Active Signal Emitter Placement In Complex Environments

TL;DR

The paper tackles automatic placement of electromagnetic signal emitters in obstacle-rich environments by interleaving device deployment with sensing. It introduces a factor-graph based probabilistic lighting model that fuses an analytical ray-based propagation with real measurements, enabling obstacle-aware uncertainty reasoning, and a reconfiguration trigger that decides when to replan emitter placement. An informative path planning framework using a rollout-based POMDP and a Nelder-Mead optimizer for configuration yields both accurate light distributions and adaptive deployment. Empirical results in simulation and field tests show the approach reduces median error by up to 9.8% and outperforms baselines, demonstrating robust emitter placement in complex environments and potential applicability to other electromagnetic signals.

Abstract

Placement of electromagnetic signal emitting devices, such as light sources, has important usage in for signal coverage tasks. Automatic placement of these devices is challenging because of the complex interaction of the signal and environment due to reflection, refraction and scattering. In this work, we iteratively improve the placement of these devices by interleaving device placement and sensing actions, correcting errors in the model of the signal propagation. To this end, we propose a novel factor-graph based belief model which combines the measurements taken by the robot and an analytical light propagation model. This model allows accurately modelling the uncertainty of the light propagation with respect to the obstacles, which greatly improves the informative path planning routine. Additionally, we propose a method for determining when to re-plan the emitter placements to balance a trade-off between information about a specific configuration and frequent updating of the configuration. This method incorporates the uncertainty from belief model to adaptively determine when re-configuration is needed. We find that our system has a 9.8% median error reduction compared to a baseline system in simulations in the most difficult environment. We also run on-robot tests and determine that our system performs favorably compared to the baseline.

Figures (8)

• Figure 1: Overview: a) The desired lighting intensity, chosen by randomly placing lights, b) the lighting intensity in the environment which is unknown to the robot a priori, as well as the obstacles, c) the final light source configuration, lighting intensity and robot path produced by the proposed system, d) the final light source configuration, lighting intensity and robot path produced by the baseline system, e) example field trial. Lights circled in red are deployed by the robot, while lights circled in green are unknown to the robot.
• Figure 2: Overview of our System: A description of each module and their connections to other modules are described in \ref{['sec:approach']}. The principle modules we propose in this work are the light source reconfiguration trigger, the light source configuration algorithm and the probabilistic lighting model.
• Figure 3: Probabilistic Lighting Model. This model, described in \ref{['sec:light_belief']}, allows the robot to combine the ray marching based analytical lighting model for the configured light sources with the real-world measurements of the light intensities using additive measurement factors, $f_m$. In this example, the robot has taken a measurement at locations $(0,0)$ and $(3,1)$. The robot has previously taken a measurement at $(1,1)$ before the light sources were re-configured, which is reflected to the previous configuration factor, $f_p$. There is an obstacle at $(2,1)$, therefore, there are no variables there and distance based link factors, $f_l$, are removed.
• Figure 4: Light Belief Model Results We show the reduction in error when using the model proposed in \ref{['sec:light_belief']} when compared to a Gaussian process baseline model.
• Figure 5: Light Source Reconfiguration Triggers. Comparison of RMSE when different triggers with different parameters are used. We see that there is a balance between reconfiguring the light sources more and less often in both Logprob and Every $n$ triggers. Logprob $\alpha=1.07$ results in lowest RMSE.