Nonlinear Trajectory Optimization Models for Energy-Sharing UAV-UGV Systems with Multiple Task Locations

Abstract

Energy-sharing UAV-UGV systems extend the endurance of Uncrewed Aerial Vehicles (UAVs) by leveraging Uncrewed Ground Vehicles (UGVs) as mobile charging stations, enabling persistent autonomy in infrastructure-sparse environments. Trajectory optimization for these systems is often challenging due to UGVs' terrain access constraints and the discrete nature of task scheduling. We propose a smooth nonlinear program model for the joint trajectory optimization for these systems. Unlike existing models, the proposed model allows smooth parameterization of UGVs' terrain access constraints and supports partial UAV recharging. Further, it introduces a smooth approximation of disjunctive constraints that eliminates the need for computationally expensive integer programming and enables efficient solutions via nonlinear programming algorithms. We demonstrate the proposed model on a one-UAV-one-UGV system with multiple task locations. Compared with mixed-integer nonlinear programs, this model reduces the computation time by orders of magnitude.

Figures (4)

• Figure 2: Example problem with $m^{\texttt{A}}=10$ UAV task locations (red stars) and $m^{\texttt{G}}=3$ arms, whose associated UGV task locations are shown as magenta circles.
• Figure 3: Convergence of different NLP algorithms and smoothing functions over 100 problem instances with randomly generated UAV task locations with $m^\texttt{A} = 10$. The solid lines represent the median values of the simulations, while the lower and upper bars indicate the interquartile range, spanning from the 0.25 quantile to the 0.75 quantile.
• Figure 4: UAV-UGV trajectory computed via NLP (ALM with $\ell_p$-norm) for the problem shown in Fig. \ref{['fig: an_example']}. Each red asterisk marks the point along the trajectory where the UAV reaches a task location.
• Figure 5: Median computation time versus $m^{\texttt{A}}$ over 100 Monte Carlo runs with randomly generated aerial task positions for each value of $m^{\texttt{A}}$, with a maximum computation time of 6 hours. Error bars indicate the 0.25--0.75 quantiles, and the median constraint violation is on the order of $10^{-6}$.