This paper outlines a bi-level optimization method to concurrently optimize robot hardware parameters and control trajectories that ensure robust performance. The outer loop consists in a genetic algorithm that optimizes the hardware according to its average performance when tracking a locally optimal trajectory in perturbed simulations. The tracking controller exploits the locally optimal feedback gains computed in the inner loop with a Differential Dynamic Programming algorithm, which also finds the optimal reference trajectories. Our simulations feature a complete actuation model, including friction compensation and bandwidth limits. Our method can potentially account for arbitrary perturbations, and it discards hardware designs that cannot robustly track the reference trajectories. Our results show improved performance of the designed platform in realistic application scenarios, autonomously leading to the selection of lightweight and more transparent hardware.