Jessy W. Grizzle

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In Summer 2008, we completed assembly of a novel planar bipedal robot for use at the University of Michigan. The robot, named MABEL, was designed in collaboration with Jonathan Hurst, Al Rizzi and Jessica Hodgins of the Robotics Institute, Carnegie Mellon. Jonathan Hurst was responsible for the design of the mechanical systems of the robot. MABEL is comprised of five links assembled to form a torso and two legs with knees. The legs are terminated in point feet. The planar nature of the robot is manifested in the hips, which are constrained to revolute motion in the sagittal plane. The robot is attached to a boom and hence walks or runs in a circle; when the radius is sufficiently large, this corresponds to locomotion along a straight line. Up to this point, the robot is similar to RABBIT, the French robot on which we collaborated from 2001 through 2004.

The novel aspects of MABEL, and there are many, appear in the transmission or powertrain . First of all, all of the actuators (four DC-brushless motors, two for each leg) are located in the torso, so that the legs are as light as possible; this is done for running efficiency. In RABBIT and most other robots, the knee actuators are mounted on the thigh. Secondly, the actuated degrees of freedom of each leg do not correspond to the knee and the hip angles (the hip angle being the relative angle between the torso and thigh). Instead, for each leg, a collection of differentials is used to connect two motors (once again, located in the torso) to the hip and knee joints in such a way that one motor controls the angle of the virtual leg consisting of the line connecting the hip to the toe, and the second motor is connected--in series with a spring--in order to control the length (or shape) of the virtual leg.

Roughly speaking, the rationale for this design is that it makes the robot a hybrid of RABBIT, a robot that walks extremely well, but never achieved a stable running gait, and a Raibert Hopper, a robot that ``runs'' remarkably well, but can't walk, in part because it has only one leg, but more fundamentally, walking is quite different from bouncing. The springs in MABEL serve to isolate the reflected rotor inertia of the leg-shape motors from the impact forces at leg touchdown and to store energy in the compression phase of a running gait, when the support leg must decelerate the downward motion of the robot's center of mass; the energy stored in the spring can then be used to redirect the center of mass upwards for the subsequent flight phase, when both legs will be off the ground. Both of these properties (shock isolation and energy storage) enhance the energy efficiency of running and reduce overall actuator power requirements. This is also true for walking on flat ground, but to a lesser extent, due to the lower forces at leg impact and the reduced vertical travel of the center of mass. We hypothesize that shock isolation and compliance will be very useful for walking on uneven terrain.

The third novelty in MABEL's powertrain is that the springs in series with the leg shape motors are unilateral in the sense that they compress, but do not extend beyond their nominal rest length; instead, once a spring reaches its rest length, the position of the leg-shape motor and the shape of the virtual leg are rigidly connected (i.e., directly, through a gear ratio, and no longer through a compliant element). This is a big advantage in walking where at leg exchange, when the former stance leg must be lifted from the ground, this motion does not have to ``fight'' a spring that is trying to extend due to the non-zero mass of the shin. Similarly, a unilateral spring also makes it easier to initiate take-off in running (i.e., transition from stance phase to flight phase). Roughly speaking, the springs are present when they are useful for shock attenuation and energy storage, and absent when they would be a hinderance for lifting the legs from the ground. The springs can be easily changed from one experiment to another in order to study the relation of spring stiffness to gait efficiency or robustness to perturbations, for example. An optional pre-load is easily established on the springs as well, so that compliance only comes into play when sufficiently large forces are present; this is convenient for testing simplified walking strategies while debugging the electronics and software.

The final novelty of the robot is that it is constructed from two monopods joined at the hip. By removing six bolts, half of MABEL's torso and one leg can be removed, yielding a monopod. In fact, Thumper at CMU is literally the left half of MABEL.

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