Sensor placement for improved robotic navigation

Abstract

Consider a set of fixed sensors used to estimate the state of a vehicle (e.g. position, orientation and velocity) while it attempts to follow a pre-planned trajectory. Since the sensor can only provide a measurement to the vehicle when it is within range, the deployment of the sensors will have a major impact on the ability of the vehicle to follow the trajectory. The problem addressed here is to optimally place the sensors in the environment such that the weighted function of the estimation error at each time-step is minimized. An optimization formulation is proposed that accounts for the uncertainty of the vehicle's state in determining whether it can receive a measurement from a sensor. A confidence level is introduced as a tuning parameter that controls the conservativeness of the solution. Consequently, the resulting solution increases the likelihood of the vehicle successfully following its intended trajectory. Finally, due to the interdependence between the sensors' positions, a novel incremental optimization algorithm is presented which significantly outperforms a standard nonlinear optimization procedure. Experimental and simulation results are shown which characterize the performance of the proposed algorithm.