Optimal geometric motion planning for a spin-stabilized spacecraft

James Biggs, Nadjim Horri

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

A method requiring low-computational overhead is presented which generates low-torque reference motions between arbitrary orientations for spin-stabilized spacecraft. The initial stage solves a constrained optimal control problem deriving analytical solutions for a class of smooth and feasible reference motions. Specifically, for a quadratic cost function an application of Pontryagin’s maximum principle leads to a completely integrable Hamiltonian system that is, exactly solvable in closed-form, expressed in terms of several free parameters. This is shown to reduce the complexity of a practical motion planning problem from a constrained functional optimization problem to an unconstrained parameter optimization problem. The generated reference motions are then tracked using an augmented quaternion feedback law, consisting of the sum of a proportional plus derivative term and a term to compensate nonlinear dynamics. The method is illustrated with an application to re-point a spin-stabilized agile micro-spacecraft using zero propellant. The low computational overhead of the method enhances its suitability for on-board motion generation.
LanguageEnglish
Pages609-616
Number of pages8
JournalSystems and Control Letters
Volume61
Issue number4
DOIs
Publication statusPublished - Apr 2012

Fingerprint

Motion planning
Spacecraft
Hamiltonians
Maximum principle
Propellants
Cost functions
Torque
Derivatives
Feedback

Keywords

  • nonholonomic motion planning
  • parametric optimization
  • pontryagin's maximum principle
  • attitude control
  • tracking

Cite this

Biggs, James ; Horri, Nadjim. / Optimal geometric motion planning for a spin-stabilized spacecraft. In: Systems and Control Letters. 2012 ; Vol. 61, No. 4. pp. 609-616.
@article{b7870e335c1a482eb93ed986412e33ed,
title = "Optimal geometric motion planning for a spin-stabilized spacecraft",
abstract = "A method requiring low-computational overhead is presented which generates low-torque reference motions between arbitrary orientations for spin-stabilized spacecraft. The initial stage solves a constrained optimal control problem deriving analytical solutions for a class of smooth and feasible reference motions. Specifically, for a quadratic cost function an application of Pontryagin’s maximum principle leads to a completely integrable Hamiltonian system that is, exactly solvable in closed-form, expressed in terms of several free parameters. This is shown to reduce the complexity of a practical motion planning problem from a constrained functional optimization problem to an unconstrained parameter optimization problem. The generated reference motions are then tracked using an augmented quaternion feedback law, consisting of the sum of a proportional plus derivative term and a term to compensate nonlinear dynamics. The method is illustrated with an application to re-point a spin-stabilized agile micro-spacecraft using zero propellant. The low computational overhead of the method enhances its suitability for on-board motion generation.",
keywords = "nonholonomic motion planning, parametric optimization, pontryagin's maximum principle, attitude control, tracking",
author = "James Biggs and Nadjim Horri",
year = "2012",
month = "4",
doi = "10.1016/j.sysconle.2012.02.002",
language = "English",
volume = "61",
pages = "609--616",
journal = "Systems and Control Letters",
issn = "0167-6911",
number = "4",

}

Optimal geometric motion planning for a spin-stabilized spacecraft. / Biggs, James; Horri, Nadjim.

In: Systems and Control Letters, Vol. 61, No. 4, 04.2012, p. 609-616.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Optimal geometric motion planning for a spin-stabilized spacecraft

AU - Biggs, James

AU - Horri, Nadjim

PY - 2012/4

Y1 - 2012/4

N2 - A method requiring low-computational overhead is presented which generates low-torque reference motions between arbitrary orientations for spin-stabilized spacecraft. The initial stage solves a constrained optimal control problem deriving analytical solutions for a class of smooth and feasible reference motions. Specifically, for a quadratic cost function an application of Pontryagin’s maximum principle leads to a completely integrable Hamiltonian system that is, exactly solvable in closed-form, expressed in terms of several free parameters. This is shown to reduce the complexity of a practical motion planning problem from a constrained functional optimization problem to an unconstrained parameter optimization problem. The generated reference motions are then tracked using an augmented quaternion feedback law, consisting of the sum of a proportional plus derivative term and a term to compensate nonlinear dynamics. The method is illustrated with an application to re-point a spin-stabilized agile micro-spacecraft using zero propellant. The low computational overhead of the method enhances its suitability for on-board motion generation.

AB - A method requiring low-computational overhead is presented which generates low-torque reference motions between arbitrary orientations for spin-stabilized spacecraft. The initial stage solves a constrained optimal control problem deriving analytical solutions for a class of smooth and feasible reference motions. Specifically, for a quadratic cost function an application of Pontryagin’s maximum principle leads to a completely integrable Hamiltonian system that is, exactly solvable in closed-form, expressed in terms of several free parameters. This is shown to reduce the complexity of a practical motion planning problem from a constrained functional optimization problem to an unconstrained parameter optimization problem. The generated reference motions are then tracked using an augmented quaternion feedback law, consisting of the sum of a proportional plus derivative term and a term to compensate nonlinear dynamics. The method is illustrated with an application to re-point a spin-stabilized agile micro-spacecraft using zero propellant. The low computational overhead of the method enhances its suitability for on-board motion generation.

KW - nonholonomic motion planning

KW - parametric optimization

KW - pontryagin's maximum principle

KW - attitude control

KW - tracking

U2 - 10.1016/j.sysconle.2012.02.002

DO - 10.1016/j.sysconle.2012.02.002

M3 - Article

VL - 61

SP - 609

EP - 616

JO - Systems and Control Letters

T2 - Systems and Control Letters

JF - Systems and Control Letters

SN - 0167-6911

IS - 4

ER -