Expected Free Energy-based Informative Path Planning for Robotic Mars Exploration

Planning under uncertainty requires agents to balance goal achievement with information gathering. Active inference addresses this through the Expected Free Energy (EFE), a cost function that unifies instrumental and epistemic objectives. However, existing EFE-based methods typically employ specialized optimization procedures that are difficult to extend or analyze. In this paper, we show that EFE-based planning can be formulated as Variational Free Energy minimization on a generative model augmented with epistemic priors. Our main result demonstrates that minimizing a Variational Free Energy functional with appropriately chosen priors yields a decomposition into expected plan costs (the EFE) plus a complexity term. This formulation reinforces theoretical consistency with the Free Energy Principle by casting planning as the same inferential process that governs perception and learning. We validate our approach on three environments of increasing complexity: a deterministic T-maze, a stochastic Reactivity Maze, and a partially observable MiniGrid DoorKey-8x8 environment. The experiments demonstrate that the epistemic priors induce information-seeking behavior, that the variational formulation yields policy-based inference outperforming plan-based methods under stochastic transitions, and that temporal factorization enables scalability to environments where existing tabular active inference methods cannot operate.

An agent acting under partial observability must decide when to gather information and which observations are worth their cost. Standard POMDPs value information only through its eventual effect on reward. The $ρ$-POMDP framework instead rewards uncertainty reduction directly, through a belief-dependent utility $ρ$, but in practice both the choice of $ρ$ and the weight placed on it are tuned by hand for every task. We show that active inference removes this tuning entirely. Minimizing Expected Free Energy (EFE) is exactly equivalent to solving a $ρ$-POMDP whose utility is expected information gain, and the exploration weight is fixed at $w=1$ because the variational bound expresses pragmatic and epistemic value in the same units (nats). We prove this equivalence for observe-then-commit POMDPs and extend it to factored observation POMDPs, a broader class that covers interleaved observe-act problems such as non-destructive testing and mobile sensing, where gathering information leaves the hidden state unchanged. Experiments support the theory. Across environments ranging from the classic Tiger problem to RockSample and a new Structural Inspection benchmark with over 65,000 states, the untuned weight matches or outperforms reward-only planning at the same horizon, avoids the over-exploration of bonuses tuned per task, and sits near the reward-maximizing knee of the success-reward Pareto frontier. The practical payoff is an exploration objective that works out of the box. In applications such as fault detection and medical screening, where every test has a price and every missed fault has a cost, EFE supplies a belief-dependent utility that is derived rather than tuned.

Designing learnable information-theoretic objectives for robot exploration remains challenging. Such objectives aim to guide exploration toward data that reduces uncertainty in model parameters, yet it is often unclear what information the collected data can actually reveal. Although reinforcement learning (RL) can optimize a given objective, constructing objectives that reflect parametric learnability is difficult in high-dimensional robotic systems. Many parameter directions are weakly observable or unidentifiable, and even when identifiable directions are selected, omitted directions can still influence exploration and distort information measures. To address this challenge, we propose Quasi-Optimal Experimental Design (Q{\footnotesize OED}), an adaptive information objective grounded in optimal experimental design. Q{\footnotesize OED} (i) performs eigenspace analysis of the Fisher information matrix to identify an observable subspace and select identifiable parameter directions, and (ii) modifies the exploration objective to emphasize these directions while suppressing nuisance effects from non-critical parameters. Under bounded nuisance influence and limited coupling between critical and nuisance directions, Q{\footnotesize OED} provides a constant-factor approximation to the ideal information objective that explores all parameters. We evaluate Q{\footnotesize OED} on simulated and real-world navigation and manipulation tasks, where identifiable-direction selection and nuisance suppression yield performance improvements of \SI{35.23}{\percent} and \SI{21.98}{\percent}, respectively. When integrated as an exploration objective in model-based policy optimization, Q{\footnotesize OED} further improves policy performance over established RL baselines.