# A High-Fidelity Energy Efficient Path Planner for Unmanned Airships
## 1 Introduction
In this work, the wind was added as a disturbance, and the dynamic constraints were not taken into account. [PERSON] et al. presented a Markov decision process-based fixed-wing UAV path planner that exploits wind energy to minimize energy consumption in an uncertain and time-varying wind field [17]. The simulation results showed almost 30% energy savings compared to a straight line path, but this was only conducted for one WVF sample. Furthermore, the study was conducted in 2D with a constant vehicle speed relative to the wind. Perhaps the most relevant work in this field is by [PERSON] et al., who presented an on-line, multi-objective mission planner for fixed-wing UAVs in 3D that includes time, fuel and several risk objectives in the presence of planar wind fields from weather forecasts [5]. However, their path planner uses a nodal resolution of one nautical mile with interpolated 10-nautical mile resolution wind fields to generate long-range paths which cannot account for local terrain features, an important consideration for low-altitude UAVs. Many non-deterministic methods combining genetic algorithms, ant colony algorithms, particle swarm optimization or neural networks have also been applied to the path planning of autonomous robot navigation [18]. [PERSON] et al. presented an evolutionary algorithm-based on-line planner  
Figure 1: Percent gradient wind, surface roughness \(\alpha\) and boundary layer height for different situations (data from Plate [14]). for multiple UAVs in 3D that includes optimization of multiple mission objectives such as path length, fuel and several flight risks, but has no mention of wind [15]. To address the growing complexity of problems with increased constraints such as multiple UAVs, parallel evolutionary algorithms have been implemented to decrease the execution time [19]. More recently, biologically-inspired tau-based path planning strategies such as the decentralized receding horizon optimization in [20] were developed to include velocities and time dependencies in the trajectory generation. Many path planners including evolutionary algorithms are based on uniform WVFs [21; 22; 23; 24; 25; 26] or constant vehicle velocities [6; 8; 15; 27; 28; 29; 30]. The few planners that account for variable wind conditions simplify the environment to two dimensions by assuming a fixed cruise altitude [6; 27; 28] or assume that the WVF is horizontally planar [5; 31; 32] with coarse resolution discretization of the flight space (\(\geq\)1 km). The purpose of this paper is to demonstrate that coarse resolution grids, average wind data and fixed vehicle speeds overestimate the number of feasible paths and underestimate the energy consumption. This paper also demonstrates that aggregating these parameters in the cost function yields more realistic and feasible paths and shows that corrective wind disturbance rejection methods are inadequate for under-actuated and under-powered unmanned airships. The remainder of this paper is as follows: First, a background on wind modelling and current wind usage is presented. Then, the trajectory planning method consisting of a cost wavefront expansion type trajectory planner is proposed, including a comprehensive multi-objective function to compute energy-optimized flight trajectories for small unmanned airships. The trajectory planner is then simulated in a set of randomly-generated 3D environments, and its effectiveness is evaluated based on several performance metrics.