[Paper Review] Information-Theoretic Approach to Efficient Adaptive Path Planning for Mobile Robotic Environmental Sensing

Kian Hsiang Low, John M. Dolan+1 more|arXiv (Cornell University)|May 27, 2013

Advanced Bandit Algorithms Research4 citations

TL;DR

This paper proposes an information-theoretic approach to adaptive path planning for mobile robotic environmental sensing, reformulating the cost-minimizing Multi-robot Adaptive Sampling Problem (MASP) as a reward-maximizing problem using entropy-based uncertainty measurement. This reduces time complexity independent of map resolution and improves scalability, especially for large-scale, high-resolution mapping tasks, while enabling theoretical performance bounds and superior empirical results over Gaussian process-based methods.

ABSTRACT

Recent research in robot exploration and mapping has focused on sampling environmental hotspot fields. This exploration task is formalized by Low, Dolan, and Khosla (2008) in a sequential decision-theoretic planning under uncertainty framework called MASP. The time complexity of solving MASP approximately depends on the map resolution, which limits its use in large-scale, high-resolution exploration and mapping. To alleviate this computational difficulty, this paper presents an information-theoretic approach to MASP (iMASP) for efficient adaptive path planning; by reformulating the cost-minimizing iMASP as a reward-maximizing problem, its time complexity becomes independent of map resolution and is less sensitive to increasing robot team size as demonstrated both theoretically and empirically. Using the reward-maximizing dual, we derive a novel adaptive variant of maximum entropy sampling, thus improving the induced exploration policy performance. It also allows us to establish theoretical bounds quantifying the performance advantage of optimal adaptive over non-adaptive policies and the performance quality of approximately optimal vs. optimal adaptive policies. We show analytically and empirically the superior performance of iMASP-based policies for sampling the log-Gaussian process to that of policies for the widely-used Gaussian process in mapping the hotspot field. Lastly, we provide sufficient conditions that, when met, guarantee adaptivity has no benefit under an assumed environment model.

Motivation & Objective

• To address the high computational complexity of the original MASP framework, which scales poorly with map resolution and robot team size in large-scale environmental mapping.
• To develop an efficient, adaptive path planning method that maintains high map accuracy while reducing computational burden for large-scale, high-resolution hotspot field exploration.
• To establish theoretical performance bounds for adaptive vs. non-adaptive policies and approximate vs. optimal policies under the new framework.
• To demonstrate the superiority of the log-Gaussian process (ℓGP) model over the widely used Gaussian process (GP) in capturing spatially correlated, positively skewed hotspot fields.
• To identify sufficient conditions under which adaptivity provides no performance benefit under a given environment model.

Proposed method

• Reformulates the original MASP as a reward-maximizing problem by replacing the mean-squared error uncertainty criterion with an entropy-based measure, decoupling time complexity from map resolution.
• Introduces a novel adaptive variant of maximum entropy sampling by leveraging the reward-maximizing dual of the information-theoretic formulation.
• Uses convexity properties of the entropy and uncertainty terms to derive theoretical bounds on policy performance, including the advantage of adaptive over non-adaptive strategies.
• Employs a piecewise linear approximation of the belief state using a finite set of z-samples to enable efficient computation, with convergence guarantees via iterative refinement.
• Applies the generalized Jensen bound to upper- and lower-bound the value function, enabling scalable approximate solution of the planning problem.
• Derives sufficient conditions under which adaptivity provides no benefit by analyzing the structure of the environment model and belief update dynamics.

Experimental results

Research questions

• RQ1 Can an information-theoretic reformulation of MASP reduce time complexity independent of map resolution?
• RQ2 How does the performance of adaptive policies based on the log-Gaussian process compare to non-adaptive policies and Gaussian process-based methods?
• RQ3 What theoretical bounds can be established for the performance advantage of optimal adaptive policies over non-adaptive ones?
• RQ4 Under what conditions does adaptivity provide no benefit in the context of a given environment model?
• RQ5 How does the proposed iMASP framework improve exploration efficiency in high-resolution, large-scale hotspot field mapping?

Key findings

• The time complexity of solving the iMASP problem is independent of map resolution, enabling scalable deployment in large-scale, high-resolution environments.
• The proposed iMASP-based policies achieve significantly lower map uncertainty than policies based on the Gaussian process, particularly in capturing extreme values and spatial clustering in hotspot fields.
• Theoretical bounds show that optimal adaptive policies can achieve substantial performance gains over non-adaptive policies, with the gap quantified by the model's spatial correlation structure.
• The performance of approximately optimal adaptive policies is bounded relative to the optimal policy, with convergence guarantees through iterative refinement of belief state approximations.
• Sufficient conditions were derived under which adaptivity provides no benefit, specifically when the environment model exhibits certain symmetry and independence properties in the belief update process.
• Empirical results confirm that iMASP outperforms baseline methods in both simulation and real-world scenarios involving log-Gaussian process fields, with reduced uncertainty and improved hotspot detection.