Nonlinear Control of Underactuated Mechanical Systems

本研究项目探讨欠驱动机械系统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、摆臂和行走机器人，各种柔性结构，包括柔性连杆机器人和柔性关节机器人，飞机和直升机，水下和太空飞行器，电动机，冗余机器人，以及包括执行器动力学在内的机械系统模型，以及许多经典的控制问题，如球和梁和车杆系统。研究一类欠驱动机械系统的全局和半全局稳定性及跟踪结果。使用的工具是非线性动力学的拉格朗日和哈密顿方法，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类比迄今为止已研究使用这些技术。本研究的统一主题是利用非线性动力学的底层结构来产生“自然闭环运动”，从而有效地利用无源性和能量。这项工作补充和扩展了现有的能量和被动方法以及最近的回溯方法，所有这些方法都试图通过“塑造”而不是“消除”系统中的所有非线性来更充分地利用系统固有的非线性。在实验方面，使用了许多试验台系统来测试分析研究结果。该实验室包括几个“体操机器人”（Acrobots, penddubots），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柔性关节机器人。研究项目的实验部分对目前的项目和创造灵巧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.