An Expanded Analysis and Design Framework for Robots that Move by Reshaping their Limbs and Bodies

该项目旨在扩展对具有关节体和四肢的机器人运动的理解。步态是一系列身体形状的变化，以开始时的相同形状结束，并导致身体在其环境中的净重新定位。通过一遍又一遍地重复这个序列，可以实现任意大的重新定位。四足动物的步态包括马的行走、小跑、慢跑和飞奔，以及瞪羚的驼背。机器人或动物可能会根据需要使用特定的步态——例如，所需的行进速度将影响不同步态的相对能量效率。具有类似于动物的身体结构的机器人可以使用自然适应的步态，但并非所有机器人结构都具有明显的生物对偶性。此外，严格的仿生学方法可能会错过可能改善自然系统的步态。该项目将推导出一个系统的数学框架，以在使用当前技术状态通常无法处理的情况下搜索理想的步态，包括机器人身体的某些运动无法主动控制，或者机器人的运动导致周围环境的变化，或者控制周围环境的属性以间接影响机器人的运动。这项工作的结果将应用于能够在具有挑战性的介质中机动的机器人，如水、沙子或泥浆。这些结果将在搜索和救援、环境监测和探索恶劣环境方面具有潜在的用途。研究结果还将深入了解生物有机体的运动策略。首席研究员有外展和教育活动的记录，包括机器人运动的研究生水平的教科书。步态运动利用系统与周围环境相互作用产生的反作用力的不对称性，以循环的方式获得净位移。机器人步态运动的最新研究已经建立了一个以主纤维束形式建模系统构型空间的几何框架；在这样的表述中，一个系统——无论是机器人还是动物——都有一个构型空间，这个构型空间可以分为形状空间和位置空间。步态是形状空间中的循环路径，当跟随这些路径时，会在位置空间中引起位移。这种纤维束结构已与非线性控制技术一起用于机器人运动规划的步态分析和工程设计，但先前的工作仅限于自由度可以被整齐地分解为直接驱动和参数化对称群的系统。这样的系统只代表了现实运动问题的一小部分，特别是，不包括那些可以从非线性动力学中获得能量效率的系统，这些非线性动力学涉及额外的非驱动自由度。该项目将把基于对称的建模和控制方法的适用性扩展到更广泛的孤立和协作运动问题，这些问题强调自然和工程系统边界的效率、敏捷性和设计原则。

This project seeks to extend understanding of locomotion in robots with articulated bodies and limbs. A gait is a sequence of body shape changes that ends with the same shape as it starts, and that results in a net repositioning of the body within its environment. Arbitrarily large repositioning may be achieved by repeating the sequence over and over. Examples of gaits in four-legged animals include walking, trotting, cantering, and galloping in horses, and pronking in gazelles. A robot or animal may use a particular gait depending on need -- for example, the desired speed of travel will affect the relative energy efficiency of different gaits. Robots with body configurations similar to animals may use gaits adapted from nature, however not all robot configurations have obvious biological counterparts. Furthermore a strictly biomimetic approach may miss possible gaits that improve upon natural systems. This project will derive a systematic mathematical framework to search for desirable gaits in cases that cannot generally be handled using the current state of the art, including where some movements of the robot body cannot be actively controlled, or where the movement of the robot causes changes to the surrounding environment, or where properties of the surrounding environment are controlled to indirectly influence the movement of the robot. The results of this work will be applied to robots that can maneuver through challenging media, such as water, sand or mud. These results will have potential uses in search and rescue, environmental monitoring, and exploration of hostile environments. The results will also give insight into the locomotion strategies of biological organisms. The Principal Investigator has a track record of outreach and educational activities, including a graduate-level textbook on robotic locomotion.Gait motions take advantage of asymmetries in the reaction forces generated from a system's interactions with its surroundings to gain net displacement in a cyclic way. Recent research in robotic gait locomotion has established a geometric framework for modeling a system's configuration space in the form of a principal fiber bundle; in such a formulation, a system -- either robot or animal -- has a configuration space that can be divided into a shape space and a position space. Gaits are cyclic paths in the shape space, which when followed, cause displacement in the position space. This fiber bundle structure has been used with nonlinear control techniques to analyze and engineer gaits for robotic motion planning, but prior work has been restricted to systems whose degrees of freedom can be neatly decomposed into those that are actuated directly and those that parameterize a symmetry group. Such systems represent only a fraction of the landscape of realistic locomotion problems, in particular, excluding systems in which energy efficiency can be derived from nonlinear dynamics involving additional unactuated degrees of freedom. This project will extend the applicability of symmetry-based methods for modeling and control to a broader class of problems in solitary and cooperative locomotion that emphasize efficiency, agility, and design principles at the boundary of natural and engineered systems.