arXiv:2610.37199v1 Announce Type: cross Abstract: Legged robots for lunar exploration must be designed for low gravity, where reduced contact forces and long flight phases make leg morphology and controller choice interdependent. We study this for a planar monoped in lunar gravity ($1.625$ m/s$^2$) using a bi-level co-design framework: a differential evolution outer loop searches over link lengths, and each candidate is evaluated on a vertical jump by either a quadratic program based task-space controller (QP-TSC) or a direct-collocation based trajectory optimization. The two controllers yield different optimal link lengths, and trajectory optimization outperforms the QP-TSC across most of the design space, with 17% lower Cost of Transport (COT) at their respective optima. We then extend to a 2D jump, where trajectory optimization with centroidal angular momentum regulation produces stable in-place and forward jumps, and an LQR controller absorbs impact and stabilizes the robot after touchdown. This is demonstrated on a baseline morphology with both links 0.3 m long.