Global Optimization Approaches to Sensor Placement: Model Versions and Illustrative Results
We investigate the optimized configuration of sensor cameras to be placed in a suitably defined three-dimensional cubic region E, in order to maximize the coverage of a completely embedded cube C⊂E. The sensing regions associated with each of the cameras
- PDF / 165,786 Bytes
- 13 Pages / 439.37 x 666.142 pts Page_size
- 41 Downloads / 145 Views
Global Optimization Approaches to Sensor Placement: Model Versions and Illustrative Results Giorgio Fasano and Ja´nos D. Pinte´r
Abstract We investigate the optimized configuration of sensor cameras to be placed in a suitably defined three-dimensional cubic region E, in order to maximize the coverage of a completely embedded cube CE. The sensing regions associated with each of the cameras are convex, but not necessarily identical. In order to handle this important practical problem, we present mixed integer linear programming (MILP) and mixed integer nonlinear programming (MINLP) model formulations and propose corresponding solution approaches. Illustrative numerical results are presented, and certain application aspects are also discussed. Keywords Sensor camera network design • Continuous set covering problems in three-dimensions • Global optimization • Mixed integer linear and nonlinear model forms • Solution strategies • Illustrative numerical results
10.1
Introduction
The topic discussed here originates from a case study carried out in a space engineering context, within the framework of future Mars exploration studies. We consider a drone scale model aimed at stimulating the landing phase of a robot vehicle that has to be permanently monitored by a set of sensor cameras. This scenario leads to challenging camera placement optimization issues: in this
MSC Classification (2000) 68 T20, 90 C11, 90 C30, 90 C59, 90 C90 G. Fasano (*) Thales Alenia Space Italia S.p.A., Str. Antica di Collegno 253, 10146 Turin, Italy e-mail: [email protected] J.D. Pinte´r Pinte´r Consulting Services Inc., Halifax, Canada e-mail: [email protected] G. Fasano and J.D. Pinte´r (eds.), Modeling and Optimization in Space Engineering, Springer Optimization and Its Applications 73, DOI 10.1007/978-1-4614-4469-5_10, # Springer Science+Business Media New York 2013
235
236
G. Fasano and J.D. Pinte´r
study we describe a modeling and algorithmic solution approach followed by illustrative results. The drone is supposed to move inside a three-dimensional (3D) virtual cube denoted by C. Our general objective is to cover C optimally by the union of the fields of view (FOW) of the set of cameras. The cameras can be of different types: they have to be placed outside of C but inside an external cube denoted by E that embeds C and has parallel facets to C. We assume that the (truncated) FOW of each camera is a rectangular-based pyramid, without considering sensor orientation constraints at this point. Then, in a possible modeling approach, our objective can be to minimize the total number (or total cost) of the sensors needed to assure complete coverage of C. Alternatively, we can maximize the volume (a proper subset of C) that is covered by a given set of devices; a total equipment cost constraint could also be considered. In this work we present optimization models related to the latter formulation. Although the case study discussed in this chapter is related to a specific simulation framework, many similar optimiza
Data Loading...
