From Per-Sensor Egomotion

Giamou

Peretroukhin

et al. 2019

IEEE Robot. Autom. Lett.

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We present a certifiably globally optimal algorithm for determining the extrinsic calibration between two sensors that are capable of producing independent egomotion estimates. This problem has been previously solved using a variety of techniques, including local optimization approaches that have no formal global optimality guarantees. We use a quadratic objective function to formulate calibration as a quadratically constrained quadratic program (QCQP). By leveraging recent advances in the optimization of QCQPs, we are able to use existing semidefinite program (SDP) solvers to obtain a certifiably global optimum via the Lagrangian dual problem. Our problem formulation can be globally optimized by existing general-purpose solvers in less than a second, regardless of the number of measurements available and the noise level. This enables a variety of robotic platforms to rapidly and robustly compute and certify a globally optimal set of calibration parameters without a prior estimate or operator intervention. We compare the performance of our approach with a local solver on extensive simulations and multiple real datasets. Finally, we present necessary observability conditions that connect our approach to recent theoretical results and analytically support the empirical performance of our system. Global Optimum minimize R,t JR + Jt, subject to R 2 SO(3) < l a t e x i t s h a 1 _ b a s e 6 4 = " j v M n N v m u H A y R x q A 6 N L e F c X m 9 j 2 c = " > A A A C r H i c b V F d b 9 M w F H X C x 7 b w s T I e e b G o Q E O s U Q L V y t 4 m 8 Y K Q E A P W b l J d V Y 7 j r G a O k 9 n X a C X y j + F n 8 T / 4 A b h p x D b g S J a O z 7 3 n 2 j o 3 q 6 U w k C Q / g / D W 7 T t 3 N z a 3 o n v 3 H z z c 7 j 3 a m Z j K a s b H r J K V P s 2 o 4 V I o P g Y B k p / W m t M y k / w k O 3 + 7 q p 9 8 4 9 q I S h 3 D s u a z k p 4 pz 7 3 n 2 j o 3 q 6 U w k C Q / g / D W 7 T t 3 N z a 3 o n v 3 H z z c 7 j 3 a m Z j K a s b H r J K V P s 2 o 4 V I o P g Y B k p / W m t M y k / w k O 3 + 7 q p 9 8 4 9 q I S h 3 D s u a z k p 4 p U Q h G w U v z 3 o 8 t j D G x K v c 9 H B r y g Y I W l 8 1 n t 0 c m n E G l G 3 C u I c A v o S m F E q X 4 z p 2 L v O s 5 J h e W 5 v j 9 / J r L 4 Z e t c O X d w 4 R E 7 S P t D G O z r 7 6 G o b o x 5 G o C J k J 1 v V 8 + u t 3 X L + a 9 f h I n L f C / J O 1 I H 3 U 4 m v d + k b x i t u Q K m K T G T N O k h l l D N Q g m u Y u I N b y m 7 J y e 8 a m n i p b c z J o 2 S o e f e S X H R a X 9 U Y B b 9 b q j o a U x y z L z n S W F h f m 7 t h L / V 5 t a K N 7 M G q F q C 1 y x 9 U O F l T 4 I v N o L z o X 2 u c i l J 5 R p 4 f + K 2 Y J q y s B v J i K t s b m w w i 9 z I K n P Z 2 A W l Q Z m w c T + 5 t q U Q L V y t 4 m 8 Y K Q E A P W b l J d V Y 7 j r G a O k 9 n X a C X y j + F n 8 T / 4 A b h p x D b g S J a O z 7 3 n 2 j o 3 q 6 U w k C Q / g / D W 7 T t 3 N z a 3 o n v 3 H z z c 7 j 3 a m Z j K a s b H r J K V P s 2 o 4 V I o P g Y B k p / W m t M y k / w k O 3 + 7 q p 9 8 4 9 q I S h 3 D s u a z k p 4 p U Q h G w U v z 3 o 8 t j D G x K v c 9 H B r y g Y I W l 8 1 n t 0 ...

