Introduction
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Reference trajectories for walking robots
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Control of walking robots
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(C. Chevallereau, Y. Aoustin, Ph. Lemoine, A. Formal'sky, C. Rengifo, D. Tlalolini Romero)
The criterion of energy is also important to define
the control law. Our goal is to get the benefits of the dynamic of the
motion and to avoid to constraint the robot to walk using a not natural gait.
We study robot without actuated ankle and feet to highlight the effect of
the gravity. Therefore we have to solve an under actuated problem. Our
goal is to define control law which ensure convergence to limit cycle. We
have to take into account that the model of the robot during walking is
a hybrid system; the dynamic model varies depending of the walking
phases (stance phase, impact ...).
We have designed several strategies for the control of the biped :
The more achieved approach is to achieve a geometric
tracking of a reference path instead of a classical tracking of reference
trajectories. For convenient reference path, a temporal convergence to a cycle
is naturally observed. In this context, reference trajectories of the actuated
joint variables as a polynomial function with the non-actuated variable for a gait
with single support and instantaneous double support. We proved numerically the
orbital stability of Poincaré. We improved the convergence to the cyclic motion
modifying the inclination of the trunk or the length step. Another way to build
a control law for the tracking of a reference path consist in writing the reference
motion as function of an auxiliary variables (virtual time or path coordinate). An
analytical simple condition of convergence to a known cyclic motion has been
obtained. An analytical simple condition has also been obtained to ensure the
existence of a cyclic motion corresponding to a cyclic path. This method can be
applied for a biped and for a quadruped with a trot gait. Its use for the amble and
the curvet have to be study now with more attention, because for such gaits the
angular momentum of the robot versus the leg tip of the stance legs becomes null
during the motion. Currently we extend these researches to gaits with non
instantaneous double support or flight phases. The introduction of double support
phases allows us to improve the stability margins and to start the motion directly
from zero velocity of the robot, without specific control
strategy.
Since the robot has n actuators for n+1 independent configuration
variables, a second strategy consist in a careful definition of the n output to
control. For an arbitrary choice of n joint variables as output, the zero dynamics
is a second order unstable system. Our choice of the n outputs has been devoted to
reduce the order of the zero dynamics, because it is easier to stabilise a system of
first order than a system of second order. For the biped studied no flat outputs exists.
Some output corresponding to stable zero dynamics has been defined. This work is done
in collaboration with the " Control " team of IRCCyN. The current studies concern the
test of this control approach for the walking of our robots and the avoidance of
singularities.
We have done simulation experiments to stabilize a biped robot
around its vertical pose tacking into account explicitly the limitation of the
actuators.
We built a prototype at IRCCyN. Now we implanted with success
an intuitive control for it without any information of its dynamical model. We will
work now to improve the double support phase.
For this robot we have also define in simulation an optimal
control based on its linearised model varying in time.
Semi-Quad movie
Main publications of the topic
