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In this paper we present AWEbox, a Python toolbox for modeling and optimal control of multi-aircraft systems for airborne wind energy (AWE). AWEbox provides an implementation of optimization-friendly multi-aircraft AWE dynamics for a wide range of system architectures and modeling options. It automatically formulates typical AWE optimal control problems based on these models, and finds a numerical solution in a reliable and efficient fashion. To obtain a high level of reliability and efficiency, the toolbox implements different homotopy methods for initial guess refinement. The first type of methods produces a feasible initial guess from an analytic initial guess based on user-provided parameters. The second type implements a warmstart procedure for parametric sweeps. We investigate the software performance in two different case studies. In the first case study we solve a single-aircraft reference problem for a large number of different initial guesses. The homotopy methods reduce the expected computation time by a factor of 1.7 and and the peak computation time by a factor of 8, compared to when no homotopy is applied. Overall, the CPU timings are competitive to timings reported in the literature. When the user initialization draws on expert a priori knowledge, homotopies do not increase expected performance, but the peak CPU time is still reduced by a factor of 5.5. In the second case study, a power curve for a dual-aircraft lift-mode AWE system is computed using the two different homotopy types for initial guess refinement. On average, the second homotopy type, which is tailored for parametric sweeps, outperforms the first type in terms of CPU time by a factor of 3. In conclusion, AWEbox provides an open-source implementation of efficient and reliable optimal control methods that both control experts and non-expert AWE developers can benefit from.

In this paper, we present AWEbox, a Python toolbox for modeling and optimal control of multi-aircraft systems for airborne wind energy (AWE). AWEbox provides an implementation of optimization-friendly multi-aircraft AWE dynamics for a wide range of system architectures and modeling options. It automatically formulates typical AWE optimal control problems based on these models, and finds a numerical solution in a reliable and efficient fashion. To obtain a high level of reliability and efficiency, the toolbox implements different homotopy methods for initial guess refinement. The first type of method produces a feasible initial guess from an analytic initial guess based on user-provided parameters. The second type implements a warm-start procedure for parametric sweeps. We investigate the software performance in two different case studies. In the first case study, we solve a single-aircraft reference problem for a large number of different initial guesses. The homotopy methods reduce the expected computation time by a factor of 1.7 and the peak computation time by a factor of eight, compared to when no homotopy is applied. Overall, the CPU timings are competitive with the timings reported in the literature. When the user initialization draws on expert a priori knowledge, homotopies do not increase expected performance, but the peak CPU time is still reduced by a factor of 5.5. In the second case study, a power curve for a dual-aircraft lift-mode AWE system is computed using the two different homotopy types for initial guess refinement. On average, the second homotopy type, which is tailored for parametric sweeps, outperforms the first type in terms of CPU time by a factor of three. In conclusion, AWEbox provides an open-source implementation of efficient and reliable optimal control methods that both control experts and non-expert AWE developers can benefit from.