Trajectory generation on SE(3) with applications to a class of underactuated vehicles

Mani H. Dhullipalla, Reza Hamrah, Amit Sanyal

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

This paper addresses the problem of generating a continuous and differentiable trajectory on the Lie group of rigid body motions, se(3), for a class of underactuated vehicles modeled as rigid bodies. The three rotational degrees of freedom (DOF) are independently actuated, while only one translational DOF is actuated by a body-fixed thrust vector. This model is applicable to a large set of unmanned vehicles, including fixed-wing and rotorcraft unmanned aerial vehicles (UAVs). The formulation utilizes exponential coordinates to express the underactuation constraint as an intrinsic part of the problem. It provides steps to generate a rest-to-rest trajectory after obtaining conditions that guarantee controllability. An attitude trajectory is selected to satisfy the given initial and final attitude state. The position trajectory generation is subsequently posed as an optimal control problem expressed as a linear quadratic regulator (LQR) in the exponential coordinates corresponding to position. As a result, an optimal position trajectory is obtained which ensures that the trajectory generated is feasible with realistic velocities and with given initial pose and final pose, while satisfying the underactuation constraint. Numerical simulation results are obtained that validate this trajectory generation scheme.

Original languageEnglish (US)
Title of host publication2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2557-2562
Number of pages6
Volume2018-January
ISBN (Electronic)9781509028733
DOIs
StatePublished - Jan 18 2018
Event56th IEEE Annual Conference on Decision and Control, CDC 2017 - Melbourne, Australia
Duration: Dec 12 2017Dec 15 2017

Other

Other56th IEEE Annual Conference on Decision and Control, CDC 2017
CountryAustralia
CityMelbourne
Period12/12/1712/15/17

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ASJC Scopus subject areas

  • Decision Sciences (miscellaneous)
  • Industrial and Manufacturing Engineering
  • Control and Optimization

Cite this

Dhullipalla, M. H., Hamrah, R., & Sanyal, A. (2018). Trajectory generation on SE(3) with applications to a class of underactuated vehicles. In 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017 (Vol. 2018-January, pp. 2557-2562). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2017.8264029