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Published in: Meccanica 5/2021

10-03-2021

Estimation of robot states with poisson process based on EKF approximate of Kushner filter: a completely coordinate free Lie group approach

Authors: Rohit Rana, Prerna Gaur, Vijyant Agarwal, Harish Parthasarathy

Published in: Meccanica | Issue 5/2021

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Abstract

In this paper, a Lie coordinate-free torque based Euler–Lagrange equations of motion are developed for a 3-D link (3-DOF) robot. Intentional torque and jerky torque (non-intentional torque) are considered as the inputs to the dynamic profile of the robot. The jerky torque is modelled as a superposition of compound Poisson processes, which is a unique feature. The state vector of the robot, i.e., angular position and angular velocity vector, is thus a Markov process whose transition probability generator can be expressed in terms of the rate of the compound Poisson process that defines the jerky torque. Proof of frame invariance is provided to support the coordinate-free robot dynamics profile. Noise-free measurement is investigated as an ideal case. Angular position measurement is considered with white Gaussian noise. Further, an implementable finite-dimensional EKF approximate to Kushner–Kallianpur filter is obtained to estimate the robot state vector. Finally, the simulations are implemented on commercially available Omni bundle robot.

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Literature
4.
go back to reference Constantinescu D, Croft EA (2000) Smooth and time-optimal trajectory planning for industrial manipulators along specified paths. J Robot Syst 17:233–249CrossRef Constantinescu D, Croft EA (2000) Smooth and time-optimal trajectory planning for industrial manipulators along specified paths. J Robot Syst 17:233–249CrossRef
5.
go back to reference Piazzi A, Visioli A (2000) Global minimum-jerk trajectory planning of robot manipulators. IEEE Trans Ind Electron 47:140–149CrossRef Piazzi A, Visioli A (2000) Global minimum-jerk trajectory planning of robot manipulators. IEEE Trans Ind Electron 47:140–149CrossRef
9.
go back to reference Rana R, Gaur P, Agarwal V, Parthasarathy H (2019) Tremor estimation and removal in robot-assisted surgery using Lie groups and EKF. Robotica 37(11):1904–1921CrossRef Rana R, Gaur P, Agarwal V, Parthasarathy H (2019) Tremor estimation and removal in robot-assisted surgery using Lie groups and EKF. Robotica 37(11):1904–1921CrossRef
15.
21.
go back to reference Van Trees HL, Bell KL, Tian Z (2013) 5.2.2 and 5.2.1. In: Detection estimation and modulation theory, part I: detection, estimation, and filtering theory, 2nd Edition. ISBN: 978-1-118-53992-7 Van Trees HL, Bell KL, Tian Z (2013) 5.2.2 and 5.2.1. In: Detection estimation and modulation theory, part I: detection, estimation, and filtering theory, 2nd Edition. ISBN: 978-1-118-53992-7
26.
go back to reference Applebaum D (2009) Levy processes and stochastic calculus, 2nd edn. Cambridge University Press, CambridgeCrossRef Applebaum D (2009) Levy processes and stochastic calculus, 2nd edn. Cambridge University Press, CambridgeCrossRef
Metadata
Title
Estimation of robot states with poisson process based on EKF approximate of Kushner filter: a completely coordinate free Lie group approach
Authors
Rohit Rana
Prerna Gaur
Vijyant Agarwal
Harish Parthasarathy
Publication date
10-03-2021
Publisher
Springer Netherlands
Published in
Meccanica / Issue 5/2021
Print ISSN: 0025-6455
Electronic ISSN: 1572-9648
DOI
https://doi.org/10.1007/s11012-021-01325-3

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