Simulation approach to the inverse dynamics of underactuated systems

提出了一种欠驱动机械系统逆动力学仿真的新方法。典型的示例应用是起重机和机械手。仿真方法是基于伺服问题的数值解。在起重机的情况下，伺服约束用于规定负载的轨迹。伺服问题的解决方案确定了实现负载的规定运动所需的驱动力。除了伺服约束，伺服问题还包括与机械系统有关的运动方程。因此，控制方程采用微分代数方程（DAE）的形式。DAE通常具有高索引，因此非常难以求解。提出了一种新的指数约简方法，以便于伺服问题的稳定数值解。此外，一个新的连续Galerkin方法在空间和时间的发展，这将是特别有益的机器人的逆动力学与柔性部件。

A new simulation approach to the inverse dynamics of underactuated mechanical systems is proposed. Typical sample applications are cranes and robot manipulators. The simulation approach is based on the numerical solution of servo problems. In the case of cranes servo constraints are used to prescribe the trajectory of the load. The solution of the servo problem determines the actuating forces that are required to realize the prescribed motion of the load. In addition to the servo constraints the servo problem comprises the equations of motion pertaining to the mechanical system at hand. Consequently, the governing equations assume the form of differential-algebraic equations (DAEs). The DAEs typically have high index and are thus notoriously difficult to solve. A new index reduction method is proposed to facilitate the stable numerical solution of the servo problem. Moreover, a new continuous Galerkin method in space and time is developed which will be especially beneficial for the inverse dynamics of robots with flexible components.