Simplified Continuous High Dimensional Belief Space Planning with Adaptive Probabilistic Belief-dependent Constraints

TL;DR

This paper introduces an adaptive, simplified approach for belief space planning in high-dimensional, partially observable environments, enabling faster decision-making with maintained accuracy, especially useful for information gathering tasks like active SLAM.

Contribution

It presents a novel adaptive framework for belief-dependent constrained POMDPs that accelerates online planning without sacrificing solution quality, applicable to both parametric and nonparametric beliefs.

Findings

Significantly speeds up belief space planning in high-dimensional problems.

Maintains solution quality while accelerating decision-making.

Effective in complex tasks like active SLAM.

Abstract

Online decision making under uncertainty in partially observable domains, also known as Belief Space Planning, is a fundamental problem in robotics and Artificial Intelligence. Due to an abundance of plausible future unravelings, calculating an optimal course of action inflicts an enormous computational burden on the agent. Moreover, in many scenarios, e.g., information gathering, it is required to introduce a belief-dependent constraint. Prompted by this demand, in this paper, we consider a recently introduced probabilistic belief-dependent constrained POMDP. We present a technique to adaptively accept or discard a candidate action sequence with respect to a probabilistic belief-dependent constraint, before expanding a complete set of future observations samples and without any loss in accuracy. Moreover, using our proposed framework, we contribute an adaptive method to find a maximal feasible return (e.g., information gain) in terms of Value at Risk for the candidate action sequence with substantial acceleration. On top of that, we introduce an adaptive simplification technique for a probabilistically constrained setting. Such an approach provably returns an identical-quality solution while dramatically accelerating online decision making. Our universal framework applies to any belief-dependent constrained continuous POMDP with parametric beliefs, as well as nonparametric beliefs represented by particles. In the context of an information-theoretic constraint, our presented framework stochastically quantifies if a cumulative information gain along the planning horizon is sufficiently significant (e.g. for, information gathering, active SLAM). We apply our method to active SLAM, a highly challenging problem of high dimensional Belief Space Planning. Extensive realistic simulations corroborate the superiority of our proposed ideas.