Gait shape control for 2-D.O.F bipedal robots using hybrid virtual holonomic constraints
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Date
2014-07-29
Authors
Al Lawati, Mohamed Ali
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
Motion control for bipedal robots is an active research area because
bipedal robots can perform tasks and work in terrain where wheeled
robots cannot. Researchers have developed bipedal robots that are able
to walk, run and perform predefined tasks such as stair climbing.
Mimicking human motion is one of the potential benefits of bipedal
robots. In the robotics and control literature, many controllers have
been presented that achieve dynamically stable gait motions (i.e.
stable walking). This thesis studies virtual holonomic
constraint (VHC) based control laws that generate stable gaits for
2-DOF bipedal robots.
The planar 2-DOF robot under study is modelled as a hybrid automaton
and consists of three physical components: a stance leg, a swing leg and a hip
mass. The robot is actuated by a hip torque and an ankle torque.
For the continuous phase, the dynamics of the robot are similar
to a rigid double pendulum except that the robot has an "extra" mass
attached to its hip position. At ground impact events, the system's configuration variables are
redefined and the associated velocities change instantaneously. The
ground is modelled as an inclined surface with no curvature.
Due to the hybrid nature of 2-DOF bipedal robots, this thesis extends
the notion of VHC to hybrid VHC for a general
Euler-Lagrange system with impacts and applies it to a 2-DOF bipedal robot. For any desired gait of the 2-DOF robot, the motion of the swing leg can be expressed as a
function of the stance leg. Using this function, a hybrid VHC is
generated and the control objective becomes enforcing the hybrid VHC.
A design procedure is developed that returns a feasible hybrid VHC for
the 2-DOF bipedal robot.
The concept of VHC motivates the design of feedback linearizing controllers that drive the
states of the robot to a constraint manifold. Feedback linearizing
controllers are designed that enforce the hybrid VHC. In this
framework, two possible control laws are presented. The first control
law generates a fully actuated robot in closed-loop configuration.
Sufficient conditions for stability are given and proven. The second control law
yields an under-actuated system in closed-loop configuration. This
control design is shown to consume no energy as long as the hybrid VHC that
models a passive gait is enforced. The stability of this controller
is studied numerically through the method of Poincaré sections.
Description
Keywords
bipedal robot, hybrid, virtual constraints, gait, nonlinear control