Asymptotically Stable Walking of a Five-Link Underactuated 3-D Bipedal Robot

By Christine Chevallereau, Jessy W. Grizzle, Ching-Long Shih. IEEE Transactions on robotics, 2009

302 citations recorded by the source corpus.

This paper presents three feedback controllers that achieve an asymptotically stable, periodic, and fast walking gait for a 3-D 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 six 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 (HZD), 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 3-D (spatial) bipedal walking robot. This method allows the computations for the controller design and the periodic orbit to be carried out on a 2-DOF subsystem of the 8-DOF robot model. The stability of the walking gait under closed-loop control is evaluated with the linearization of the restricted Poincare map of the HZD. 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 event-based controller to modify the eigenvalues of the (linearized) Poincare 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 event-based controller.

Subfields: Biomedical Engineering, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/0561a1e16bdeb8f2d67478d39cf0333071f1b304

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Citations in the corpus

A Compliant Hybrid Zero Dynamics Controller for Stable, Efficient and Fast Bipedal Walking on MABEL (2011, background): “Keywords bipedal robots, compliance, hybrid systems, zero dynamics.”
Capturability-based analysis and control of legged locomotion, Part 2: Application to M2V2, a lower-body humanoid (2012, methodology): “More recently, this method has been used to generate three-dimensional walking (Chevallereau et al. 2009).”
Simulation in the design and operation of manufacturing systems: state of the art and new trends (2019, methodology): “Apart from their application in dynamic models, such as trajectory calculation and bipedal robots (Chevallereau, Grizzle, and Shih 2009), they are also applied at large in production simulation, solving complex systems that may shift between discrete and continuous models.”
Models, feedback control, and open problems of 3D bipedal robotic walking (2014, methodology): “A detailed derivation for a planar point foot contact can be found in [213]; the 3D case is very similar as shown in [28].”
> Replace This Line with Your Paper Identification Number (double-click Here to Edit) < 1 (unknown): “Starting with a simple 3-link model [17] and followed by a 5-link model [5], we used the techniques of virtual constraints [9], hybrid zero dynamics [21] [14] and event-based control [10] to achieve exponentially stable, periodic walking motions.”