Quadratically constrained quadratic programs using approximations of the step-to-step dynamics: application on a 2D model of Digit

Bipedal robots are yet to achieve mainstream application because they lack robustness in real-world settings. One of the major control challenges arises due to the ankle motors' limited control authority, which prevents these robots from being fully controllable at a particular instant (e.g., like an inverted pendulum). We show that to stabilize such robots, they must achieve stability over the time scale of a step, also known as step-to-step (S2S) stability. Past approaches have used the linearization of the S2S dynamics to develop controllers, but these have limited regions of validity. Here, we use a data-driven approach to approximate S2S dynamics, including its region of validity. Our results show that linear and quadratic models can approximate the region of validity and S2S dynamics, respectively. We show that the quadratic S2S approximation generated using a data-driven full-body dynamics simulator outperforms those generated using the analytical linear S2S generated from the popularly used linear inverted pendulum model (LIPM). The S2S approximation enables us to formulate and solve a quadratically constrained quadratic program to develop walking controllers. We demonstrate the efficacy of the approach in simulation using a 2D model of Digit walking on patterned terrain. A video is linked here: https://youtu.be/MniABg2jGEA