Results 1 
3 of
3
Asymptotically stable walking of a fivelink underactuated 3D bipedal robot
 IEEE TRANS. ON ROBOTICS
, 2008
"... This paper presents three feedback controllers that achieve an asymptotically stable, periodic, and fast walking gait for a 3D bipedal robot consisting of a torso, revolute knees, and passive (unactuated) point feet. The walking surface is assumed to be rigid and flat; the contact between the robo ..."
Abstract

Cited by 38 (13 self)
 Add to MetaCart
(Show Context)
This paper presents three feedback controllers that achieve an asymptotically stable, periodic, and fast walking gait for a 3D bipedal robot consisting of a torso, revolute knees, and passive (unactuated) point feet. The walking surface is assumed to be rigid and flat; the contact between the robot and the walking surface is assumed to inhibit yaw rotation. The studied robot has 8 DOF in the single support phase and 6 actuators. In addition to the reduced number of actuators, the interest of studying robots with point feet is that the feedback control solution must explicitly account for the robot’s natural dynamics in order to achieve balance while walking. We use an extension of the method of virtual constraints and hybrid zero dynamics, a very successful method for planar bipeds, in order to simultaneously compute a periodic orbit and an autonomous feedback controller that realizes the orbit, for a 3D (spatial) bipedal walking robot. This method allows the computations for the controller design and the periodic orbit to be carried out on a 2DOF subsystem of the 8DOF robot model. The stability of the walking gait under closedloop control is evaluated with the linearization of the restricted Poincaré map of the hybrid zero dynamics. Most periodic walking gaits for this robot are unstable when the controlled outputs are selected to be the actuated coordinates. Three strategies are explored to produce stable walking. The first strategy consists of imposing a stability condition during the search of a periodic gait by optimization. The second strategy uses an eventbased controller to modify the eigenvalues of the (linearized) Poincaré map. In the third approach, the effect of output selection on the zero dynamics is discussed and a pertinent choice of outputs is proposed, leading to stabilization without the use of a supplemental eventbased controller.
Hybrid Invariant Manifolds in Systems with Impulse Effects with Application to Periodic Locomotion in Bipedal Robots
"... Motivated by the problem of controlling walking in a biped with series compliant actuation, this paper develops two main theorems relating to the stabilization of periodic orbits in systems with impulse effects. First, when a periodic orbit of a system with impulse effects lies within a hybrid invar ..."
Abstract

Cited by 25 (14 self)
 Add to MetaCart
Motivated by the problem of controlling walking in a biped with series compliant actuation, this paper develops two main theorems relating to the stabilization of periodic orbits in systems with impulse effects. First, when a periodic orbit of a system with impulse effects lies within a hybrid invariant manifold, the Jacobian linearization of the Poincaré return map results in a matrix that is block upper triangular. One diagonal block is the linearization of the return map of the hybrid zero dynamics, and the other is the product of two sensitivity matrices related to the transverse dynamics. When either sensitivity matrix is sufficiently close to zero, the stability of the return map is determined solely by the hybrid zero dynamics. The second main result of the paper details the construction of a hybrid invariant manifold by introducing impactupdated control parameters. Using the construction, entries of either (or both) of the transverse dynamics ’ sensitivity matrices can be made arbitrarily small. A simulation example is provided, where stable walking is achieved in a 5link biped with series compliant actuation.
An Analytical Approach to Asymptotically Stable Walking in Planar Biped Robots
, 2001
"... This paper summarizes recent research of the author, his colleagues, and graduate student on the control of a class of underactuated biped robots. Our goal is to develop a coherent mathematical framework for the rigorous analysis and synthesis of asymptotically stable walking motions. The presentati ..."
Abstract
 Add to MetaCart
This paper summarizes recent research of the author, his colleagues, and graduate student on the control of a class of underactuated biped robots. Our goal is to develop a coherent mathematical framework for the rigorous analysis and synthesis of asymptotically stable walking motions. The presentation attempts to achieve a balance between being precise enough to be believable, and intuitive enough to be understood. No attempt is made to review the general literature. The reader is referred elsewhere for a complete bibliography and proofs. Two movies are included that illustrate the results of the paper applied to a fivelink, underactuated, planar biped.