Optimization of Directional Landmark Deployment for Visual Observer on SE(3)

An optimization method is proposed in this article for novel deployment of given number of directional landmarks (position and orientation) within a given region in the 3-D task space. This new deployment technique is built on the geometric models of both landmarks and the monocular camera. In particular, a new concept of multiple coverage probability (MCP) is defined to characterize the probability of at least
$\bm n$
landmarks being covered simultaneously by a camera at a fixed position. The optimization is conducted with respect to the position and orientation of the given number of landmarks to maximize MCP through global exploration of the given 3-D space. By adopting the elimination genetic algorithm, the final deployment of landmarks can be obtained, which are then applied to improve the convergent performance of the visual observer on
SE
(3) as a demonstration example. Both simulation and experimental results are presented to validate the effectiveness of the proposed landmark deployment optimization method.