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

本课题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，促进国家富强和国防建设。欠驱动机械系统是那些控制输入少于其自由度数的系统。欠驱动在导弹、卫星、水下机器人和双足机器人等许多系统中自然而然地出现。在水下机器人和双足机器人等移动的欠驱动机器人系统中，重复运动是非常常见的，而保持稳定性是安全可靠操作的首要条件。这项研究的目的是通过结合大幅度、短持续时间的控制力(通常被称为脉冲力)来产生欠驱动机器人系统的稳定重复运动。虽然在不同的动力学系统中已经研究了冲力的影响，但大多数的研究都局限于理论研究。这项研究将有一个重要的实验部分，并将通过解决实施挑战，将动力系统的脉冲控制从理论转化为实践。除了科学和技术进步，该项目还将通过研究与教育的结合、多样性和外联产生广泛的影响。该项目将为本科生提供研究经验，为研究生提供学位论文选题，从而为下一代工程师和学术界的发展做出贡献。重复运动在欠驱动机器人系统中很常见，其抗扰动能力取决于轨道的稳定性。这项研究将通过将脉冲输入包括在允许的控制集合中来消除当前用于欠驱动系统轨道镇定的方法的局限性。对于不受冲击的欠驱动系统，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。本研究中的方法，既使用连续输入，又使用脉冲输入，将得到一个线性时不变系统，降低了控制设计的计算成本和复杂性。它还将允许估计轨道周围的吸引区域，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，研究将专注于两足动物，其中连续和脉冲输入都将用于步态稳定；以及魔鬼棒，其中只使用脉冲输入。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。本研究将对标称步态进行解析设计。可以很容易地检查标称步态的稳定性和可控性，并调整控制器参数以获得可控步态。无冲击标称步态将确保将因冲击造成的能量损失和硬件磨损降至最低。对于魔杖，纯粹的冲动控制将被设计用于各种杂耍问题。分析和实验调查将导致非缠绕操纵的新模式。这一裁决反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.