Co-Designing Robots by Differentiating Motion Solvers

We present a modular algorithm for the computational co-design of legged robots and dynamic maneuvers. Current state-of-the-art approaches are based on random sampling or concurrent optimization. We propose a bilevel optimization approach that exploits the derivatives of the motion planning sub-problem (the inner level). Our approach allows for the use of any differentiable motion planner in the inner level, similarly to sampling methods, but also allows for an upper level that captures arbitrary design constraints and costs. Our approach can optimize the robot's morphology and actuator parameters while considering its full dynamics, joint limits and physical constraints such as friction cones. We demonstrate these capabilities by studying jumping and trotting gaits and verify our results in a physics simulator, showing it successfully minimizes the energy used.