Hierarchical Planning for Long-Horizon Multi-Target Tracking Under Target Motion Uncertainty

TL;DR

The paper addresses long-horizon, multi-target tracking with a single UAV in large open spaces where targets move and uncertainty accumulates when unseen. It introduces a hierarchical approach: a low-level shifting-spiral coverage path searches within dynamically expanding belief ellipses, and a high-level MCTS-based global planner that sequences target pursuit by predicting coverage outcomes with a probabilistic estimator. Key contributions include the shifting-spiral coverage strategy, a coverage-outcome estimator that converts the problem into an MDP, and an MCTS-based target sequencing framework, all validated in simulations showing 11-70% reductions in final uncertainty and demonstrated in real-world UAV experiments. The results advance long-horizon active tracking by jointly modeling motion, sensing, and uncertainty, enabling more robust reacquisition and sustained tracking in large-scale, dynamic environments.

Abstract

Achieving persistent tracking of multiple dynamic targets over a large spatial area poses significant challenges for a single-robot system with constrained sensing capabilities. As the robot moves to track different targets, the ones outside the field of view accumulate uncertainty, making them progressively harder to track. An effective path planning algorithm must manage uncertainty over a long horizon and account for the risk of permanently losing track of targets that remain unseen for too long. However, most existing approaches rely on short planning horizons and assume small, bounded environments, resulting in poor tracking performance and target loss in large-scale scenarios. In this paper, we present a hierarchical planner for tracking multiple moving targets with an aerial vehicle. To address the challenge of tracking non-static targets, our method incorporates motion models and uncertainty propagation during path execution, allowing for more informed decision-making. We decompose the multi-target tracking task into sub-tasks of single target search and detection, and our proposed pipeline consists a novel low-level coverage planner that enables searching for a target in an evolving belief area, and an estimation method to assess the likelihood of success for each sub-task, making it possible to convert the active target tracking task to a Markov decision process (MDP) that we solve with a tree-based algorithm to determine the sequence of sub-tasks. We validate our approach in simulation, demonstrating its effectiveness compared to existing planners for active target tracking tasks, and our proposed planner outperforms existing approaches, achieving a reduction of 11-70% in final uncertainty across different environments.

Figures (7)

• Figure 1: A UAV tracking two moving targets in an open environment. Each target's belief region expands over time due to motion uncertainty and contracts upon detection. In this snapshot, the UAV has just detected the purple target and is initiating a coverage path to search for the red target.
• Figure 2: An overview of the system. The target belief manager updates targets’ beliefs using prediction models \ref{['eq:prediction_model']}, and applies observation, shrinking the uncertainty whenever a target is observed. It provides information for the global planner to decide the next target to pursue, then a coverage planner generates a path accordingly.
• Figure 3: An example coverage path over a moving target. We use the static elliptic spiral (Fig. \ref{['fig: coverage static']}) to generate a path with equal distance between waypoints (Fig. \ref{['fig: coverage full']}) to cover a moving target belief area. The path is extended by finding the next waypoint on the shifted static spiral (Fig. \ref{['fig: coverage shift']}). In each step, a line search from $\theta_k$ acquires $\theta_{k+1}$ that ensures the agent's displacement matches its constant speed (Fig. \ref{['fig: coverage step']}).
• Figure 4: An example of coverage result estimation. During the coverage, (a) shows that the covered area catches up the ellipse areas of some example confidence levels $p=\{0.3, 0.6, 0.8\}$, eventually becoming tangent to the highest attainable probability $p_\text{find}$. (b) illustrates the growth of target-finding probability. Both plots share the same time axis, and the intersection points in (a) correspond to the respective probabilities in (b). In this example, $t_\text{cutoff}=53.0$ and $p_\text{find}=0.746$ are determined by the reach of maximum target-finding probability.
• Figure 5: Planning process example with 2 targets. The initial plan selects target 1 first. During the search for target 1, the system replans with the current action fixed, generates a conditional policy based on the coverage outcome, and repeats this replanning process for subsequent targets until the budget is depleted.