Motions of a rimless spoked wheel: a simple three-dimensional system with impacts

Coleman, Michael J.; Chatterjee, Anindya; Ruina, Andy

doi:10.1080/02681119708806242

Cited by 150 publications

(83 citation statements)

References 15 publications

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“…non-dissipative, this behavior seems counterintuitive. However, it also constitutes a piecewise holonomic system experiencing phase-dependent dynamics (the different stance and flight-phase dynamics), and several recent investigations demonstrate that such systems can exhibit asymptotic stability (Coleman et al, 1997;Ruina, 1998;Coleman and Holmes, 1999).…”

Section: Introductionmentioning

confidence: 99%

Spring-mass running: simple approximate solution and application to gait stability

Geyer

Seyfarth

Blickhan

2005

Journal of Theoretical Biology

250

232

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The planar spring-mass model is frequently used to describe bouncing gaits (running, hopping, trotting, galloping) in animal and human locomotion and robotics. Although this model represents a rather simple mechanical system, an analytical solution predicting the center of mass trajectory during stance remains open. We derive an approximate solution in elementary functions assuming a small angular sweep and a small spring compression during stance. The predictive power and quality of this solution is investigated for model parameters relevant to human locomotion. The analysis shows that (i), for spring compressions of up to 20% (angle of attack X60 ; angular sweep p60 ) the approximate solution describes the stance dynamics of the center of mass within a 1% tolerance of spring compression and 0:6 tolerance of angular motion compared to numerical calculations, and (ii), despite its relative simplicity, the approximate solution accurately predicts stable locomotion well extending into the physiologically reasonable parameter domain. (iii) Furthermore, in a particular case, an explicit parametric dependency required for gait stability can be revealed extending an earlier, empirically found relationship. It is suggested that this approximation of the planar spring-mass dynamics may serve as an analytical tool for application in robotics and further research on legged locomotion. r

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Section: Introductionmentioning

confidence: 99%

Spring-mass running: simple approximate solution and application to gait stability

Geyer

Seyfarth

Blickhan

2005

Journal of Theoretical Biology

250

232

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“…the velocity of the center of mass of the feet can be written as : 57) and the absolute velocity of the swing (i.e., impacting) foot can be expressed as ω…”

Section: Transition Map From the Underactuated Phase To The Fully Actmentioning

confidence: 99%

Feedback Control of Dynamic Bipedal Robot Locomotion

Westervelt¹,

et al. 2018

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To our loved ones. A tous ceux que nous aimons. DRAFT --May 15, 2007 --DRAFT --May 15, 2007 --DR PrefaceThe objective of this book is to present systematic methods for achieving stable, agile and efficient locomotion in bipedal robots. The fundamental principles presented here can be used to improve the control of existing robots and provide guidelines for improving the mechanical design of future robots. The book also contributes to the emerging control theory of hybrid systems. Models of legged machines are fundamentally hybrid in nature, with phases modeled by ordinary differential equations interleaved with discrete transitions and reset maps. Stable walking and running correspond to the design of asymptotically stable periodic orbits in these hybrid systems and not equilibrium points. Past work has emphasized quasi-static stability criteria that are limited to flat-footed walking. This book represents a concerted effort to understand truly dynamic locomotion in planar bipedal robots, from both theoretical and practical points of view.The emphasis on sound theory becomes evident as early as Chapter 3 on modeling, where the class of robots under consideration is described by lists of hypotheses, and further hypotheses are enumerated to delineate how the robot interacts with the walking surface at impact, and even the characteristics of its gait. This careful style is repeated throughout the remainder of the book, where control algorithm design and analysis are treated. At times, the emphasis on rigor makes the reading challenging for those less mathematically inclined. Do not, however, give up hope! With the exception of Chapter 4 on the method of Poincaré sections for hybrid systems, the book is replete with concrete examples, some very simple, and others quite involved. Moreover, it is possible to cherry-pick one's way through the book in order to "just figure out how to design a controller while avoiding all the proofs." This is mapped out below and in Appendix A.The practical side of the book stems from the fact that it grew out of a project grounded in hardware. More details on this are given in the acknowledgements, but suffice it to say that every stage of the work presented here has involved the interaction of roboticists and control engineers. This interaction has led to a control theory that is closely tied to the physics of bipedal robot locomotion. The importance and advantage of doing this was first driven home to one of the authors when a multipage computation involving the Frobenius Theorem produced a quantity that one of the other authors identified as angular momentum, and she could reproduce the desired result in two lines! Fortunately, the power of control theory produced its share of eye-opening moments on the robotic side of the house, such as when days and DRAFT --May 15, 2007 --DRAFT --May 15, 2007 --DR days of simulations to tune a "physically-based" controller were replaced by a ten minute design of a PI-controller on the basis of a restricted Poincaré map, and the controller worked l...

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“…Many of the fundamental results for legged robots have come from detailed analytical and computational investigations of simplified models (e.g., [3,5,7,10,11]). These analyses reveal the limit cycle nature of ideal walking systems and employ Poincaré map analysis to assess the stability of these limit cycles.…”

Section: Introductionmentioning

confidence: 99%

Metastable Walking on Stochastically Rough Terrain

Byl

Tedrake

2008

Robotics: Science and Systems IV

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Abstract-Simplified models of limit-cycle walking on flat terrain have provided important insights into the nature of legged locomotion. Real walking robots (and humans), however, do not exhibit true limit cycle dynamics because terrain, even in a carefully designed laboratory setting, is inevitably non-flat. Walking systems on stochastically rough terrain may not satisfy strict conditions for limit-cycle stability but can still demonstrate impressively long-living periods of continuous walking. Here, we examine the dynamics of rimless-wheel and compass-gait walking on randomly generated rough terrain and employ tools from stochastic processes to describe the 'stochastic stability' of these gaits. This analysis generalizes our understanding of walking stability and may provide statistical tools for experimental limit cycle analysis on real walking systems.

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Motions of a rimless spoked wheel: a simple three-dimensional system with impacts

Cited by 150 publications

References 15 publications

Spring-mass running: simple approximate solution and application to gait stability

Spring-mass running: simple approximate solution and application to gait stability

Feedback Control of Dynamic Bipedal Robot Locomotion

Metastable Walking on Stochastically Rough Terrain

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