Toward a vocabulary of legged leaping

Abstract

Toward a Vocabulary of Legged Leaping AbstractAs dynamic robot behaviors become more capable and well understood, the need arises for a wide variety of equally capable and systematically applicable transitions between them. We use a hybrid systems framework to characterize the dynamic transitions of a planar "legged" rigid body from rest on level ground to a fully aerial state. The various contact conditions fit together to form a topologically regular structure, the "ground reaction complex". The body's actuated dynamics excite multifarious transitions between the cells of this complex, whose regular adjacency relations index naturally the resulting "leaps" (path sequences through the cells from rest to free flight). We exhibit on a RHex robot some of the most interesting "words" formed by these achievable path sequences, documenting unprecedented levels of performance and new application possibilities that illustrate the value of understanding and expressing this vocabulary systematically. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This conference paper is available at ScholarlyCommons: http://repository.upenn.edu/ese_papers/662 Toward a Vocabulary of Legged LeapingAaron M. Johnson and D. E. Koditschek Abstract-As dynamic robot behaviors become more capable and well understood, the need arises for a wide variety of equally capable and systematically applicable transitions between them. We use a hybrid systems framework to characterize the dynamic transitions of a planar "legged" rigid body from rest on level ground to a fully aerial state. The various contact conditions fit together to form a topologically regular structure, the "ground reaction complex". The body's actuated dynamics excite multifarious transitions between the cells of this complex, whose regular adjacency relations index naturally the resulting "leaps" (path sequences through the cells from rest to free flight). We exhibit on a RHex robot some of the most interesting "words" formed by these achievable path sequences, documenting unprecedented levels of performance and new application possibilities that illustrate the value of understanding and expressing this vocabulary systematically.

Tail-assisted rigid and compliant legged leaping

“…1. Similar leaps executed on Jerboa [2] (top) and RHex [4] (bottom, from [1]) showing similar qualitative behavior in response to similar control policies despite significant kinematic and dynamic differences (Table I). These transitional behaviors are difficult to analyze with classical dynamical systems theory since they cannot be encoded in terms of stable attractors and their dynamics change depending on which subset of ground contacts is active (cyan) or inactive (magenta).…”

“…of the Ground Reaction Complex (GRC) abstraction [1]not merely for exhaustively navigating the space of possible leaps, but for revealing the similar consequences of similar leaps executed by two radically dissimilar and seemingly incomparable morphologies (Section III); and (c) empirical demonstration of novel behaviors with useful real world applications (Section IV). 1 We now describe each of these results in detail.…”

“…The machine bounds up a ledge one and one half its hip height and crosses a gap of nearly two bodylengthsthe former achieving and the latter exceeding the mark set by [1]. Such highly energetic, agile transitional maneuvers uniquely distinguish the province of legged mobility [3] from its wheeled and tracked counterparts.…”

“…This paper develops a novel combination of intuition and formal reasoning originated in [1] to generate a variety of leaps on the Penn Jerboa [2] (an tailed biped whose four actuators are dynamically coupled across twelve degrees of freedom) with the aim of exciting a diverse array of energetic behaviors. The machine bounds up a ledge one and one half its hip height and crosses a gap of nearly two bodylengthsthe former achieving and the latter exceeding the mark set by [1].…”

Adaptive Control of Quadruped Locomotion Through Variable Compliance of Revolute Spiral Feet

“…The principle adopted for the presented foot design has similarities to the RHex hexapod C-leg solutions [24,25]. The RHex C-leg is designed as a compliant C-shaped beam which is rotated by a single actuator.…”