Tracking a joint path for the walk of an underactuated 
biped

Chevallereau, Christine; Formal’sky, A.; Djoudi, D.

doi:10.1017/s0263574703005460

Cited by 60 publications

(64 citation statements)

References 10 publications

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“…The torques Γ are bounded, thus they do not affect the instantaneous double support. The impact model can be written as (8):…”

Section: Impact Modelmentioning

confidence: 99%

“…Thus the system is under-actuated and its motion cannot be freely chosen. Studies of control of such an underactuated biped (6), (8) have shown that a geometric evolution of the robot q(s) can be chosen. For a given function q(s) within some limits, function s(t) defining a motion compatible with the dynamic model can be deduced using equation (11).…”

Section: The Foot-rotation Sub-phasementioning

confidence: 99%

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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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“…The torques Γ are bounded, thus they do not affect the instantaneous double support. The impact model can be written as (8):…”

Section: Impact Modelmentioning

confidence: 99%

Section: The Foot-rotation Sub-phasementioning

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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“…Though not indicated in the figure, massless springs may be attached between links and between links and the inertial reference frame; prismatic joints between links are also allowed. This class of systems clearly includes the Acrobot [2,36,52], the brachiating robots of [15,34,35,46], the gymnast robots of [32,39,57] when pivoting on a high bar, and the stance phase models of Raibert's onelegged hopper [1,6,14,26,33,42] as well as RABBIT [7][8][9][10]41]. The control objectives will be to stabilize the system about an equilibrium point or to track a set of reference trajectories with internal stability.…”

Section: Motivating Classes Of Systemsmentioning

confidence: 99%

“…In the above, note that σ, given by (9), is the usual angular momentum of the robot about the attachment point. Since the robot is constrained to a horizontal plane, if the spring constant were zero, then angular momentum would be conserved and asymptotic stabilization to an equilibrium point would be impossible.…”

Section: ) Mathematical Representationmentioning

confidence: 99%

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Nonlinear control of mechanical systems with one degree of underactuation

Chevallereau¹,

Grizzle

Moog³

2004

IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004

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Abstract-Numerous robotic tasks associated with underactuation have been studied in the literature. For a large number of these in the plane, the mechanical models have a cyclic variable, the cyclic variable is unactuated, and all shape variables are independently actuated. This paper formulates and solves two control problems for this class of models. If the generalized momentum conjugate to the cyclic variable is not conserved, conditions are found for the existence of a set of outputs that yields a system with a one-dimensional exponentially stable zero dynamics -i.e. an exponentially minimum-phase system -along with a dynamic extension that renders the system locally input-output decouplable. If the generalized momentum conjugate to the cyclic variable is conserved, a reduced system is constructed and conditions are found for the existence of a set of outputs that yields an empty zero dynamics, along with a dynamic extension that renders the system feedback linearizable. A common element in these two feedback problems is the construction of a scalar function of the configuration variables that has relative degree three with respect to one of the input components. The function arises by partially integrating the conjugate momentum. The results are illustrated on two balancing tasks and on a ballistic flip motion.

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First Steps toward Automatically Generating Bipedal Robotic Walking from Human Data

Ames

2012

Lecture Notes in Control and Information Sciences

123

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Tracking a joint path for the walk of an underactuated biped

Cited by 60 publications

References 10 publications

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

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

Nonlinear control of mechanical systems with one degree of underactuation

First Steps toward Automatically Generating Bipedal Robotic Walking from Human Data

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