Non-linear model predictive control (nMPC) is a powerful approach to control complex robots (such as humanoids, quadrupeds, or unmanned aerial manipulators (UAMs)) as it brings important advantages over other existing techniques. The full-body dynamics, along with the prediction capability of the optimal control problem (OCP) solved at the core of the controller, allows to actuate the robot in line with its dynamics. This fact enhances the robot capabilities and allows, e.g., to perform intricate maneuvers at high dynamics while optimizing the amount of energy used. Despite the many similarities between humanoids or quadrupeds and UAMs, full-body torque-level nMPC has rarely been applied to UAMs. This paper provides a thorough description of how to use such techniques in the field of aerial manipulation. We give a detailed explanation of the different parts involved in the OCP, from the UAM dynamical model to the residuals in the cost function. We develop and compare three different nMPC controllers: Weighted MPC, Rail MPC, and Carrot MPC, which differ on the structure of their OCPs and on how these are updated at every time step. To validate the proposed framework, we present a wide variety of simulated case studies. First, we evaluate the trajectory generation problem, i.e., optimal control problems solved offline, involving different kinds of motions (e.g., aggressive maneuvers or contact locomotion) for different types of UAMs. Then, we assess the performance of the three nMPC controllers, i.e., closed-loop controllers solved online, through a variety of realistic simulations. For the benefit of the community, we have made available the source code related to this work.

翻译：非线性模型预测控制（nMPC）是一种控制复杂机器人（如人形机器人、四足机器人或无人空中操作器（UAM））的强大方法，相比现有其他技术具有显著优势。控制器核心所求解的最优控制问题（OCP）结合全身动力学与预测能力，使机器人能够遵循其动态特性进行驱动。这一特性增强了机器人的能力，例如可在高动态条件下执行复杂动作，同时优化能量消耗。尽管人形机器人、四足机器人与UAM之间存在诸多相似性，但全身力矩级nMPC极少应用于UAM。本文详细阐述了如何将此类技术用于空中操作领域。我们提供了OCP各组成部分的详尽说明，涵盖从UAM动力学模型到代价函数残差的设计。我们开发并比较了三种不同的nMPC控制器：加权MPC、轨道MPC与胡萝卜MPC，其区别在于OCP结构及每次迭代中的更新方式。为验证所提框架，我们展示了多种仿真案例研究：首先评估轨迹生成问题（即离线求解的最优控制问题），涉及不同类型UAM的多种运动模式（如激进机动与接触运动）；随后通过多种逼真仿真评估三种nMPC控制器（即在线求解的闭环控制器）的性能。为促进学术社区发展，我们已公开本工作的相关源代码。