Source-linked AI summary
Expected Free Energy-based Informative Path Planning for Robotic Mars Exploration
Ajith Anil Meera, Pablo Lanillos, Wouter Kouw
TL;DR
Budgeted robotic exploration must simultaneously learn an accurate information map and find its highest-value regions despite costly travel and measurements. The paper uses adaptive Expected Free Energy to plan continuous, budget-constrained trajectories, jointly improving map accuracy and optimization over competing baselines.
Problem
Budgeted informative path planning must balance accurate map reconstruction with locating the field’s most valuable region while limiting costly travel and measurements.
Method
The planner uses adaptive Expected Free Energy to score continuous trajectories, combine exploration and exploitation, and respect a hard movement budget through fantasy-path belief updates.
Results
Adaptive EFE jointly minimized map RMSE and simple regret, outperforming information-theoretic, Bayesian-optimization, and coverage baselines across realizations.
Takeaways & Limitations
EFE provides a single budget-aware objective for robotic information gathering that supports both map learning and value-region optimization.
Takeaways & Limitations
The evaluation is conducted across realizations on a continuous scalar field, leaving broader deployment settings outside the reported scope.
Abstract
from arXiv · showhide
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.
1 Introduction
Robotic exploration must jointly locate high-value regions, learn the surrounding information field, and respect limited travel, energy, and time budgets. The paper proposes Expected Free Energy as a principled unified objective and introduces a budget-constrained planner that outperforms stated baselines on map accuracy and simple regret.
- Problem: Robots must identify where a phenomenon is strongest while learning its information field under limited travel, energy, and time resources.The introduction lists exploration tasks including finding water, monitoring oil spills, mapping radiation, surveying crops, locating cyanobacteria, and finding survivors.
- Limitations of existing criteria: Information-theoretic criteria produce accurate maps but ignore value locations, whereas Bayesian-optimization acquisitions target optima while neglecting the rest of the map.Practitioners therefore choose one objective or hand-tune a weighted sum without a principled balance.
- Expected Free Energy: Expected Free Energy unifies goal-seeking and information-seeking through one coherent criterion rather than arbitrary weighting.The paper frames EFE as a brain-inspired active-inference objective that resolves exploration versus exploitation.
- Proposed framework: The proposed adaptive, non-myopic, computationally tractable framework plans continuous trajectories in a receding-horizon loop under a hard travel budget.This contribution is presented as an EFE-based informative path-planning framework.
- Budget-aware balancing: A budget-aware EFE annealing schedule adaptively balances exploration and exploitation according to the fraction of budget consumed.The schedule is explicitly designed to account for resource use during planning.
- Evaluation: The proposed planner outperforms information-theoretic and Bayesian-optimization baselines on map accuracy and simple regret.The comparison is stated for the evaluated planning setting.
2 Problem Statement
The problem is to explore a bounded region with noisy measurements of an unobserved information field under a finite travel budget. Informative planning must jointly reconstruct the field accurately and locate its most valuable region.
- Problem formulation: The robot explores a bounded region Ω⊂R2 containing an unknown scalar information field f: Ω→R that it cannot observe directly.It learns f only by traveling to locations and collecting noisy measurements.
- Problem formulation: Each measurement is taken at a selected position along a continuous path and is corrupted by additive sensor noise.The path yields N samples at positions X1, . . . , XN∈Ω.
- Problem formulation: A movement budget B>0 limits the path’s total length ℓ(γ), requiring the robot to allocate travel carefully.Travel is explicitly treated as a constrained resource rather than a free operation.
- Problem formulation: The IPP objective defines informativeness as jointly reconstructing an accurate map of f across Ω and locating the field’s most valuable region.A utility J scores both objectives.
3 Method
The method combines a Gaussian-process belief with expected-free-energy scoring to plan continuous, budget-constrained exploration trajectories. A fantasy-path evaluator and receding-horizon replanning update decisions after each measurement while balancing information gain and high-value observations.
- Gaussian-process belief: A Gaussian process reconstructs the unknown field online from noisy samples, providing closed-form posterior mean and predictive uncertainty for planning.The planner uses the posterior mean as its field estimate and the GP belief as its only environmental summary.
- Expected-free-energy objective: Expected free energy scores candidate measurements through pragmatic value for preferred observations and epistemic value from expected posterior-uncertainty reduction.The preference target is set optimistically as y⋆ = ybest + κ, where κ > 0 controls the aspiration offset.
- Budget-aware exploration: A budget-aware temperature schedule shifts the same objective from exploration early in the mission toward exploitation as the consumed budget fraction increases.The transition is controlled by p0, the halfway budget fraction, and k, which controls transition sharpness.
