  In this paper, we aim to improve the robustness of dynamic quadrupedal
locomotion through two aspects: 1) fast model predictive foothold planning, and
2) applying LQR to projected inverse dynamic control for robust motion
tracking. In our proposed planning and control framework, foothold plans are
updated at 400 Hz considering the current robot state and an LQR controller
generates optimal feedback gains for motion tracking. The LQR optimal gain
matrix with non-zero off-diagonal elements leverages the coupling of dynamics
to compensate for system underactuation. Meanwhile, the projected inverse
dynamic control complements the LQR to satisfy inequality constraints. In
addition to these contributions, we show robustness of our control framework to
unmodeled adaptive feet. Experiments on the quadruped ANYmal demonstrate the
effectiveness of the proposed method for robust dynamic locomotion given
external disturbances and environmental uncertainties.
