A Mixed-Integer Convex Optimization-Based Approach for Hybrid UAV Path Planning in Noise-Restricted Zones

This paper presents an integrated approach for efficient path planning and energy management in hybrid unmanned aerial vehicles (HUAVs) equipped with dual fuel-electric propulsion systems. These HUAVs operate in environments that include noise-restricted zones, referred to as quiet zones, where only electric mode is permitted. We address the problem by parameterizing the position of a point along the side of the quiet zone using its endpoints and a scalar parameter, which transforms the problem into a variant of finding the shortest path over a graph of convex sets. We formulate this problem as a mixed-integer convex program (MICP), which can be efficiently solved using commercial solvers. Additionally, a tight lower bound can be obtained by relaxing the path-selection variable. Through extensive computations across 200 instances over four maps, we show a substantial improvement in computational efficiency over a state-of-the-art method, achieving up to a 100-fold and 10-fold decrease in computation time for calculating the lower bound and the exact solution, respectively. Moreover, the average gap between the exact cost and the lower bound was approximately 0.24%, and the exact cost was 1.05% lower than the feasible solution obtained from the state-of-the-art approach on average, highlighting the effectiveness of our proposed method. We also extend our approach to plan the route of the HUAV to visit a set of targets and return to its starting location in environments with quiet zones, yielding a Traveling Salesman Problem (TSP). We employ two methodologies to solve the TSP: one wherein the battery's State of charge (SOC) at each target is discretized, whereas, in another approach, the battery's SOC at each target is assumed to be the minimum allowable level when the HUAV departs it. A comparative analysis reveals that the second method achieves a cost within 1.02% of the first method on average while requiring significantly less computational time.