Sampling-Based Risk-Aware Path Planning Around Dynamic Engagement Zones

TL;DR

The paper tackles the problem of risk-aware, time-optimal path planning for a fixed-wing Dubins vehicle navigating through many dynamic engagement zones (EZs). It introduces a lifting technique that maps dynamic EZs into static obstacles in the 3D configuration space $(x,y,\psi)$, enabling the use of a sampling-based RRT$^*$ planner to handle large EZ sets. Key contributions include (i) a lifted-space representation of dynamic EZs as static 3D obstacles, (ii) a risk-aware RRT$^*$ planning framework that respects Dubins dynamics, and (iii) Monte Carlo validation showing how solution quality and success rate scale with the number of EZs and available compute time. Findings indicate that longer compute budgets improve performance and that the method achieves high reliability for moderate EZ counts (approximately eight) under realistic constraints, while larger EZ ensembles demand significantly more planning time. The approach offers scalable, practical navigation around dynamic threat regions where traditional variational or optimal-control methods struggle to scale or avoid local minima.

Abstract

Existing methods for avoiding dynamic engagement zones (EZs) and minimizing risk leverage the calculus of variations to obtain optimal paths. While such methods are deterministic, they scale poorly as the number of engagement zones increases. Furthermore, optimal-control based strategies are sensitive to initial guesses and often converge to local, rather than global, minima. This paper presents a novel sampling-based approach to obtain a feasible flight plan for a Dubins vehicle to reach a desired location in a bounded operating region in the presence of a large number of engagement zones. The dynamic EZs are coupled to the vehicle dynamics through its heading angle. Thus, the dynamic two-dimensional obstacles in the (x,y) plane can be transformed into three-dimensional static obstacles in a lifted (x,y,ψ) space. This insight is leveraged in the formulation of a Rapidly-exploring Random Tree (RRT*) algorithm. The algorithm is evaluated with a Monte Carlo experiment that randomizes EZ locations to characterize the success rate and average path length as a function of the number of EZs and as the computation time made available to the planner is increased.

Figures (6)

• Figure 1: Example scenario with three dynamic EZs and an aircraft moving along a straight path. Each EZ is drawn by sweeping out $\theta_i \in [0, 2\pi)$ in \ref{['eq:rho_Rmin_zero']}. The EZ geometry depends on the relative $\lambda_i$ and $\xi_i$ that vary with aircraft motion.
• Figure 2: Left three panels: Example scenario (identical to Fig. \ref{['fig:setup']}) with three EZ regions and aircraft moving along a straight line path. The red colored EZ obstacles are drawn by varying $\lambda_i \in [0, 2\pi)$ in \ref{['eq:rho_lam_psi']} for a fixed heading angle $\psi = \pi/4$. The "+" markers indicate locations at which both the EZ obstacle and dynamic EZ intersect. These points correspond to locations that are a distance $\rho_{{\rm max},i}$ from the aircraft. Right panel: Slices of the EZ obstacle at different heading planes in the lifted space.
• Figure 3: The engagement zone rotates on each heading plane (indicated by the vector field of allowable motion).
• Figure 4: Left: Example of RRT solution with superimposed circles of $R_{\rm max}$ at WEZ locations. Right: The same trajectory in the configuration space $(x,y,\psi)$ with static EZ obstacles. Bottom: Corresponding turn-rate.
• Figure 5: Eight snapshots in time of the aircraft traversing the path in Fig. \ref{['fig:example']} and the corresponding dynamic EZs. The aircraft position at each timestamp shown in the upper right corner is denoted by a circular marker.