Optimal Reference Motions for Walking of a Biped Robot

Djoudi, D.; Chevallereau, Christine; Aoustin, Yannick

doi:10.1109/robot.2005.1570407

Cited by 32 publications

(27 citation statements)

References 6 publications

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“…11.1. This trajectory includes only the fully actuated and double support phases, and has been designed using [69]. Polynomials of degree 4 were used.…”

Section: Simulationsmentioning

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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“…11.1. This trajectory includes only the fully actuated and double support phases, and has been designed using [69]. Polynomials of degree 4 were used.…”

Section: Simulationsmentioning

confidence: 99%

Feedback Control of Dynamic Bipedal Robot Locomotion

Westervelt¹,

et al. 2018

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“…In the design of reference trajectories, the biped robots can present underactuated phases (7), (24), (10), (23), over-actuated phases (17), (15) or completely actuated phase (12).…”

Section: Introductionmentioning

confidence: 99%

Comparison of different gaits with rotation of the feet for a planar biped

Tlalolini

Chevallereau

Aoustin

2009

Robotics and Autonomous Systems

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Fast human walking includes a phase where the stance heel rises from the ground and the stance foot rotates about the stance toe. This phase where the biped becomes under-actuated is not present during the walk of humanoid robots. The objective of this study is to determine if this phase is useful to reduce the energy consumed in the walking. In order to study the efficiency of this phase, six cyclic gaits are presented for a planar biped robot. The simplest cyclic motion is composed of successive single support phases with flat stance foot on the ground. The most complex cyclic motion is composed of single support phases that include a subphase of rotation of the stance foot about the toe and of finite time double support phase. For the synthesis of these walking gaits, optimal motions with respect to the torque cost, are defined by taking into account given performances of actuators. It is shown that for fast motions a foot rotation sub-phase is useful to reduce the criteria cost. In the optimization process, under-actuated phase (foot rotation phase), fullyactuated phase (flat foot phase) and over-actuated phase (double support phase) are considered.

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“…HYBRID ZERO DYNAMICS OF WALKING Control design for underactuated walking robots has been a topic of extensive investigation in the literature [9], [11], [12]. The main idea is to design a set of virtual holonomic constraints and enforce them by input-output feedback linearization.…”

Section: B Rigid Impactmentioning

confidence: 99%

Online motion planning over uneven terrain with walking primitives and regression

Apostolopoulos

Leibold

Buss

2016

2016 IEEE International Conference on Robotics and Automation (ICRA)

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Abstract-This paper introduces an online motion planning algorithm and a motion generation methodology for underactuated dynamic planar walking on uneven terrain. The key idea is to utilize a database of Motion Primitives and use them as training examples in a regression methodology, which is utilized when there is no match between the terrain variation and the Motion Primitives in the database. Among the key features which enable the algorithm to be suitable for real-time purposes is the proposed best first graph search approach and the small inference time of the regression methodology, which in this paper is the Gaussian Process.

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Optimal Reference Motions for Walking of a Biped Robot

Cited by 32 publications

References 6 publications

Feedback Control of Dynamic Bipedal Robot Locomotion

Feedback Control of Dynamic Bipedal Robot Locomotion

Comparison of different gaits with rotation of the feet for a planar biped

Online motion planning over uneven terrain with walking primitives and regression

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