[Paper Review] On Sensing, Agility, and Computation Requirements for a Data-gathering Agile Robotic Vehicle

Fangchang Ma, Sertaç Karaman|arXiv (Cornell University)|Apr 7, 2017

Optimization and Search Problems59 references3 citations

TL;DR

This paper proposes a theoretical framework to co-design sensing, agility, and computation capabilities for data-gathering robotic vehicles operating in stochastic environments with unknown, Poisson-distributed targets. By modeling the problem as a maximum-reward collection task linked to last-passage percolation in statistical mechanics, it derives that performance improves with higher maneuverability (diminishing returns) and sensing range, while computation demands grow more rapidly for planning than inference, especially under increased sensing and agility.

ABSTRACT

We consider a robotic vehicle tasked with gathering information by visiting a set of spatially-distributed data sources, the locations of which are not known a priori, but are discovered on the fly. We assume a first-order robot dynamics involving drift and that the locations of the data sources are Poisson-distributed. In this setting, we characterize the performance of the robot in terms of its sensing, agility, and computation capabilities. More specifically, the robot's performance is characterized in terms of its ability to sense the target locations from a distance, to maneuver quickly, and to perform computations for inference and planning. We also characterize the performance of the robot in terms of the amount and distribution of information that can be acquired at each data source. The following are among our theoretical results: the distribution of the amount of information among the target locations immensely impacts the requirements for sensing targets from a distance; performance increases with increasing maneuvering capability, but with diminishing returns; and the computation requirements increase more rapidly for planning as opposed to inference, with both increasing sensing range and maneuvering ability. We provide computational experiments to validate our theoretical results. Finally, we demonstrate that these results can be utilized in the co-design of sensing, actuation, and computation capabilities of mobile robotic systems for an information-gathering mission. Our proof techniques establish novel connections between the fundamental problems of robotic information-gathering and the last-passage percolation problem of statistical mechanics, which may be of interest on its own right.

Motivation & Objective

• To establish provable performance bounds for robotic vehicles gathering data from unknown, spatially distributed sources.
• To characterize the interplay between sensing range, vehicle agility, and computational load in information-gathering missions.
• To provide a co-design framework for selecting UAV hardware and software capabilities based on mission requirements.
• To link robotic information-gathering to statistical mechanics via the last-passage percolation model.
• To validate theoretical results through computational experiments and apply them to sensor selection for unattended ground sensors.

Proposed method

• Model the robot’s motion and data collection as a maximum-reward collection problem in a stochastic reward field.
• Reduce the discrete version of the problem to the last-passage percolation model from statistical mechanics.
• Use known results from statistical mechanics to derive asymptotic performance bounds on reward collection.
• Extend discrete results to continuous space using scaling and limit arguments.
• Validate theoretical predictions with extensive computational experiments on trajectory planning and reward collection.
• Apply findings to sensor network design, comparing homogeneous vs. randomized sensor precision for improved estimation confidence.

Experimental results

Research questions

• RQ1 How does the distribution of information at target locations affect the required sensing range for effective data gathering?
• RQ2 How does increasing vehicle agility impact data collection performance, and does it exhibit diminishing returns?
• RQ3 How do sensing range and maneuvering capability jointly influence the computational load for planning versus inference?
• RQ4 Can randomizing sensor precision improve estimation confidence compared to uniform precision in unattended ground sensor networks?
• RQ5 To what extent can results from last-passage percolation in statistical mechanics be applied to robotic information-gathering problems?

Key findings

• Performance increases with higher maneuvering capability, but with diminishing returns as agility improves.
• The expected reward collection rate converges to √(2λ) per unit length almost surely when rewards are uniformly 1 and agility is bounded.
• Randomizing sensor precision (e.g., exponential distribution with mean 1) yields a mean precision gain of at least 2.1, significantly outperforming homogeneous sensors with gain √2.
• Variance in sensor precision leads to faster decay in estimation error variance, improving robustness and confidence in inference.
• Computation requirements grow more rapidly for planning than for inference as sensing range and agility increase.
• Theoretical results derived from last-passage percolation provide tight bounds on optimal data collection performance in stochastic environments.