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Walking
Machine: Mechanical Design & Control Outline
This
interest group is headed by Dr. Jaime Gómez Silva at Universidad Iberoamericana.
The goal behind this project is
to explore biped legged locomotion with the fewest degrees of freedom possible.
The initial main idea is illustrated in the movie were, through quasiestatic
motion, a robot first shifts its balance to one leg and then performs a rotation
around it. By alternating balance and rotation, walking is achieved with only
two degrees of freedom per leg. One degree of freedom at the ankle for balance-shifting
and another at the hip for rotation were considered. However this would have
required very wide overlapping feet to achieve alternating balance and the
rotation would have been unstable as the center of mass moved within a tilted
plane.
To solve the previous
problem both degrees of freedom were moved to the ankle, thus balancing occurred
by tilting both legs simultaneously until the center of mass was above the supporting
leg. A three bevel-gear mechanism powered by two worm & worm-gears with
a DC motor each (as shown in figure) was chosen to utilize the full torque of
both motors for both degrees of freedom. The worm & worm-gears were chosen
to provide reduction from the motor and to allow the articulation to remain
rigid without powering the motors.
The next challenge
was to solve the hip articulation, which needed to be rigid without introducing
other motors. A symmetrical four-beam mechanism, which allowed the legs to be
tilted while maintaining the hip parallel to the ground, was used on each leg.
It was proposed to position the motors at the hip, elevating the center of mass
thus facilitating balancing, and using the shafts as beams. However this could
have caused unnecessary flexion on the shafts so actual beams were used but
the motors were still placed at the hips. Bellow are a few renders of the final
mechanical design and the blueprints to manufacture the parts.
Walking Control Outline
To balance the robot on one leg the first step
was to tilt both legs until the center of mass was above the supporting leg.
The idea was to use a closed feedback-loop with several pressure sensors on
both feet. The supporting leg was to tilt until the sum from the pressure sensors
on the opposing leg returned a value near cero. Meanwhile the opposing leg would
simply follow the tilting of the supporting leg through potentiometers or encoders
on both ankles.
Once the robot was nearly balanced on the supporting
leg the opposing one started to lift. To do this the opposing ankle would now
become the master by continuing to tilt. As the leg lifted the center of mass
would shift in the direction of the lifting leg so the supporting leg would
need to compensate by tilting more. The compensation was planned to receive
feedback from opposing pressure sensors on the supporting leg while the lifting
leg would only continue to raise if the difference from pressure sensors in
the supporting leg remained within a safe value.
Once the robot was balanced and standing on
one leg rotation was no major problem. However, since it would require both
motors to rotate in perfect synchrony the balancing feedback loop would still
remain active to compensate for discrepancies while rotating. It is important
to mention that additional control loops would also be necessary between tilting
and rotation on each ankle to assure that they tilted without rotating or vice
versa. Finally the entire sequence was carried out in reverse order to return
to the star position and repeated for the other leg.
Construction
Due
to lack of support from the university the construction only reached a very
early stage and the project was put on hold. Three years latter another student
took the initiative and built it with a some modifications. The robot did walk
as expected.
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