ReSPIRe: Informative and Reusable Belief Tree Search for Robot Probabilistic Search and Tracking in Unknown Environments

TL;DR

ReSPIRe tackles target search and tracking under severe uncertainty in unknown cluttered environments by integrating a sigma-point mutual information approximation for non-Gaussian beliefs, a hierarchical particle representation to balance global guidance and local uncertainty, and a reusable belief-tree search to accelerate online planning. The method provides a theoretical bound $|H_r- ext{hat}{H_r}|\\le c m \sigma_{ ext{max}}^2$ for the SP-based entropy approximation and demonstrates superior MI accuracy, planning efficiency, and real-time capability in both simulations and real-world indoor/outdoor experiments. Empirical results show ReSPIRe outperforms representative baselines in search speed, tracking stability, and computational efficiency, achieving practical frequencies around 9–10 Hz in planning and 20–30 Hz on hardware. These advances enable robust, informative SAT in challenging unknown environments and pave the way for multi-robot extensions and broader deployment in rescue and exploration tasks.

Abstract

Target search and tracking (SAT) is a fundamental problem for various robotic applications such as search and rescue and environmental exploration. This paper proposes an informative trajectory planning approach, namely ReSPIRe, for SAT in unknown cluttered environments under considerably inaccurate prior target information and limited sensing field of view. We first develop a novel sigma point-based approximation approach to fast and accurately estimate mutual information reward under non-Gaussian belief distributions, utilizing informative sampling in state and observation spaces to mitigate the computational intractability of integral calculation. To tackle significant uncertainty associated with inadequate prior target information, we propose the hierarchical particle structure in ReSPIRe, which not only extracts critical particles for global route guidance, but also adjusts the particle number adaptively for planning efficiency. Building upon the hierarchical structure, we develop the reusable belief tree search approach to build a policy tree for online trajectory planning under uncertainty, which reuses rollout evaluation to improve planning efficiency. Extensive simulations and real-world experiments demonstrate that ReSPIRe outperforms representative benchmark methods with smaller MI approximation error, higher search efficiency, and more stable tracking performance, while maintaining outstanding computational efficiency.

Figures (10)

• Figure 1: The process of target SAT in unknown (a) indoor cluttered environment and (b) outdoor environment with irregular terrains and unstructured obstacles. The robot and target trajectories are displayed in red and green, respectively. The contour represents different stages: cyan contour for target search, pink contour for target being found, and orange contour for target tracking.
• Figure 2: The overview of the proposed framework for SAT under unknown environments.
• Figure 3: Illustration of the three-layer hierarchical particle structure. Along with the original particles for belief update, refined particles that cluster by grids of different sizes are used for overall route efficiency and local uncertainty reduction.
• Figure 4: Illustration of RBTS. A novel recycling step is introduced to leverage past information stored in the rollout cache, thereby simultaneously expanding multiple nodes to enhance planning efficiency.
• Figure 5: Comparison of the MI approximation considering particle dispersion (top row) and sensor noise (bottom row). MI result (left column), absolute approximation error (middle column), and computation time (right column) are displayed. The absolute error and computation time are zoomed in for clear visualization.