Shape

Highly articulated systems are capable of executing a variety of behaviors by coordinating their many internal degrees of freedom to help them move more effectively in complex terrains. However, this inherent variety poses significant challenges that have been the subject of a great deal of previous work: What are the most effective or most efficient methods for achieving the intrinsic coordination necessary to produce desired global objectives? This work takes these questions one step further, asking how different levels of coordination, which we quantify in terms of kinematic coupling, affect articulated locomotion in environments with different degrees of underlying structure. We introduce shape functions as the analytical basis for specifying kinematic coupling relationships that constrain the relative motion among the internal degrees of freedom for a given system during its nominal locomotion. Furthermore, we show how shape functions are used to derive shape-based controllers (SBCs) that manage the compliant interaction between articulated bodies and the environment while explicitly preserving the inter-joint coupling defined by shape functions. Initial experimental evidence provides a comparison of the benefits of different levels of coordination for two separate platforms in environments with different degrees of inherent structure. The experimental results show that decentralized implementations, where there is relatively little inter-joint coupling, perform well across a spectrum of different terrains but that there are potential benefits to higher degrees of coupling in structured terrains. We discuss how this observation has implications related to future planning and control approaches that actively “tune” their underlying structure by dynamically varying the assumed level of coupling as a function of task specification and local environmental conditions