Design of reference trajectory to stabilize desired nominal cyclic gait of a biped

Aoustin, Yannick; Formal’sky, A.

doi:10.1109/romoco.1999.791069

Cited by 18 publications

(23 citation statements)

References 8 publications

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“…In view of simplifying the analysis of periodic orbits in Section 10.4, the transition is assumed to occur at a prespecified point in the fully actuated phase. 7 Hence, H u a = θ a (q a ) − θ − a,0 , where θ a (q a ) is the angle of the hips with respect to the stance ankle (see Fig. 10.3) and θ − a,0 is a constant to be determined.…”

Section: Foot Rotation or Transition From Full Actuation To Underactmentioning

confidence: 99%

“…It is assumed here that the actuator time constant is small enough that it need not be modeled. 7 When the transition condition is met, namely, θa = θ − a,0 , a jump in the torque is made to achieveq N < 0. This moves the FRI point in front of the foot.…”

Section: Foot Rotation or Transition From Full Actuation To Underactmentioning

confidence: 99%

“…In the case of the van der Pol oscillator, suppose we suspect that a limit cycle passes through the x 2 -axis for 7 1 < x 2 < 3. Define a hyper surface S := {( Fig.…”

Section: B31 Poincaré Return Mapmentioning

confidence: 99%

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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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Section: Foot Rotation or Transition From Full Actuation To Underactmentioning

confidence: 99%

Section: Foot Rotation or Transition From Full Actuation To Underactmentioning

confidence: 99%

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Feedback Control of Dynamic Bipedal Robot Locomotion

Westervelt¹,

et al. 2018

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“…In consequence, their interaction with the ground is essential and many characteristics, problems have to be taken into account, underactuated [1], [2] or over actuated phases [16], impacts [9], [10], [14], balancing stability, [4], stability of cyclic motion, [1], [11], [12], [15]. In future many applications such as medical assistance, inspection or manipulation tasks in human environment would be entrusted to biped robots.…”

Section: Introductionmentioning

confidence: 99%

“…In [7], authors show that model results and experimental data both support the proposition that the primary function of the arms during gait is to reduce fluctuations in angular momentum. The orientation of the trunk, the varying length of the step can improve the stability of a cyclic walking gait [1], [2]. The ballistic running was considered by [18] with a study of symmetry properties of the joint variables and their velocities during the flight for a biped with massless feet.…”

Section: Introductionmentioning

confidence: 99%

On optimal swinging of the biped arms

Aoustin

Formalskii

2008

2008 IEEE/RSJ International Conference on Intelligent Robots and Systems

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Abstract-A ballistic walking gait is designed for a planar biped with two identical two-link legs, a trunk and two onelink arms. This seven-link biped is controlled via impulsive torques at the instantaneous double support to obtain a cyclic gait. These impulsive torques are applied in six inter-link joints. Then infinity of solutions exists to find the impulsive torques. An energy cost functional of these impulsive torques is calculated to choose a unique solution by its minimization. Numerical results show that for a given time period of the walking gait step and a length of the step, there exists an optimal swinging amplitude of arms. For this optimal motion of the arms, mentioned above cost functional is minimum.

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