Nonlinear Control of Underactuated Mechanical Systems

这项研究项目研究欠驱动机械系统的非线性控制律的设计、分析和实时实现的基本问题。这类系统相当广泛，包括平衡、扶手和行走机器人，各种灵活的结构，包括柔性连杆机器人，柔性关节机器人，飞机和直升机，水下和太空飞行器，电机，冗余机器人，以及包括执行器动力学的机械系统模型，以及许多经典的控制问题，如球、梁和小车-杆系统。本课题研究了一类欠驱动机械系统的全局和半全局稳定性和跟踪结果。所使用的工具是非线性动力学的拉格朗日方法和哈密顿方法、几何非线性控制理论、混合控制和饱和。这些结果也适用于比迄今为止使用这些技术所研究的更大类别的系统。这项研究的统一主题是利用非线性动力学的基本结构来产生有效利用被动和能量的“自然闭环系统运动”。这项工作补充和扩展了现有的能量法和无源法以及更新的反推方法，所有这些方法都试图更充分地利用系统的固有非线性，通过‘整形’而不是‘取消’系统中的所有非线性。在实验方面，利用多个试验台系统对分析研究成果进行了验证。该实验室包括几个体操机器人(AcRobots，Pendubots)，一个三自由度空中曲棍球机器人，两个直接驱动机器人，和一个柔性关节机器人。研究项目的实验部分对于目前的项目和创造灵巧机器的最终目标都是至关重要的。

This research project investigates fundamental issues in the design, analysis, and real-time implementation of nonlinear control laws for underactuated mechanical systems. This class of systems is quite broad and encompasses balancing, brachiating, and walking robots, flexible structures of all kinds including flexible link robots, and flexible joint robots, airplanes and helicopters, underwater and space vehicles, electric motors, redundant robots, as well as mechanical system models that include actuator dynamics, and many of the classical control problems like the ball and beam and cart-pole systems. Global and semi-global stability and tracking results for classes of underactuated mechanical systems are investigated in this project. The tools used are Lagrangian and Hamiltonian methods of nonlinear dynamics, geometric nonlinear control theory, hybrid control, and saturation. The results also apply to a larger class of systems than have heretofore been investigated using these techniques. The unifying theme of this research is to exploit the underlying structure of the nonlinear dynamics to generate `natural closed loop motions` that make efficient use of passivity and energy. This work complements and extends existing energy and passivity methods and more recent backstepping methods, all of which attempt to exploit more fully the inherent nonlinearities of the system, by `shaping` rather than by `canceling` all of the nonlinearities in the system. On the experimental side, a number of testbed systems are used to test analytical research results. The laboratory includes several `gymnastic robots,` (Acrobots, Pendubots), a three degree-of-freedom air hockey playing robot, two direct drive robots, and a flexible joint robot. The experimental component of the research project is of vital importance both to the present project and to the ultimate goal of creating dextrous machines.