A Bi-level Co-design Framework for Lunar Monoped with 2D Jump and Landing Control

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.