  We present parametric trajectory optimization, a method for simultaneously
computing physical parameters, actuation requirements, and robot motions for
more efficient robot designs. In this scheme, robot dimensions, masses, and
other physical parameters are solved for concurrently with traditional motion
planning variables, including dynamically consistent robot states, actuation
inputs, and contact forces. Our method requires minimal user domain knowledge,
requiring only a coarse guess of the target robot configuration sequence and a
parameterized robot topology as input. We demonstrate our results on four
simulated robots, one of which we physically fabricated in order to demonstrate
physical consistency. We demonstrate that by optimizing robot body parameters
alongside robot trajectories, motion planning problems which would otherwise be
infeasible can be made feasible, and actuation requirements can be
significantly reduced.
