Legged Self-Manipulation

Abstract

This paper introduces self-manipulation as a new formal design methodology for legged robots with varying ground interactions. The term denotes a set of modeling choices that permit a uniform and bodycentric representation of the equations of motion-essentially a guide to the selection and configuration of coordinate frames. We present the hybrid system kinematics, dynamics, and transitions in the form of a consistently structured representation that simplifies and unites the account of these, otherwise bewilderingly diverse differential algebraic equations. Cleaving as closely as possible to the modeling strategies developed within the mature manipulation literature, self-manipulation models can leverage those insights and results where applicable, while clarifying the fundamental differences. Our primary motivation is not to facilitate numerical simulation but rather to promote design insight. We instantiate the abstract formalism for a simplified model of RHex, and illustrate its utility by applying a variety of analytical and computational techniques to derive new results bearing on behaviors, controllers, and platform design. For each example, we present empirical results documenting the specific benefits of the new insight into the robot's transitions from standing to moving in place and to leaping.INDEX TERMS Legged locomotion, Robot control, Robot kinematics, Manipulator dynamics. I. INTRODUCTIONLegged robots, such as the notional mechanism in Fig. 1, will necessarily experience a variety of changing contact conditions as they perform ever more complex tasks requiring greater autonomy on novel, and possibly shifting, terrain. As 310

Tail-assisted rigid and compliant legged leaping

“…however, following [5,6], when the leg is unconstrained (in the air) we may drop it from the dynamics and use simply M b as the inertia tensor. The potential energy and actuator forces, [6,Eqns.…”

“…1 for Leap 1, focusing on contact mode 010 but also including some aspects of 000 and 011. We express these equations of motion by following [5,6], which we summarize here.…”

“…where λ are the constraint forces (e.g in mode 010, λ " " λt λn ‰ , normal and tangential toe forces), and N is the force due to the potential energy, V pqq, [6,Eqn. 31].…”

“…The first use of its simple 3-contact GRC, [1], Section II-A, is to achieve result (a), summarized above. Namely, the GRC organizes our analytical investigation of the "tailless" machine's (relatively) simple associated self-manipulation hybrid system [5,6] dynamics, Section II-B, leading up to the key formal conclusion of the paper (Prop. 1): a centered hip, rigid leg version of the mechanism cannot achieve a level leap with any control policy (Section II-C).…”

Core Actuation Promotes Self-manipulability on a Direct-Drive Quadrupedal Robot

“…Additionally, using gearing in the spine allows an individual motor to provide the mass center a significantly higher amount of sustained, work-producing force than it can on a transmission-free leg, without affecting leg linkage transparency. We quantify both of these advantages and demonstrate them on a physical platform in a series of experiments involving leaping from level ground and an isolated foothold (an archetypal feature of unstructured terrain), a task requiring both large ground forces as well as a large workspace to facilitate balancing and self-manipulation [15].…”