Optimal visibility-based path and motion planning of mobile observers for 3-D objects

Various optimization problems derived from visibility-based path and motion planning of mobile observers for three-dimensional objects such as asteroids are considered. First, the mathematical formulations of these problems are presented. These problems are generally non-smooth. Then, sufficient con...

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Bibliographic Details
Published in:Nonlinear analysis 2009-12, Vol.71 (12), p.e839-e848
Main Author: Wang, P.K.C.
Format: Article
Language:English
Subjects:
Asteroids
Computation
Mathematical analysis
Mathematical models
Mobile observers
Motion planning
Non-smooth optimization problem
Nonlinearity
Observers
Optimal control
Optimal motion planning
Optimal path planning
Optimization
Visibility
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Summary:Various optimization problems derived from visibility-based path and motion planning of mobile observers for three-dimensional objects such as asteroids are considered. First, the mathematical formulations of these problems are presented. These problems are generally non-smooth. Then, sufficient conditions for the existence of solutions are established. The nature of the optimal solutions to some of the posed problems is illustrated by simple examples. Next, the computational complexities in the solution of these problems are discussed briefly. Finally, explicit necessary optimality conditions for asteroid-observer optimal motion planning problems are presented.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2008.12.008