Generating Stable Repetitive Motion of Underactuated Robotic Systems Using Large-Amplitude Short-Duration Control Forces

本项目通过研究欠驱动机器人系统稳定重复运动的产生，将促进科学进步，促进国家繁荣和国防。欠驱动机械系统是指控制输入小于其自由度的系统。欠驱动现象在导弹、卫星、水下航行器、水下机器人等系统中普遍存在。重复运动在欠驱动机器人系统中非常常见，例如水下航行器和水下机器人，保持稳定性对于安全可靠的操作至关重要。本研究的目的是产生稳定的重复运动的欠驱动机器人系统，通过将大振幅，短时间的控制力，通常被称为脉冲力。虽然脉冲力的影响已经在不同的动力系统中进行了研究，但大多数研究仅限于理论研究。这项研究将有一个重要的实验组成部分，并将动力系统的脉冲控制从理论转化为实践，解决实施的挑战。除了科学和技术进步，该项目将通过研究和教育，多样性和外联的整合产生广泛的影响。该项目将为本科生提供研究经验，为研究生提供论文题目，从而为未来一代工程师和学者的发展做出贡献。重复运动在欠驱动机器人系统中很常见，它们拒绝干扰的能力取决于轨道的稳定性。该研究将消除现有方法的不足驱动系统的轨道稳定的限制，包括脉冲输入的容许控制集。对于不受影响的欠驱动系统，目前的方法需要在轨道上的每一点检查系统的可控性，并通过求解周期Ricatti微分方程在线计算控制器增益。在本研究中的方法，它使用连续和脉冲输入，将导致一个线性时不变的系统，并减少计算成本和控制设计的复杂性。它还将允许估计轨道周围的吸引区域，这将用于确定应用脉冲输入的最佳位置。为了考虑受到冲击的系统，研究将集中在两足动物，其中连续和脉冲输入将用于步态稳定;和魔鬼棒，其中仅使用脉冲输入。对于两足动物，目前的方法使用数值方法来搜索稳定的步态。本研究将以解析方式设计名义步态。这将是可能的，很容易检查的稳定性和可控性的标称步态和调整控制器参数，以获得可控的步态。无冲击标称步态将确保能量损失和硬件磨损由于冲击将被最小化。对于魔鬼棒，纯粹的脉冲控制将被设计用于各种杂耍问题。该奖项反映了NSF的法定使命，并被认为是值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估的支持。

This project will promote the progress of science and advance the national prosperity and national defense, by studying generation of stable repetitive motion for underactuated robotic systems. Underactuated mechanical systems are those that have fewer control inputs than the number of their degrees-of-freedom. Underactuation appears naturally in many systems such as missiles, satellites, underwater vehicles and biped robots. Repetitive motion is very common in underactuated robotic systems that undergo locomotion, such as underwater vehicles and biped robots, and maintaining stability is paramount for safe and reliable operation. The objective of this research is to generate stable repetitive motion of underactuated robotic systems by incorporating large-amplitude, short-duration control forces, commonly referred to as impulsive forces. Although the effect of impulsive forces has been studied in diverse dynamical systems, the majority of the studies have been limited to theoretical investigations. This research will have a significant experimental component and will translate impulsive control of dynamical systems from theory to practice by addressing the challenges of implementation. In addition to scientific and technological advances, this project will have broad impact through integration of research and education, diversity, and outreach. The project will provide research experience for undergraduate students and dissertation topics for graduate students and thereby contribute towards the development of the future generation of engineers and academics.Repetitive motion is common in underactuated robotic systems and their ability to reject disturbances depends on the stability property of the orbit. This research will eliminate the limitations of current approaches to orbital stabilization of underactuated systems by including impulsive inputs in the set of admissible controls. For underactuated systems that are not subjected to impact, current approaches require controllability of the system to be checked at every point on the orbit and controller gains to be computed online by solving a periodic Ricatti differential equation. The approach in this research, which uses both continuous and impulsive inputs, will result in a linear time-invariant system and reduce the computational cost and complexity of control design. It will also allow estimation of the region of attraction around the orbit, which will be used to determine the optimal location for application of the impulsive inputs. To consider systems that are subjected to impact, the research will focus on bipeds, where both continuous and impulsive inputs will be used for gait stabilization; and the devil-stick, where only impulsive inputs will used. For bipeds, current approaches use numerical methods to search for stable gaits. This research will design nominal gaits analytically. It will be possible to easily check the stability and controllability of a nominal gait and tune controller parameters to obtain controllable gaits. Impact-free nominal gaits will ensure that energy loss and hardware wear and tear due to impact will be minimized. For the devil-stick, purely impulsive control will be designed for a variety of juggling problems. The analytical and experimental investigations will lead to new modalities of non-prehensile manipulation.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.