Comparative simulation study of three control techniques applied to a biped robot

Raibert, M.; Tzafestas, Spyros G.; Tzafestas, Costas S.

doi:10.1109/icsmc.1993.384792

Cited by 38 publications

(26 citation statements)

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“…Corollary 1: a) There exists a nontrivial periodic orbit of the hybrid zero dynamics if, and only if, and (57) b) There exists an exponentially stable periodic orbit of the hybrid zero dynamics if, and only if, (57) holds and (58) Remark 3: The Lagrangian of the zero dynamics (28) and (29) can be shown to be , where is given by (48) and (59) The interpretation of this result will be presented elsewhere.…”

Section: A Poincaré Analysis Of the Zero Dynamicsmentioning

confidence: 99%

“…In the broader spectrum of dynamically dexterous machines, this work builds on the ideas of Koditschek et al [11], [37], [41], [49] where the goal is not to prescribe the dynamics of systems via reference trajectories, as is often done in the control of legged locomotion (see [15], [29], [34], [35], and [48], for example) but rather to encode the dynamic task via a lower dimensional target, itself represented by a set of differential equations. Given the demonstrated appearance of internal dynamical 0018-9286/03$17.00 © 2003 IEEE models in the animal nervous system [36], and the emerging evidence that these models incorporate a state-event based (as opposed to explicit time-based) representations of the plant [18], it seems plausible to hypothesize that task encoding via internal target dynamics may also play a significant role in animal motor control [21].…”

Section: Introductionmentioning

confidence: 99%

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Hybrid zero dynamics of planar biped walkers

Westervelt

Grizzle

Koditschek

2003

IEEE Trans. Automat. Contr.

744

721

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Planar, underactuated, biped walkers form an important domain of applications for hybrid dynamical systems. This paper presents the design of exponentially stable walking controllers for general planar bipedal systems that have one degree-of-freedom greater than the number of available actuators. The within-step control action creates an attracting invariant set-a two-dimensional zero dynamics submanifold of the full hybrid model-whose restriction dynamics admits a scalar linear time-invariant return map. Exponentially stable periodic orbits of the zero dynamics correspond to exponentially stabilizable orbits of the full model. A convenient parameterization of the hybrid zero dynamics is imposed through the choice of a class of output functions. Parameter optimization is used to tune the hybrid zero dynamics in order to achieve closed-loop, exponentially stable walking with low energy consumption, while meeting natural kinematic and dynamic constraints. The general theory developed in the paper is illustrated on a five link walker, consisting of a torso and two legs with knees. KeywordsBipeds, hybrid systems, Poincaré sections, underactuated system, zero dynamics 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. Abstract-Planar, underactuated, biped walkers form an important domain of applications for hybrid dynamical systems. This paper presents the design of exponentially stable walking controllers for general planar bipedal systems that have one degree-of-freedom greater than the number of available actuators. The within-step control action creates an attracting invariant set-a two-dimensional zero dynamics submanifold of the full hybrid model-whose restriction dynamics admits a scalar linear time-invariant return map. Exponentially stable periodic orbits of the zero dynamics correspond to exponentially stabilizable orbits of the full model. A convenient parameterization of the hybrid zero dynamics is imposed through the choice of a class of output functions. Parameter optimization is used to tune the hybrid zero dynamics in order to achieve closed-loop, exponentially stable walking with low energy consumption, while meeting natural kinematic and dynamic constraints. The general theory developed in the paper is illustrated on a five link walker, consisting of a torso and two legs with knees.

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Section: A Poincaré Analysis Of the Zero Dynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hybrid zero dynamics of planar biped walkers

Westervelt

Grizzle

Koditschek

2003

IEEE Trans. Automat. Contr.

744

721

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“…To control walking in a planar, five-DOF biped, Mitobe et al [156] used computed torque to regulate the biped's COM and swing leg end position. To control walking in a planar, five-DOF biped, Raibert, Tzafestas, and Tzafestas [186] In this way, the control action is "clocked" to events on the robot's path and not to an externally supplied time-based trajectory.…”

Section: Control Of Bipedal Locomotionmentioning

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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“…With this aim, it is assumed that the impact with the ground of the current swing leg, at the end of each step, produces an instantaneous change of the joint velocities without implying a change in the posture of the robot. This approach has been widely considered in the literature; see for instance [4] and [27]. For the analysis of the double support phase, it has been considered two additional coordinates, …”

Section: Structural Propertiesmentioning

confidence: 99%

Design and Real-Time Control of a 4-DOF Biped Robot

Vázquez

Velasco-Villa

2013

International Journal of Advanced Robotic Systems

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This work is focused on the design, construction and model based control of a biped robot during the walking cycle on the sagittal plane. For the analysis, the single support phase is considered to be the dominating dynamics, by assuming an instantaneous double support phase which is only described by the impact phenomenon. The joint tracking problem is analyzed by means of a model based control strategy, which incorporates a reformulation of the Coriolis matrix that allows the cancellation of non antisymmetric terms in order to formally proof the asymptotic stability of the coordinate error system representation in a local sense. Some experiments are carried out for a pre-defined reference trajectory for the walking cycle of a 4-DOF biped robot.

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Comparative simulation study of three control techniques applied to a biped robot

Cited by 38 publications

References 10 publications

Hybrid zero dynamics of planar biped walkers

Hybrid zero dynamics of planar biped walkers

Feedback Control of Dynamic Bipedal Robot Locomotion

Design and Real-Time Control of a 4-DOF Biped Robot

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