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

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

Ajith Anil Meera, Pablo Lanillos, Wouter Kouw · N/A · 2026

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Summary

An autonomous robot efficiently exploring an unknown environment, such as looking for water sources on Mars, faces two simultaneous demands: building an accurate information map while quickly finding the regions of greatest value, and paying for every meter of travel and the cost of every measurement it takes.

Abstract Summary

An autonomous robot efficiently exploring an unknown environment, such as looking for water sources on Mars, faces two simultaneous demands: building an accurate information map while quickly finding the regions of greatest value, and paying for every meter of travel and the cost of every measurement it takes. Classical information-seeking and reward-seeking criteria address only one of these objectives at a time. Here, we propose Expected Free Energy (EFE), the principled action-selection objective from active inference, as a unifying criterion for budgeted robotic informative path planning. Maintaining a Gaussian-process belief over the information field, our agent plans continuous trajectories that minimize expected free energy under hard path-length constraints. The results from multiple realizations show that EFE-based planning yields accurate posterior maps and locates the highest-value regions simultaneously, outperforming information-theoretic baselines under the same settings. In robotic exploration, these unified, easy-to-tune principled information-gathering strategies facilitate autonomous deployment while enforcing efficiency and resource constraints.

Key Points

  • An autonomous robot efficiently exploring an unknown environment, such as looking for water sources on Mars, faces two simultaneous demands: building an accurate information map while quickly finding the regions of greatest value, and paying for every meter of travel and the cost of every measurement it takes.
  • Classical information-seeking and reward-seeking criteria address only one of these objectives at a time.
  • Here, we propose Expected Free Energy (EFE), the principled action-selection objective from active inference, as a unifying criterion for budgeted robotic informative path planning.
  • Maintaining a Gaussian-process belief over the information field, our agent plans continuous trajectories that minimize expected free energy under hard path-length constraints.
  • The results from multiple realizations show that EFE-based planning yields accurate posterior maps and locates the highest-value regions simultaneously, outperforming information-theoretic baselines under the same settings.

Problem Statement

A robot explores a bounded region $\Omega\subset\mathbb{R}^{2}$ in search of an unknown scalar information field $f:\Omega\to\mathbb{R}$ that it cannot observe directly. The only way the robot learns $f$ is by traveling to a location and taking a noisy measurement there.

Following a continuous path $\gamma$, the robot collects $N$ samples at chosen positions $X_{1},\dots,X_{N}\in\Omega$, each corrupted by additive sensor noise, with noise variance $\sigma_{n}^{2}>0$.

Problem Statement — Expected Free Energy-based Informative Path Planning for Robotic Mars Exploration
Figure 2: The top panel shows the ground truth of the information map, the final GP posterior mean and uncertainty, after following the path shown in the top right panel. The bottom panel shows the EFE objective function, the order of next locations selected for information gathering, the RMSE of the information map and the simple regret plotted against robot path length.

Method

We maintain a probabilistic belief over the field, plan short trajectories that maximize expected free energy per unit travel, and execute them in a receding-horizon loop until the movement budget is spent. Algorithm 1 summarizes the procedure. The following sections will explain the methodology followed by each subprocess within the algorithm. We model the unknown field $f$ as a GP.

Method — Expected Free Energy-based Informative Path Planning for Robotic Mars Exploration
Figure 3: Instances of the final (continuous) path executed by the robot navigator in the realistic simulation environment.

Results

We show our proposed EFE-IPP behavior and compare it with other state-of-the-art methods within the synthetic Mars exploration environment. The robot does not have access to the ground truth belief and has to explore the environment, taking measurements/samples to build an accurate information map, limited by the travel length budget.

Figure 2 shows the results of one simulation experiment (details of the simulation setup in Appendix A).

Results — Expected Free Energy-based Informative Path Planning for Robotic Mars Exploration
Figure 4: The map quality (RMSE) and optimization quality (simple regret) of all methods (results of 20 seeds: mean and SEM) plotted with respect to the robot path length.

Sources and Demonstrations

Figures are reproduced from Meera et al. See the full paper for experimental details and the project page, when the paper links one, for demonstrations and videos.

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