Informative Path Planning

Efficient monitoring of sparse benthic phenomena, such as coral colonies, presents a great challenge for Autonomous Underwater Vehicles. Traditional exhaustive coverage strategies are energy-inefficient, while recent adaptive sampling approaches rely on costly vertical maneuvers. To address these limitations, we propose HIMoS (Hierarchical Informative Multi-Modal Search), a fixed-altitude framework for sparse coral search-and-sample missions. The system integrates a heterogeneous sensor suite within a two-layer planning architecture. At the strategic level, a Global Planner optimizes topological routes to maximize potential discovery. At the tactical level, a receding-horizon Local Planner leverages differentiable belief propagation to generate kinematically feasible trajectories that balance acoustic substrate exploration, visual coral search, and close-range sampling. Validated in high-fidelity simulations derived from real-world coral reef benthic surveys, our approach demonstrates superior mission efficiency compared to state-of-the-art baselines.

Off-world multi-robot exploration is challenged by sparse targets, limited sensing, hazardous terrain, and restricted communication. Many scientifically valuable clues are visually ambiguous and often require close-range observations, making efficient and safe informative path planning essential. Existing methods often rely on predefined areas of interest (AOIs), which may be incomplete or biased, and typically handle terrain risk only through soft penalties, which are insufficient for avoiding non-recoverable regions. To address these issues, we propose a multi-agent informative path planning framework for sparse evidence discovery based on Gaussian belief mapping and dual-domain coverage. The method maintains Gaussian-process-based interest and risk beliefs and combines them with trajectory-intent representations to support coordinated sequential decision-making among multiple agents. It further prioritizes search inside the AOI while preserving limited exploration outside it, thereby improving robustness to AOI bias. In addition, the risk-aware design helps agents balance information gain and operational safety in hazardous environments. Experimental results in simulated lunar environments show that the proposed method consistently outperforms sampling-based and greedy baselines under different budgets and communication ranges. In particular, it achieves lower final uncertainty in risk-aware settings and remains robust under limited communication, demonstrating its effectiveness for cooperative off-world robotic exploration.

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.

Navigating an environment with uncertain connectivity requires a strategic balance between minimizing the cost of traversal and seeking information to resolve map ambiguities. Unlike previous approaches that rely on local sensing, we utilize a framework where nodes possess varying visibility levels, allowing for observation of distant edges from certain vantage points. We propose a novel heuristic algorithm that balances the cost of detouring to high-visibility locations against the gain in information by optimizing the sum of a custom observation reward and the cost of traversal. We introduce a technique to sample the shortest path on numerous realizations of the environment, which we use to define an edge's utility for observation and to quickly estimate the path with the highest reward. Our approach can be easily adapted to a variety of scenarios by tuning a single hyperparameter that determines the importance of observation. We test our method on a variety of uncertain navigation tasks, including a map based on real-world topographical data. The method demonstrates lower mean cost of traversal compared to a shortest path baseline that does not consider observation and has exponentially lower computational overhead compared to an existing method for balancing observation with path cost minimization.

The problem of planning sensing trajectories for a mobile robot to collect observations of a target and predict its future trajectory is known as active target tracking. Enabled by probabilistic motion models, one may solve this problem by exploring the belief space of all trajectory predictions given future sensing actions to maximise information gain. However, for multi-modal motion models the notion of information gain is often ill-defined. This paper proposes a planning approach designed around maximising information regarding the target's homotopy class, or high-level motion. We introduce homotopic information gain, a measure of the expected high-level trajectory information given by a measurement. We show that homotopic information gain is a lower bound for metric or low-level information gain, and is as sparsely distributed in the environment as obstacles are. Planning sensing trajectories to maximise homotopic information results in highly accurate trajectory estimates with fewer measurements than a metric information approach, as supported by our empirical evaluation on real and simulated pedestrian data.

Mutual information (MI) is a principled and widely used objective for robotic information gathering (RIG), providing strong theoretical guarantees for sensor placement (SP) and informative path planning (IPP). However, its high computational cost - dominated by repeated log-determinant evaluations - has limited its use in real-time planning. This paper presents Schur-MI, a Gaussian process (GP) MI formulation that (i) leverages the iterative structure of RIG to precompute and reuse expensive intermediate quantities across planning steps, and (ii) uses a Schur-complement factorization to avoid large determinant computations. Together, these methods reduce the per-evaluation cost of MI from $\mathcal{O}(|\mathcal{V}|^3)$ to $\mathcal{O}(|\mathcal{A}|^3)$, where $\mathcal{V}$ and $\mathcal{A}$ denote the candidate and selected sensing locations, respectively. Experiments on real-world bathymetry datasets show that Schur-MI achieves up to a $12.7\times$ speedup over the standard MI formulation. Field trials with an autonomous surface vehicle (ASV) performing adaptive IPP further demonstrate the method's practicality. By making MI computation tractable for online planning, Schur-MI helps bridge the gap between information-theoretic objectives and real-time robotic exploration. Our code is available at: www.sgp-tools.com