This paper presents an approach to motion planning for left-invariant kinematic systems defined on the 6-D frame bundles of symmetric spaces of constant cross-sectional curvature. A covering map is used to convert the original differential equation into two coupled equations each evolving on a 3-D Lie group. These lower dimensional systems lend themselves to a minimal global representation that avoid singularities associated with the use of exponential coordinates. Open-loop and closed-loop kinematic control problems are addressed to demonstrate the use of this mapping for analytical and numerical based motion planning methods. The approach is applied to a spacecraft docking problem using two different types of actuation: (i) a fully-actuated continuous low-thrust propulsion system and (ii) an under-actuated single impulsive thruster and reaction wheel system.

Motion planning on a class of 6-D Lie groups via a covering map

Biggs, James Douglas;Henninger, Helen
2019

Abstract

This paper presents an approach to motion planning for left-invariant kinematic systems defined on the 6-D frame bundles of symmetric spaces of constant cross-sectional curvature. A covering map is used to convert the original differential equation into two coupled equations each evolving on a 3-D Lie group. These lower dimensional systems lend themselves to a minimal global representation that avoid singularities associated with the use of exponential coordinates. Open-loop and closed-loop kinematic control problems are addressed to demonstrate the use of this mapping for analytical and numerical based motion planning methods. The approach is applied to a spacecraft docking problem using two different types of actuation: (i) a fully-actuated continuous low-thrust propulsion system and (ii) an under-actuated single impulsive thruster and reaction wheel system.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
File in questo prodotto:
File Dimensione Formato  
BIGGJ02-19.pdf

Accesso riservato

Descrizione: Paper
: Publisher’s version
Dimensione 776.71 kB
Formato Adobe PDF
776.71 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
BIGGJ_OA_03-19.pdf

embargo fino al 06/12/2019

Descrizione: Paper open access
: Post-Print (DRAFT o Author’s Accepted Manuscript-AAM)
Dimensione 1.13 MB
Formato Adobe PDF
1.13 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11311/1070373
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 5
  • ???jsp.display-item.citation.isi??? 6
social impact