Analysis of Large Amplitude, Short Duration Control Forces for Guiding Underactuated Mechanical Systems into Safe Operating Regions

在完全驱动的机械系统中，每个自由度都有独立的控制力。具有比自由度少的独立控制的系统被称为“欠驱动”。“许多重要的系统自然属于这一类，包括某些类型的导弹，卫星，水下航行器和双足机器人。正如可以从控制输入的短缺预期的那样，欠驱动系统的稳定和转向是具有挑战性的。该项目通过使用大振幅、短持续时间的控制力（称为脉冲力）来扩大系统的吸引区域，从而改进了现有的方法。吸引区域是系统能够达到其期望操作点的初始配置和速度的集合。如果系统离开了它的吸引区域，它就会偏离它所期望的行为，例如，对应于导弹或航天器的失控。扩大吸引区域意味着更安全的操作，因为系统可以容忍由于大的干扰力或意外的初始条件造成的干扰。该项目的一个主要的新贡献将是通过对广泛接受的基准测试台系统进行仔细的实验验证，弥合纯理论研究与实际应用之间的差距。 动态系统不断地受到干扰，它们拒绝干扰的能力在很大程度上取决于其平衡位形的稳定性。这项研究将扩大欠驱动动力系统的稳定运行区域，并减少不稳定行为的发生率，这种行为通常具有负面影响。稳定运行的区域将被扩大的应用程序的冲击力，这将包括在一组容许的控制输入。在这个项目中，脉冲控制将在短时间内使用高增益反馈来实现，并且将使用奇异摄动方法等数学工具来分析和设计高增益反馈系统。高增益反馈的实现将需要使用非常快的观测器来估计未测量的速度。为此，将通过多时间尺度奇异摄动方法设计和分析高增益观测器。有许多具有挑战性的技术问题需要解决，使这种设计可行。这包括开发有效的算法，该算法可以使用脉冲输入的单个应用或多个应用将系统配置从稳定操作区域外部转移到区域内部。所开发的算法将在简单的欠驱动系统上进行实验测试，但该方法将适用于更复杂的问题，如卫星的轨道转移，导弹和水下航行器的快速机动，以及主动假肢装置。

In a fully actuated mechanical system, an independent control force is available for each degree of freedom. Systems with fewer independent controls than degrees-of-freedom are called "underactuated." Many important systems are naturally of this class, including certain types of missiles, satellites, underwater vehicles, and bipedal robots. As might be expected from the shortage of control inputs, underactuated systems are challenging to stabilize and to steer. This project improves upon existing approaches by using large-amplitude, short-duration control forces -- called impulsive forces -- to expand the region of attraction of the system. The region of attraction is the set of initial configurations and velocities from which the system will be able to reach its desired operating point. If the system ever leaves its region of attraction, it will depart from its desired behavior, corresponding to, for example, the loss of control of a missile or spacecraft. Expanding the region of attraction means safer operation, since the system can tolerate upsets due to large disturbance forces or unexpected initial conditions. A major new contribution of this project will be to bridge the gap between purely theoretical studies and practical applications, through careful experimental validation on widely accepted benchmark test bed systems. Dynamical systems are continuously subjected to disturbances and their ability to reject them largely depend on the stability property of their equilibrium configurations. This research will enlarge the region of stable operation of underactuated dynamical systems and reduce the incidence of unstable behavior, behavior that typically has negative consequences. The region of stable operation will be enlarged by application of impulsive forces, which will be included in the set of admissible control inputs. In this project, impulsive control will be implemented using high-gain feedback over short intervals of time and mathematical tools such as singular perturbation methods will be used to analyze and design the high-gain feedback systems. The implementation of high-gain feedback will require the use of very fast observers to estimate the unmeasured velocities. To this end, high-gain observers will be designed and analyzed via multi-time-scale singular perturbation methods. There are many challenging technical issues that need to be solved to make such designs feasible. This includes the development of efficient algorithms that can transfer the system configuration from outside the region of stable operation to inside the region, using a single application or multiple applications of impulsive inputs. The developed algorithms will be tested experimentally on simple underactuated systems; but the methods will be applicable to more complex problems such as orbital transfer of satellites, rapid maneuvering of missiles and underwater vehicles, and active prosthetic devices.