QP Chaser: Polynomial Trajectory Generation for Autonomous Aerial Tracking

TL;DR

This work tackles robust airborne target tracking under occlusion and prediction errors by proposing a two-stage pipeline: reachable-area prediction using Bernstein-polynomial primitives and a single QP-based chasing planner that enforces target visibility via Target Visible Regions (TVR) while guaranteeing collision avoidance and dynamic feasibility. By incorporating path homotopy and full-body target visibility, the TVR framework reduces occlusion risk even with prediction uncertainty and dynamic obstacles, for both single- and dual-target scenarios. The approach yields real-time performance (tens of milliseconds) and outperforms baselines in simulations and indoor experiments, demonstrating practical viability for cinematography, surveillance, and multi-target tracking. The method’s core innovations include a sample-check prediction of reachable areas, a TVR construction that accounts for homotopy and FOV, and a convex QP formulation that integrates segmentation, constraints, and costs, enabling robust, scalable aerial tracking in complex environments.

Abstract

Maintaining the visibility of the target is one of the major objectives of aerial tracking missions. This paper proposes a target-visible trajectory planning pipeline using quadratic programming. Our approach can handle various tracking settings, including single and dual target following and both static and dynamic environments, unlike other works that focus on a single specific setup. In contrast to other studies that fully trust the predicted trajectory of the target and consider only the visibility of the center of the target, our pipeline considers error in target path prediction and the entire body of the target to maintain the target visibility robustly. First, a prediction module uses a sample-check strategy to quickly calculate the reachable areas of moving objects, which represent the areas their bodies can reach, considering obstacles. Subsequently, the planning module formulates a single QP problem, considering path homotopy, to generate a tracking trajectory that maximizes the visibility of the target's reachable area among obstacles. The performance of the planner is validated in multiple scenarios, through high-fidelity simulations and real-world experiments.

Figures (16)

• Figure 1: Target tracking mission in a realistic situation. (a): A target (red) moves in an indoor arena, and a dynamic obstacle (green) interrupts the visibility of the target. (b): Two targets (red and green) move among stacked bins (grey). A chaser drone (cross) generates a trajectory (blue) consistently tracking the targets without occlusion.
• Figure 2: Comparison between two viewpoints. The target can be observed at Viewpoint A (on a blue path), and the target is occluded by an obstacle at Viewpoint B (on a yellow path). Each arrow (purple, orange) represents the Line-of-Sight between the target and the drone. A red cross means target occlusion by an obstacle.
• Figure 3: Pipeline of the proposed chasing system.
• Figure 4: (a): Sampled endpoints $\mathcal{S}_{p}$ (red) and primitives $\mathcal{P}_{p}$ (black) among obstacles (grey). (b): Primitives $\mathcal{P}_{p}$ (black) and non-colliding primitives $\mathcal{P}_{s}$ (green). (c): The best primitive $\hat{\textbf{p}}(t)$ (blue), reachable area $\mathcal{R}_{\textbf{p}}(t)$ (light blue), and the farthest primitive (magenta). (d): The prediction with the outlier factor $\epsilon_{p} = 0.3$.
• Figure 5: Prediction accuracy. Red, green, and blue lines represent $Q=$ 0.1, 0.5, 1.0 [$\text{m}^{2}/\text{s}^{3}$] cases, respectively.

Theorems & Definitions (3)

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