  Global position control for underactuated bipedal walking is a challenging
problem due to the lack of actuation on the feet of the robots. In this paper,
we apply the Hybrid-Linear Inverted Pendulum (H-LIP) based stepping on 3D
underactuated bipedal robots for global position control. The step-to-step
(S2S) dynamics of the H-LIP walking approximates the actual S2S dynamics of the
walking of the robot, where the step size is considered as the input. Thus the
feedback controller based on the H-LIP approximately controls the robot to
behave like the H-LIP, the differences between which stay in an error invariant
set. Model Predictive Control (MPC) is applied to the H-LIP for global position
control in 3D. The H-LIP stepping then generates desired step sizes for the
robot to track. Moreover, turning behavior is integrated with the step
planning. The proposed framework is verified on the 3D underactuated bipedal
robot Cassie in simulation together with a proof-of-concept experiment.
