Simplified Continuous High-Dimensional Belief Space Planning With Adaptive Probabilistic Belief-Dependent Constraints

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 article, we consider a recently introduced probabilistic belief-dependent constrained partially observable Markov decision process (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 sampled future observations episodes 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 and a corresponding action sequence, given a set of candidate action sequences, 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 the online decision making. Our universal framework applies to any belief-dependent constrained continuous POMDP with parameteric beliefs, as well as nonparameteric 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 (for e.g., Information Gathering, active simultaneous localization and mapping (SLAM)). As a case study, we apply our method to two challenging problems of high dimensional belief space planning: active SLAM and sensor deployment. Extensive realistic simulations corroborate the superiority of our proposed ideas.