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，每个自由度都有一个独立的控制力。独立控制比自由度少的系统被称为“欠驱动”。许多重要的系统自然就属于这一类，包括某些类型的导弹、卫星、水下机器人和两足机器人。正如可以从控制输入的短缺中预料到的那样，驱动不足的系统在稳定和转向方面面临挑战。这个项目通过使用大幅度、持续时间短的控制力--称为脉冲力--来改进现有的方法，以扩大系统的吸引力区域。吸引区是一组初始配置和速度，系统将能够从这些配置和速度到达其所需的运行点。如果系统离开其吸引区域，它将偏离其期望的行为，例如，失去对导弹或航天器的控制。扩大吸引区意味着更安全的操作，因为系统可以容忍由于大干扰力或意外初始条件而造成的干扰。该项目的一个主要新贡献将是通过在广泛接受的基准试验台系统上进行仔细的实验验证，弥合纯理论研究和实际应用之间的差距。动力系统不断地受到干扰，其抑制干扰的能力在很大程度上取决于其平衡构型的稳定性。这项研究将扩大欠驱动动力系统稳定运行的范围，减少不稳定行为的发生，这种行为通常会产生负面后果。通过施加脉冲力来扩大稳定运行的范围，这些脉冲力将被包括在允许的控制输入集中。在这个项目中，脉冲控制将在短时间间隔内使用高增益反馈来实现，并将使用奇异摄动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，将利用多时间尺度奇异摄动方法设计和分析高增益观测器。要使这种设计可行，需要解决许多具有挑战性的技术问题。这包括开发有效的算法，使用单个应用程序或多个脉冲输入应用程序，将系统配置从稳定运行区域外部转移到区域内部。开发的算法将在简单的欠驱动系统上进行实验测试；但这些方法将适用于更复杂的问题，如卫星的轨道转移、导弹和水下机器人的快速机动，以及主动假肢设备。

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.