Multi-Step Gaussian Process Propagation for Adaptive Path Planning

Exploration and object search require robots to perceive their environment, identify regions of interest, and plan trajectories that improve target-detection likelihood or maximize information gain. Many IPP methods, especially in continuous environmental monitoring, rely on Gaussian-process belief models, while object-search settings often produce complex, multimodal belief maps from semantic or open-vocabulary perception. Global trajectory generation directly conditioned on such non-Gaussian belief maps remains comparatively underexplored. Although diffusion-based planners offer strong capabilities for modeling such distributions, their use in informative path planning remains limited. In this work, we propose DIFF-IPPO, a pipeline that integrates an open-vocabulary belief map generator with a diffusion-based planner for global trajectory generation over belief maps. The method generates trajectories that concentrate sensor coverage over high-belief regions, achieving normalized detection scores between 81.49% and 86.55% across different dataset scenarios. We validate the system in a simulated search-and-rescue scenario where the planner searches candidate building regions to locate a burning building. In this setting, a team of five drones using batched belief-map-conditioned trajectory generation achieves first detections in 3.5 minutes.

This paper presents a framework for mapping unknown scalar fields using a sensor-equipped autonomous robot operating in unsafe environments. The unsafe regions are defined as regions of high-intensity, where the field value exceeds a predefined safety threshold. For safe and efficient mapping of the scalar field, the sensor-equipped robot must avoid high-intensity regions during the measurement process. In this paper, the scalar field is modeled as a sample from a Gaussian process (GP), which enables Bayesian inference and provides closed-form expressions for both the predictive mean and the uncertainty. Concurrently, the spatial structure of the high-intensity regions is estimated in real-time using the Hough transform (HT), leveraging the evolving GP posterior. A safe sampling strategy is then employed to guide the robot towards safe measurement locations, using probabilistic safety guarantees on the evolving GP posterior. The estimated high-intensity regions also facilitate the design of safe motion plans for the robot. The effectiveness of the approach is verified through two numerical simulation studies and an indoor experiment for mapping a light-intensity field using a wheeled mobile robot.

Obstacle avoidance is essential for safe navigation and motion planning. Recent radiance field reconstruction methods enable object detection and modeling with high fidelity, but remain too memory- and compute-intensive for on-board perception-based path planning. To address these limitations, we propose PolyMerge to convert a large, photorealistic 3D Gaussian Splatting (3DGS) model of a scene into a lightweight representation of convex polytopes whose union provably over-approximates all obstacles in the original 3DGS model. PolyMerge tunes the polytope count to trade off conservativeness and compute cost, and integrates with control barrier functions (CBFs) to plan collision-free paths. We showcase PolyMerge in simulation and hardware experiments on a Crazyflie drone, which uses PolyMerge to compute and follow safe trajectories in real time under severe onboard compute constraints, outperforming baselines in speed while guaranteeing safety. For our code and videos, visit https://athlon76.github.io/PolyMerge-website/.