Beyond Inverted Pendulums: Task-optimal Simple Models of Legged Locomotion

Reduced-order models (ROM) are popular in online motion planning due to their simplicity. A good ROM captures the bulk of the full model's dynamics while remaining low dimension. However, planning within the reduced-order space unavoidably constrains the full model, and hence we sacrifice the full potential of the robot. In the community of legged locomotion, this has lead to a search for better model extensions, but many of these extensions require human intuition, and there has not existed a principled way of evaluating the model performance and discovering new models. In this work, we propose a model optimization algorithm that automatically synthesizes reduced-order models, optimal with respect to any user-specified cost function. To demonstrate our work, we optimized models for a bipedal robot Cassie. We show in hardware experiment that the optimal ROM is simple enough for real time planning application and that the real robot achieves higher performance by using the optimal ROM.