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

这个项目旨在扩展对具有关节身体和四肢的机器人的运动的理解。步态是一系列身体形状的变化，以与开始时相同的形状结束，并导致身体在其环境中净重新定位。可以通过一遍又一遍地重复该序列来实现任意大的重新定位。四足动物的步态包括步行、小跑、慢跑、骑马奔跑和瞪羚发音。机器人或动物可以根据需要使用特定的步态--例如，期望的移动速度将影响不同步态的相对能量效率。机器人的身体结构与动物相似，可以使用从自然中改编的步态，但并不是所有的机器人结构都有明显的生物对应。此外，严格的仿生方法可能会错过改进自然系统的可能步态。该项目将得出一个系统的数学框架，以在通常不能使用当前技术状态处理的情况下寻找理想的步态，包括机器人身体的一些运动不能被主动控制，或者机器人的运动导致周围环境的变化，或者周围环境的属性被控制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水、沙或泥等具有挑战性的介质中进行机动的机器人。这些结果将在搜救、环境监测和对恶劣环境的探索中具有潜在的用途。这一结果还将使人们对生物有机体的运动策略有深入的了解。首席调查员有推广和教育活动的记录，包括一本关于机器人运动的研究生水平的教科书。步态运动利用系统与环境相互作用产生的反作用力中的不对称性，以循环的方式获得净位移。最近对机器人步态运动的研究已经建立了一个几何框架，用于以主纤维束的形式建模系统的构形空间；在这样的公式中，无论是机器人还是动物，系统都具有可分为形状空间和位置空间的构形空间。步态是形状空间中的循环路径，当跟随这些路径时，会导致位置空间中的位移。这种纤维束结构已经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，但以前的工作仅限于将自由度巧妙地分解为直接驱动的自由度和将对称群参数化的系统。这样的系统只代表现实运动问题的一小部分，特别是不包括那些能效可以从涉及额外的非致动自由度的非线性动力学中获得的系统。这个项目将把基于对称性的建模和控制方法的适用性扩展到更广泛的一类问题，即孤立运动和协作运动中的问题，强调自然和工程系统边界的效率、灵活性和设计原则。

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.