Dynamic Legged Mobility---an Overview

Ability to translate to a goal position under the constrains imposed by complex environmental conditions is a key capability for biological and artificial systems alike. Over billions of years evolutionary processes have developed a wide range of solutions to address mobility needs in air, in water and on land. The efficacy of such biological locomotors is beyond the capabilities of engineering solutions that has been produced to this date. Nature has been and will surely remain to be a source of inspiration for engineers in their quest to bring real mobility to their creations. In recent years a new class of dynamic legged terrestrial robotic systems \cite{Autumn-Buehler-Cutkosky.SPIE2005,Raibert.Book1986,Raibert-Blankesport-Nelson.IFAC2008,Saranli-Buehler-Koditschek.IJRR2001} have been developed inspired by, but without mimicking, the examples from the Nature. The experimental work with these platforms over the past decade has led to an improved appreciation of legged locomotion. This paper is an overview of fundamental advantages dynamic legged locomotion offers over the classical wheeled and tracked approaches

Laboratory on Legs: An Architechture for Adjustable Morphology with Legged Robots

For mobile robots, the essential units of actuation, computation, and sensing must be designed to fit within the body of the robot. Additional capabilities will largely depend upon a given activity, and should be easily reconfigurable to maximize the diversity of applications and experiments. To address this issue, we introduce a modular architecture originally developed and tested in the design and implementation of the X-RHex hexapod that allows the robot to operate as a mobile laboratory on legs. In the present paper we will introduce the specification, design and very earliest operational data of Canid, an actively driven compliant-spined quadruped whose completely different morphology and intended dynamical operating point are nevertheless built around exactly the same “Lab on Legs” actuation, computation, and sensing infrastructure. We will review as well, more briefly a second RHex variation, the XRL latform, built using the same components. For more information: Kod*La

Free-Standing Leaping Experiments with a Power-Autonomous, Elastic-Spined Quadruped

We document initial experiments with Canid, a freestanding, power-autonomous quadrupedal robot equipped with a parallel actuated elastic spine. Research into robotic bounding and galloping platforms holds scientific and engineering interest because it can both probe biological hypotheses regarding bounding and galloping mammals and also provide the engineering community with a new class of agile, efficient and rapidly-locomoting legged robots. We detail the design features of Canid that promote our goals of agile operation in a relatively cheap, conventionally prototyped, commercial off-the-shelf actuated platform. We introduce new measurement methodology aimed at capturing our robot’s “body energy” during real time operation as a means of quantifying its potential for agile behavior. Finally, we present joint motor, inertial and motion capture data taken from Canid’s initial leaps into highly energetic regimes exhibiting large accelerations that illustrate the use of this measure and suggest its future potential as a platform for developing efficient, stable, hence useful bounding gaits. For more information: Kod*La

X-RHex: A Highly Mobile Hexapedal Robot for Sensorimotor Tasks

We report on the design and development of X-RHex, a hexapedal robot with a single actuator per leg, intended for real-world mobile applications. X-RHex is an updated version of the RHex platform, designed to offer substantial improvements in power, run-time, payload size, durability, and terrain negotiation, with a smaller physical volume and a comparable footprint and weight. Furthermore, X-RHex is designed to be easier to build and maintain by using a variety of commercial off-the-shelf (COTS) components for a majority of its internals. This document describes the X-RHex architecture and design, with a particular focus on the new ability of this robot to carry modular payloads as a laboratory on legs. X-RHex supports a variety of sensor suites on a small, mobile robotic platform intended for broad, general use in research, defense, and search and rescue applications. Comparisons with previous RHex platforms are presented throughout, with preliminary tests indicating that the locomotive capabilities of X-RHex can meet or exceed the previous platforms. With the additional payload capabilities of X-RHex, we claim it to be the first robot of its size to carry a fully programmable GPU for fast, parallel sensor processing

Toward a Vocabulary of Legged Leaping

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. For more information: Kod*La

Comparison of Spider-Robot Information Models

The paper deduces a mathematical model of a spider-robot with six three-link limbs. Many limbs with a multi-link structure greatly complicate the process of synthesizing a model, since in total the robot has twenty-four degrees of freedom, i.e., three coordinates of the center of mass of the body in space, three angles of rotation of the body relative to its center of mass and three degrees of freedom for each limb, to describe the position of the links. The derived mathematical model is based on the Lagrange equations with a further transformation of the equations to the Cauchy normal form in a matrix form. To test the resulting model in a SimInTech environment, an information model is synthesized and two simple experiments ar carried out to simulate the behavior of real spiders: moving forward in a straight line and turning in place at a given angle. The experimental results demonstrate that the synthesized information model can well cope with the tasks and the mathematical model underlying it can be used for further research

The Penn Jerboa: A Platform for Exploring Parallel Composition of Templates

We have built a 12DOF, passive-compliant legged, tailed biped actuated by four brushless DC motors. We anticipate that this machine will achieve varied modes of quasistatic and dynamic balance, enabling a broad range of locomotion tasks including sitting, standing, walking, hopping, running, turning, leaping, and more. Achieving this diversity of behavior with a single under-actuated body, requires a correspondingly diverse array of controllers, motivating our interest in compositional techniques that promote mixing and reuse of a relatively few base constituents to achieve a combinatorially growing array of available choices. Here we report on the development of one important example of such a behavioral programming method, the construction of a novel monopedal sagittal plane hopping gait through parallel composition of four decoupled 1DOF base controllers. For this example behavior, the legs are locked in phase and the body is fastened to a boom to restrict motion to the sagittal plane. The platform's locomotion is powered by the hip motor that adjusts leg touchdown angle in flight and balance in stance, along with a tail motor that adjusts body shape in flight and drives energy into the passive leg shank spring during stance. The motor control signals arise from the application in parallel of four simple, completely decoupled 1DOF feedback laws that provably stabilize in isolation four corresponding 1DOF abstract reference plants. Each of these abstract 1DOF closed loop dynamics represents some simple but crucial specific component of the locomotion task at hand. We present a partial proof of correctness for this parallel composition of template reference systems along with data from the physical platform suggesting these templates are anchored as evidenced by the correspondence of their characteristic motions with a suitably transformed image of traces from the physical platform.Comment: Technical Report to Accompany: A. De and D. Koditschek, "Parallel composition of templates for tail-energized planar hopping," in 2015 IEEE International Conference on Robotics and Automation (ICRA), May 2015. v2: Used plain latex article, correct gap radius and specific force/torque number