Assisted Path Planning for a UGV-UAV Team Through a Stochastic Network

TL;DR

The paper tackles stochastic, multi-agent path planning where a UGV is assisted by a UAV to minimize travel time in networks with uncertain impeded edges. It introduces an online framework that decomposes the problem into a UGV solution via Dynamic $k$-Shortest Path Planning (D*-KSPP) and a UAV solution via Rural Postman Problem with Time Windows (RPP-TW), with a scalable Priority Assignment Algorithm (PAA) for large-scale UAV tasks. The key contributions are the D*-KSPP integration with Yen's $k$-shortest paths, the RPP-TW/RPP-DFS approach for UAV inspection planning, and the PAA heuristic, all validated through extensive simulations and a real-world OpenStreetMap case study across six cities. The work demonstrates practical, real-time coordination benefits for time-critical missions in urban environments and offers insights into scalability and limitations, paving the way for multi-vehicle extensions and richer uncertainty models.

Abstract

In this article, we consider a multi-agent path planning problem in a stochastic environment. The environment, which can be an urban road network, is represented by a graph where the travel time for selected road segments (impeded edges) is a random variable because of traffic congestion. An unmanned ground vehicle (UGV) wishes to travel from a starting location to a destination while minimizing the arrival time at the destination. UGV can traverse through an impeded edge but the true travel time is only realized at the end of that edge. This implies that the UGV can potentially get stuck in an impeded edge with high travel time. A support vehicle, such as an unmanned aerial vehicle (UAV) is simultaneously deployed from its starting position to assist the UGV by inspecting and realizing the true cost of impeded edges. With the updated information from UAV, UGV can efficiently reroute its path to the destination. The UGV does not wait at any time until it reaches the destination. The UAV is permitted to terminate its path at any vertex. The goal is then to develop an online algorithm to determine efficient paths for the UGV and the UAV based on the current information so that the UGV reaches the destination in minimum time. We refer to this problem as Stochastic Assisted Path Planning (SAPP). We present Dynamic $k$-Shortest Path Planning (D*KSPP) algorithm for the UGV planning and Rural Postman Problem (RPP) formulation for the UAV planning. Due to the scalability challenges of RPP, we also present a heuristic based Priority Assignment Algorithm (PAA) for the UAV planning. Computational results are presented to corroborate the effectiveness of the proposed algorithm to solve SAPP.

Figures (5)

• Figure 1: (a) A sample instance for the SAPP. Black edges represent unimpeded edges and red edges represent impeded edges. UAV has the same set of edges as UGV. Travel times are represented as follows: for unimpeded edges $(T_e, \tau_e)$, for impeded edges $(T_e^{min}, T_e^{max}, \tau_e)$. Let the true cost of $e_1$ and $e_2$ be 12 and 18. In (b), (c), and (d) the convoy and the service vehicle paths are represented by green and blue colors, respectively. The dashed path represents the true cost of the impeded edge realized by the vehicle associated with the corresponding color. In (b), the UGV reaches the destination without the assistance of the UAV. In (c), the UAV decides to inspect the nearby edge $e_1$, whereas in (d), the UAV inspects the edge $e_2$.
• Figure 2: Comparison between D*KSPP-RPP and Naive Method for 100 randomly generated grid $20\times10$ grid instances. Number of UGV paths considered for D*KSPP is 5. A lower bound is provided to indicate the quality of the solution.
• Figure 3: Sample instance.
• Figure 4: Computation time of D*KSPP with $k$ set to $4$ and $5$ for different graph sizes.
• Figure 5: OpenStreetMapOpenStreetMap road networks from six major cities in the USA.