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Analysis of exit probability for a trajectory tracking robot in case of a rare event

Published online by Cambridge University Press:  09 July 2021

Rohit Rana Open the ORCID record for Rohit Rana [Opens in a new window] ,
Prerna Gaur Open the ORCID record for Prerna Gaur [Opens in a new window] ,
Vijyant Agarwal Open the ORCID record for Vijyant Agarwal [Opens in a new window]  and
Harish Parthasarathy
Rohit Rana*
Affiliation:
Instrumentation and Control Engineering Department, Netaji Subhas University of Technology, New Delhi, India
Prerna Gaur
Affiliation:
Instrumentation and Control Engineering Department, Netaji Subhas University of Technology, New Delhi, India
Vijyant Agarwal
Affiliation:
Mechanical Engineering Department, Netaji Subhas University of Technology, New Delhi, India
Harish Parthasarathy
Affiliation:
Electronics and Communication Engineering Department, Netaji Subhas University of Technology, New Delhi, India
*
*Corresponding author. E-mail: [email protected]
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Abstract

In this paper, a novel statistical application of large deviation principle (LDP) to the robot trajectory tracking problem is presented. The exit probability of the trajectory from stability zone is evaluated, in the presence of small-amplitude Gaussian and Poisson noise. Afterward, the limit of the partition function for the average tracking error energy is derived by solving a fourth-order system of Euler–Lagrange equations. Stability and computational complexity of the proposed approach is investigated to show the superiority over the Lyapunov method. Finally, the proposed algorithm is validated by Monte Carlo simulations and on the commercially available Omni bundleTM robot.

Keywords

nonlinear dynamicslarge deviation theoryPoisson processGaussian noiserobotprobabilityrobotics
Type
Research Article
Information
Robotica , Volume 40 , Issue 4 , April 2022 , pp. 907 - 932
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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