Online trajectory optimization and optimal control methods are crucial for enabling sustainable unmanned aerial vehicle (UAV) services, such as agriculture, environmental monitoring, and transportation, where available actuation and energy are limited. However, optimal controllers are highly sensitive to model mismatch, which can occur due to loaded equipment, packages to be delivered, or pre-existing variability in fundamental structural and thrust-related parameters. To circumvent this problem, optimal controllers can be paired with parameter estimators to improve their trajectory planning performance and perform adaptive control. However, UAV platforms are limited in terms of onboard processing power, oftentimes making nonlinear parameter estimation too computationally expensive to consider. To address these issues, we propose a relaxed, affine-in-parameters multirotor model along with an efficient optimal parameter estimator. We convexify the nominal Moving Horizon Parameter Estimation (MHPE) problem into a linear-quadratic form (LQ-MHPE) via an affine-in-parameter relaxation on the nonlinear dynamics, resulting in fast quadratic programs (QPs) that facilitate adaptive Model Predictve Control (MPC) in real time. We compare this approach to the equivalent nonlinear estimator in Monte Carlo simulations, demonstrating a decrease in average solve time and trajectory optimality cost by 98.2% and 23.9-56.2%, respectively.

翻译：在线轨迹优化与最优控制方法对于实现可持续的无人机服务至关重要，例如在农业、环境监测和运输等领域，这些场景中可用的驱动与能量均有限。然而，最优控制器对模型失配高度敏感，这种失配可能源于搭载的设备、待交付的包裹，或是基本结构与推力相关参数中预先存在的变异性。为规避此问题，可将最优控制器与参数估计器结合，以提升其轨迹规划性能并实现自适应控制。然而，无人机平台的机载处理能力有限，非线性参数估计往往因计算成本过高而难以实施。针对这些问题，我们提出一种松弛的、参数仿射的多旋翼模型，以及一种高效的最优参数估计器。通过对非线性动力学施加参数仿射松弛，我们将名义上的移动视界参数估计问题凸化为线性二次形式，从而得到可快速求解的二次规划问题，这有助于实现实时的自适应模型预测控制。在蒙特卡洛模拟中，我们将该方法与等效的非线性估计器进行比较，结果表明平均求解时间和轨迹最优性成本分别降低了98.2%和23.9-56.2%。