[Paper Review] Visibility-aware Trajectory Optimization with Application to Aerial Tracking

Qianhao Wang, Yuman Gao+3 more|arXiv (Cornell University)|Mar 11, 2021

Robotic Path Planning Algorithms4 citations

TL;DR

This paper proposes a differentiable, visibility-aware trajectory optimization method for aerial robots that jointly optimizes position and yaw to maximize target visibility, considering observation distance, angle, and occlusion. Evaluated in real-world quadrotor tracking, the method significantly improves tracking robustness and success rate compared to state-of-the-art planners.

ABSTRACT

The visibility of targets determines performance and even success rate of various applications, such as active slam, exploration, and target tracking. Therefore, it is crucial to take the visibility of targets into explicit account in trajectory planning. In this paper, we propose a general metric for target visibility, considering observation distance and angle as well as occlusion effect. We formulate this metric into a differentiable visibility cost function, with which spatial trajectory and yaw can be jointly optimized. Furthermore, this visibility-aware trajectory optimization handles dynamic feasibility of position and yaw simultaneously. To validate that our method is practical and generic, we integrate it into a customized quadrotor tracking system. The experimental results show that our visibility-aware planner performs more robustly and observes targets better. In order to benefit related researches, we release our code to the public.

Motivation & Objective

• To address the lack of comprehensive visibility-aware trajectory planning in aerial robotics, particularly in maintaining target visibility during dynamic tracking.
• To develop a differentiable visibility cost function that explicitly models observation distance, angle, and occlusion effects.
• To jointly optimize spatial trajectory and yaw angle under dynamic feasibility and safety constraints.
• To validate the method's robustness and generality in real-world aerial tracking applications.
• To release open-source code to support broader adoption and further research in visibility-aware planning.

Proposed method

• A differentiable visibility cost function is designed to quantify visibility based on three criteria: observation distance, observation angle, and occlusion from obstacles.
• The visibility cost is integrated into a joint optimization framework that simultaneously optimizes position and yaw trajectories.
• The optimization includes dynamic feasibility constraints for position and yaw, ensuring physical realizability of the planned motion.
• The method is embedded into a customized quadrotor tracking system with a kinodynamic occlusion-avoidance front-end for initial path generation.
• A polynomial-based trajectory representation enables continuous, differentiable optimization that scales well with state dimension.
• The planner is evaluated using both simulated and real-world experiments under varying target motion and obstacle conditions.

Experimental results

Research questions

• RQ1 How can visibility in trajectory planning be modeled as a continuous, differentiable function that accounts for distance, angle, and occlusion?
• RQ2 Can joint optimization of position and yaw improve target tracking robustness compared to sequential or decoupled planning?
• RQ3 How does visibility-aware trajectory optimization affect tracking success rate in dynamic, obstacle-rich environments?
• RQ4 To what extent does the method outperform state-of-the-art planners in real-world aerial tracking scenarios?
• RQ5 Can the proposed method be generalized across diverse tracking scenarios, including unpredictable target motion and random obstacle layouts?

Key findings

• In a general test with randomly deployed obstacles, the proposed method achieved a failure time of 100 seconds at 0.5 m/s target speed, compared to 39.1 seconds for Fast-Tracker, indicating superior robustness.
• At 1.5 m/s target speed, the proposed method maintained a failure time of 100 seconds, while Fast-Tracker failed at 66.25 seconds.
• At 2.5 m/s, the proposed method failed at 85.7 seconds, significantly outperforming Fast-Tracker’s 11.0-second failure time.
• The tracking angle error for the proposed method remained within the FOV boundary throughout all tests, whereas Fast-Tracker frequently lost the target due to large angle errors.
• Heat map analysis confirmed that the proposed method consistently kept the target in the central region of the FOV, enhancing observation quality, while Fast-Tracker failed to maintain consistent visibility.
• The real-world experiment demonstrated that visibility-aware planning prevents occlusion, especially during sharp turns, ensuring continuous target tracking.