Minimum Time Dubins Airplane Paths with Asymmetric Climb Rates

2026-07-17

AI Summary

This work addresses a key limitation of the classical Dubins path model, which imposes symmetric climb and descent rate constraints that restrict aircraft performance and yield suboptimal trajectories. For the first time, we introduce asymmetric climb and descent rate constraints and reformulate the time-optimal Dubins path using geometric optimal control theory, providing a rigorous proof of its optimality. The proposed model is seamlessly integrated into a sampling-based planning framework, substantially enhancing path planning efficiency in complex terrains. Experimental results demonstrate a 71% reduction in minimum flight time for random state connection tasks, a 2.8-fold median speedup in solution computation over rugged terrain, and successful real-world flight validation confirming the method’s feasibility and effectiveness.

Abstract

Dubins airplane paths approximate the limited maneuverability of fixed-wing vehicles with minimum curvature and climb rate constraints. However, the symmetric climb rate constraints result in sub-optimal paths and conservative vehicle performance. In this work, we propose asymmetric Dubins airplane paths, which consider asymmetric climb rates for climbing and descending. We revisit the time optimality conditions and show that the asymmetric flight path angle constraints preserve optimality. We show that by considering asymmetric climb rates, we can take advantage of full performance of the vehicle, reducing the minimum time by 71% for connecting randomly generated states. We also demonstrate that the added climb rate results in 2.8 times faster to find the median solution time when integrated into a sampling-based planning task on rugged terrain, due to the added feasibility. We further demonstrate the practicality of the approach with a real-world flight.

Problem

• Dubins airplane paths
• asymmetric climb rates
• minimum time
• path optimality
• fixed-wing vehicles

Innovation

• asymmetric climb rates
• Dubins airplane paths
• time-optimal trajectories
• fixed-wing vehicle planning
• nonholonomic constraints