Optimally Trading Energy for Information through Speed Trajectory Optimization of Sustainably Powered Mobile Robots

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.

This paper presents a comprehensive methodology, backed by simulation and experimental results, for an adaptive mission planning strategy that is mathematically grounded in the maximization of the information-driven quantity of clarity. In particular, the methodology introduced in this work addresses the use of sustainably powered autonomous surface vessels (ASVs) to perform scientific missions that prioritize locations of maximum interest. Because these locations of maximum interest are not known a priori but are rather identified based on in-situ measurements, online adaptation is essential for mission planning. Furthermore, the reliance on a limited-power renewable resource requires an adaptation strategy that maximizes information gathering subject to mobility restrictions imposed by the renewable resource. Our approach addresses these challenges through a clarity-driven ergodic search, where clarity represents a mathematical quantity that has been rigorously linked to differential (information) entropy. In our approach, a target clarity map is adapted online to reflect the prioritization of certain areas based on in-situ measurements, and an ergodic path planner continually re-plans based on the target clarity map and ASV speed limitations (driven by the renewable propulsion source). Focusing on a solar-powered ASV, we present simulations and experiments conducted at Jordan Lake, North Carolina, demonstrating the effectiveness of the proposed approach.

In classical Informative Path Planning (C-IPP), robots are typically modeled as mobile sensors that acquire digital measurements such as images or radiation levels. In this model, since making a measurement leaves the robot's physical state unchanged, the cost of traversing an edge remains static regardless of when it is traversed. This is a natural assumption for many missions, but does not extend to settings involving physical sample collection, where each collected sample adds mass and increases the energy cost of all subsequent motion. As a result, IPP formulations that ignore this coupling between information gain and load-dependent traversal cost can produce plans that are distance-efficient but energy-suboptimal, collecting fewer samples and less data than the energy budget would permit. In this paper, we first introduce Load-aware Informative Path Planning (LIPP), a strict generalization of C-IPP that explicitly models this coupling, with C-IPP recovered as the special case of zero sample mass. We then formulate LIPP as a Mixed-Integer Quadratic Program (MIQP) that jointly optimizes visitation location, order, and per-location sampling count under an energy budget. We further derive theoretical bounds on the path-length increase of LIPP relative to C-IPP, characterizing the trade-off for improved energy efficiency. Finally, through extensive simulations across 2,000 diverse mission scenarios, we demonstrate that LIPP progressively achieves higher uncertainty reduction per unit energy as sample mass increases.