  Reduced-order models (ROM) are popular in online motion planning due to their
simplicity. A good ROM for control captures critical task-relevant aspects of
the full dynamics while remaining low dimensional. However, planning within the
reduced-order space unavoidably constrains the full model, and hence we
sacrifice the full potential of the robot. In the community of legged
locomotion, this has lead to a search for better model extensions, but many of
these extensions require human intuition, and there has not existed a
principled way of evaluating the model performance and discovering new models.
In this work, we propose a model optimization algorithm that automatically
synthesizes reduced-order models, optimal with respect to a user-specified
distribution of tasks and corresponding cost functions. To demonstrate our
work, we optimized models for a bipedal robot Cassie. We show in simulation
that the optimal ROM reduces the cost of Cassie's joint torques by up to 23%
and increases its walking speed by up to 54%. We also show hardware result that
the real robot walks on flat ground with 10% lower torque cost. All videos and
code can be found at https://sites.google.com/view/ymchen/research/optimal-rom.
