Sensor Placement Algorithms for Triangulation Based Localization

Robots operating in a workspace can localize themselves by querying nodes of a sensor-network deployed in the same workspace. This paper addresses the problem of computing the minimum number and placement of sensors so that the localization uncertainty at every point in the workspace is less than a given threshold. We focus on triangulation based state estimation where measurements from two sensors must be combined for an estimate. We show that the general problem for arbitrary uncertainty models is computationally hard. For the general problem, we present a solution framework based on integer linear programming and demonstrate its practical feasibility with simulations. Finally, we present an approximation algorithm for a geometric uncertainty measure which simultaneously addresses occlusions, angle and distance constraints.