  We present a framework to generate periodic trajectory references for a 3D
under-actuated bipedal robot, using a linear inverted pendulum (LIP) based
controller with adaptive neural regulation. We use the LIP template model to
estimate the robot's center of mass (CoM) position and velocity at the end of
the current step, and formulate a discrete controller that determines the next
footstep location to achieve a desired walking profile. This controller is
equipped on the frontal plane with a Neural-Network-based adaptive term that
reduces the model mismatch between the template and physical robot that
particularly affects the lateral motion. Then, the foot placement location
computed for the LIP model is used to generate task space trajectories (CoM and
swing foot trajectories) for the actual robot to realize stable walking. We use
a fast, real-time QP-based inverse kinematics algorithm that produces joint
references from the task space trajectories, which makes the formulation
independent of the knowledge of the robot dynamics. Finally, we implemented and
evaluated the proposed approach in simulation and hardware experiments with a
Digit robot obtaining stable periodic locomotion for both cases.
