Trajectory tracking problems for underactuated manipulators represent an actual research topic, which is sustained by the interest in a lighter and faster automatic class of mechanical systems, bringing some benefits as lower energy consumption, higher productivity and a more convenient human–machine interaction. This work presents a feedforward design method, which is based on the inverse dynamics of underactuated manipulators. To achieve this aim, an optimal control problem is formulated based on a direct multiple shooting method and the mechanical model is formulated according to the nonlinear finite element approach. Based on the proposed formulation, a bounded solution of the inverse dynamics problem can be achieved. The main contributions of this work are: (1) the development of an alternative formulation for the trajectory tracking problem of underactuated manipulators; (2) a parallel computation method for the inverse dynamics of underactuated manipulators; (3) a comparison/validation with the direct transcription method and the stable inversion method. A planar underactuated manipulator with one passive joint is considered as an illustrative example, but the methodology is general and could be applied to more complex systems, e.g. with flexible bodies, with parallel kinematics and in 3D.

中文翻译：

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欠驱动机械手开环控制设计与并行计算分析

欠驱动机械手的轨迹跟踪问题代表了一个实际的研究课题，它是由对更轻、更快的自动机械系统的兴趣维持的，带来了一些好处，如更低的能耗、更高的生产力和更方便的人机交互。这项工作提出了一种前馈设计方法，该方法基于欠驱动机械手的逆动力学。为实现这一目标，基于直接多次射击方法制定了最优控制问题，并根据非线性有限元方法制定了力学模型。基于所提出的公式，可以实现逆动力学问题的有界解。这项工作的主要贡献是：(1) 欠驱动机械手轨迹跟踪问题的替代公式的开发；(2) 欠驱动机械臂逆动力学的并行计算方法；(3) 与直接转录法和稳定反演法的比较/验证。一个带有一个被动关节的平面欠驱动机械手被认为是一个说明性的例子，但该方法是通用的，可以应用于更复杂的系统，例如具有柔性体、平行运动学和 3D 的系统。