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Technical Brief

Stochastic Optimal Motion Planning for the Attitude Kinematics of a Rigid Body With Non-Gaussian Uncertainties

[+] Author and Article Information
Taeyoung Lee

Assistant Professor
Department of Mechanical and Aerospace Engineering,
George Washington University,
Washington, DC 20052
e-mail: tylee@gwu.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received January 31, 2014; final manuscript received June 6, 2014; published online October 21, 2014. Assoc. Editor: Jongeun Choi.

J. Dyn. Sys., Meas., Control 137(3), 034502 (Oct 21, 2014) (7 pages) Paper No: DS-14-1054; doi: 10.1115/1.4027950 History: Received January 31, 2014; Revised June 06, 2014

This paper investigates global uncertainty propagation and stochastic motion planning for the attitude kinematics of a rigid body. The Fokker–Planck equation on the special orthogonal group is numerically solved via noncommutative harmonic analysis to propagate a probability density function along flows of the attitude kinematics. Based on this, a stochastic optimal control problem is formulated to rotate a rigid body while avoiding obstacles within uncertain environments in an optimal fashion. The proposed intrinsic, geometric formulation does not require the common assumption that uncertainties are Gaussian or localized. It can be also applied to complex rotational maneuvers of a rigid body without singularities in a unified way. The desirable properties are illustrated by numerical examples.

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Figures

Grahic Jump Location
Fig. 1

Attitude uncertainty propagation (diffusion)

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Fig. 2

Attitude uncertainty propagation (diffusion and advection)

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Fig. 3

Stochastic motion planning of a rigid body: (ε = 0.3)

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Fig. 4

Stochastic motion planning of a rigid body: (ε = 0.1)

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