Ergodic Trajectory Planning with Dynamic Sensor Footprints

TL;DR

This paper introduces a novel ergodic trajectory planning method that accounts for dynamic, resolution-varying sensor footprints, improving information gathering efficiency in robotic systems such as aerial drones.

Contribution

It develops a new metric for ergodic planning that incorporates changing sensor footprints, along with optimization algorithms and theoretical analysis.

Findings

Achieves up to tenfold improvement in ergodicity over traditional methods.

Successfully plans trajectories for multi-drone systems to cover 3D objects.

Demonstrates the effectiveness of dynamic sensor footprint modeling in real-world scenarios.

Abstract

This paper addresses the problem of trajectory planning for information gathering with a dynamic and resolution-varying sensor footprint. Ergodic planning offers a principled framework that balances exploration (visiting all areas) and exploitation (focusing on high-information regions) by planning trajectories such that the time spent in a region is proportional to the amount of information in that region. Existing ergodic planning often oversimplifies the sensing model by assuming a point sensor or a footprint with constant shape and resolution. In practice, the sensor footprint can drastically change over time as the robot moves, such as aerial robots equipped with downward-facing cameras, whose field of view depends on the orientation and altitude. To overcome this limitation, we propose a new metric that accounts for dynamic sensor footprints, analyze the theoretic local optimality conditions, and propose numerical trajectory optimization algorithms. Experimental results show that the proposed approach can simultaneously optimize both the trajectories and sensor footprints, with up to an order of magnitude better ergodicity than conventional methods. We also deploy our approach in a multi-drone system to ergodically cover an object in 3D space.