Nonlinear Control of Underactuated Mechanical Systems

本研究计画探讨欠驱动机械系统之非线性控制法则之设计、分析与即时执行之基本问题。这类系统相当广泛，包括平衡、臂架和行走机器人，包括柔性连杆机器人和柔性关节机器人在内的各种柔性结构，飞机和直升机，水下和太空飞行器，电动机，冗余机器人，以及包括致动器动力学的机械系统模型，和许多经典的控制问题，如球和梁和车杆系统。本计画主要研究一类欠驱动机械系统的整体与半整体稳定性与追踪结果。所使用的工具是拉格朗日和哈密顿方法的非线性动力学，几何非线性控制理论，混合控制，和饱和。结果也适用于一个更大的系统比迄今为止已经调查使用这些技术。本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性和能量的“自然闭环运动”。这项工作的补充和扩展现有的能源和被动性的方法和最近的backstepping方法，所有这些都试图更充分地利用系统的固有非线性，通过“塑造”，而不是通过“取消”所有的非线性系统。在实验方面，一些试验台系统用于测试分析研究结果。该实验室包括几个“体操机器人”（Acrobots，Pendubots），一个三自由度的空气曲棍球机器人，两个直接驱动机器人，和一个灵活的关节机器人。该研究项目的实验部分对本项目和创造卡修斯机器的最终目标都至关重要。

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.