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Section: Related Workmentioning

confidence: 99%

“…This final expression is found in many calibration papers [7], [9] and will allow us to form a cost function based on the noisy relative motion measurementsV at andV bt .…”

Section: B Extrinsic Calibration From Per-sensor Egomotionmentioning

confidence: 99%

Certifiably Globally Optimal Extrinsic Calibration From Per-Sensor Egomotion

Giamou

Peretroukhin

et al. 2019

IEEE Robot. Autom. Lett.

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“…The internal structure of any orthogonal dual tensor R ∈ SO 3 is illustrated in a series of results which were detailed in our previous work [17,18,23]. …”

Section: Rigid Body Motion Parameterization Using Dual Lie Algebramentioning

confidence: 99%

“…Orthogonal dual tensorial maps are a powerful instrument in the study of the rigid motion with respect to an inertial and noninertial reference frames. More on dual numbers, dual vectors and dual tensors can be found in [2,[16][17][18][19][20][21][22][23].2.1. Isomorphism between Lie group of the rigid displacements SE 3 and Lie group of the orthogonal dual tensors SO 3…”

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On Six DOF Relative Orbital Motion of Satellites

Condurache¹

2018

Space Flight

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In this chapter, we reveal a dual-tensor-based procedure to obtain exact expressions for the six degree of freedom (6-DOF) relative orbital law of motion in the specific case of two Keplerian confocal orbits. The result is achieved by pure analytical methods in the general case of any leader and deputy motion, without singularities or implying any secular terms. Orthogonal dual tensors play a very important role, with the representation of the solution being, to the authors' knowledge, the shortest approach for describing the complete onboard solution of the 6-DOF orbital motion problem. The solution does not depend on the local-vertical-local-horizontal (LVLH) properties involves that is true in any reference frame of the leader with the origin in its mass center. A representation theorem is provided for the full-body initial value problem. Furthermore, the representation theorems for rotation part and translation part of the relative motion are obtained.Keywords: relative orbital motion, full body problem, dual algebra, Lie group, Lie algebra, closed form solution IntroductionThe relative motion between the leader and the deputy in the relative motion is a six-degreesof-freedom (6-DOF) motion engendered by the joining of the relative translational motion with the rotational one. Recently, the modeling of the 6-DOF motion of spacecraft gained a special attention [1][2][3][4][5], similar to the controlling the relative pose of satellite formation that became a very important research subject [6][7][8][9][10]. The approach implies to consider the relative translational and rotational dynamics in the case of chief-deputy spacecraft formation to be modeled using vector and tensor formalism.In this chapter we reveal a dual algebra tensor based procedure to obtain exact expressions for the six D.O.F relative orbital law of motion for the case of two Keplerian confocal orbits.© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Orthogonal dual tensors play a very important role, the representation of the solution being, to the authors' knowledge, the shortest approach for describing the complete onboard solution of the six D.O.F relative orbital motion problem. Because the solution does not depend on the LVLH properties involves that is true in any reference frame of the Leader with the origin in its mass center. To obtain this solution, one has to know only the inertial motion of the Leader spacecraft and the initial conditions of the deputy satellite in the local-vertical-local-horizontal (LVLH) frame. For the full body initial value problem, a general representation theorem is given. More, the real and imaginary parts are split and representation theorems for the rotation and translation parts of the relative orbital motion are obtained. Regarding translation, we w...

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Satellite Assembly Technology by Robot Under Visual Guidance and Force Feedback Control

Long

Zhang

2018

Advances in Intelligent Systems and Computing

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Orthogonal dual tensor method for solving the A X = X B sensor calibration problem

Cited by 77 publications

References 23 publications

Certifiably Globally Optimal Extrinsic Calibration From Per-Sensor Egomotion

Certifiably Globally Optimal Extrinsic Calibration From Per-Sensor Egomotion

On Six DOF Relative Orbital Motion of Satellites

Satellite Assembly Technology by Robot Under Visual Guidance and Force Feedback Control

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