Optimal Coupled Sensor Placement and Path-Planning in Unknown Time-Varying Environments

TL;DR

This paper introduces a coupled sensor placement and path-planning method in unknown, dynamic environments, using a novel information measure to efficiently minimize threat exposure with fewer sensors.

Contribution

It presents a new CRMI measure for joint sensor placement and path planning, and an iterative algorithm that efficiently finds near-optimal paths in changing environments.

Findings

CRMI is submodular, enabling greedy optimization.

The algorithm achieves low-variance, near-optimal paths with fewer sensors.

Numerical simulations validate the efficiency and effectiveness of the approach.

Abstract

We address path-planning for a mobile agent to navigate in an unknown environment with minimum exposure to a spatially and temporally varying threat field. The threat field is estimated using pointwise noisy measurements from a mobile sensor network. For this problem, we present a new information gain measure for optimal sensor placement that quantifies reduction in uncertainty in the path cost rather than the environment state. This measure, which we call the context-relevant mutual information (CRMI), couples the sensor placement and path-planning problem. We propose an iterative coupled sensor configuration and path-planning (CSCP) algorithm. At each iteration, this algorithm places sensors to maximize CRMI, updates the threat estimate using new measurements, and recalculates the path with minimum expected exposure to the threat. The iterations converge when the path cost variance, which is an indicator of risk, reduces below a desired threshold. We show that CRMI is submodular, and therefore, greedy optimization provides near-optimal sensor placements while maintaining computational efficiency of the CSCP algorithm. Distance-based sensor reconfiguration costs are introduced in a modified CRMI measure, which we also show to be submodular. Through numerical simulations, we demonstrate that the principal advantage of this algorithm is that near-optimal low-variance paths are achieved using far fewer sensor measurements as compared to a standard sensor placement method.