- Continuous trajectory evaluation: The planner scores smooth continuous polynomial trajectories by total EFE per metre, using a fantasy path that treats each predicted mean as an imagined measurement before scoring the next waypoint.A positive segment-length floor δ prevents vanishingly short segments from dominating the objective.
- Receding-horizon execution: Receding-horizon model-predictive control commits only to the first planned segment, takes a noisy measurement, updates the GP, and replans until the movement budget is exhausted.Differential Evolution optimizes the resulting non-convex, 2n-dimensional continuous path problem.
4 Results
Results show that EFE-based planning learns accurate information maps while directing exploration toward high-value regions under travel constraints. The framework also executes adaptive continuous paths and is evaluated against established Bayesian optimization and informative path-planning baselines.
- Experimental setting: The experiments assess exploration without ground-truth belief, requiring measurement-based map construction within a travel-length budget.The robot must explore the environment while taking measurements or samples.
- Simulation behavior: The planner’s posterior mean closely matches the ground truth, while measurements reduce uncertainty around sampled locations.In one simulation, exploration initially covers the map before concentrating near the maximum-value region.
- Comparative evaluation: Figure 4 evaluates map quality with RMSE and optimization quality with simple regret against robot path length.Results are reported as mean and SEM across 20 seeds.
- Simulation behavior: The high-level planner supplies paths that the low-level controller adapts continuously to terrain-height changes, orientation errors, and other real-time uncertainties.This demonstrates adaptive exploration in a realistic simulation setting.
- Comparative evaluation: The evaluation compares joint optimization and learning using 20 seeds across aEFE, Expected Improvement, UCB, Mutual Information, VAR (variance σ2), and coverage planner.Expected Improvement and UCB are Bayesian Optimization acquisition functions, while Mutual Information, VAR, and coverage planner are IPP benchmarks.
5 Conclusion
The paper presents a budget-aware adaptive Expected Free Energy formulation that unifies map learning and optimization for informative path planning. It evaluates continuous, non-myopic trajectory planning under a hard movement budget, reporting faster reductions in map RMSE and simple regret across realizations.
- 5 Conclusion: The proposed adaptive EFE formulation unifies map learning and optimization under a single objective.The objective is described as budget-aware and brain-inspired.
- 5 Conclusion: Per-distance EFE scores continuous trajectories while a fantasy path rolls the belief forward for non-myopic planning.This combines trajectory evaluation with belief propagation during planning.
- 5 Conclusion: A hard movement budget constrains the planner while it explores a continuous scalar field across multiple realizations.The constraint is enforced during trajectory planning.
- 5 Conclusion: Map RMSE and simple regret decrease faster than under information-theoretic, Bayesian-optimization, and coverage-based alternatives.The supplied passage states this comparative outcome but does not provide numerical values.
Appendix · A: Simulation settings
The simulations use a standardized 20 m×20 m Gaussian-bump field, fixed sensing and travel budgets, and shared planning conditions to compare seven objectives. A PyBullet Mars-like rover environment provides a qualitative demonstration of the EFE planner.
- A: Simulation settings: The workspace is 20 m×20 m with a hidden field formed by two Gaussian bumps peaking at (5, 6) and (5, 16) m.The field is standardized so comparisons across objectives are scale-invariant.
- A: Simulation settings: Each run starts with N0 = 3 Sobol measurements and grants the robot a travel budget of B = 200 m.The per-segment travel cap is ℓmax = 5 m, with planning horizon n = 3 via-points.
- A: Simulation settings: Measurements have Gaussian noise with standard deviation σn = 0.3 in the standardized output.The passage also specifies a Gaussian-process belief, but the provided text ends before its full description.
- A: Simulation settings: The comparison includes EFE, aEFE, EI, UCB, MI, VAR, and a deterministic lawnmower Coverage baseline.EFE uses fixed τ2 = 7 and y⋆ = ybest + 0.1; aEFE uses τ2: 20 → 0.6, midpoint p0 = 0.4, and steepness k = 10.
- A: Simulation settings: All methods share the same fantasy-path framework, Gaussian process, fantasy rollout, optimizer, and budget; only the per-point objective score differs.The reported metrics are map RMSE and simple regret, summarized by mean and standard error over 20 independent seeds.
- A: Simulation settings: The qualitative demonstration embeds the EFE planner in a PyBullet environment approximating Martian conditions with procedurally generated 128×128 terrain.The terrain extends a 3 m margin beyond the planner’s domain so the rover never reaches a cliff.
- A: Simulation settings: The Mars-like environment uses a publicly available Mars albedo map and simulated Mars surface gravity of 3.71 m/s2.The provided passage describes the setting as a qualitative demonstration.
- A: Simulation settings: A Husky skid-steer rover follows via-points using a proportional heading-and-speed controller.The supplied passage truncates immediately after introducing the rover’s synthetic setup.