  Selecting robot design parameters can be challenging since these parameters
are often coupled with the performance of the controller and, therefore, the
resulting capabilities of the robot. This leads to a time-consuming and often
expensive process whereby one iterates between designing the robot and manually
evaluating its capabilities. This is particularly challenging for bipedal
robots, where it can be difficult to evaluate the behavior of the system due to
the underlying nonlinear and hybrid dynamics. Thus, in an effort to streamline
the design process of bipedal robots, and maximize their performance, this
paper presents a systematic framework for the co-design of humanoid robots and
their associated walking gaits. To this end, we leverage the framework of
hybrid zero dynamic (HZD) gait generation, which gives a formal approach to the
generation of dynamic walking gaits. The key novelty of this paper is to
consider both virtual constraints associated with the actuators of the robot,
coupled with design virtual constraints that encode the associated parameters
of the robot to be designed. These virtual constraints are combined in an HZD
optimization problem which simultaneously determines the design parameters
while finding a stable walking gait that minimizes a given cost function. The
proposed approach is demonstrated through the design of a novel humanoid robot,
ADAM, wherein its thigh and shin are co-designed so as to yield energy
efficient bipedal locomotion.
