  Model Predictive Control (MPC) is a popular strategy for controlling robots
but is difficult for systems with contact due to the complex nature of hybrid
dynamics. To implement MPC for systems with contact, dynamic models are often
simplified or contact sequences fixed in time in order to plan trajectories
efficiently. In this work, we extend Hybrid iterative Linear Quadratic
Regulator to work in a MPC fashion (HiLQR MPC) by 1) modifying how the cost
function is computed when contact modes do not align, 2) utilizing
parallelizations when simulating rigid body dynamics, and 3) using efficient
analytical derivative computations of the rigid body dynamics. The result is a
system that can modify the contact sequence of the reference behavior and plan
whole body motions cohesively -- which is crucial when dealing with large
perturbations. HiLQR MPC is tested on two systems: first, the hybrid cost
modification is validated on a simple actuated bouncing ball hybrid system.
Then HiLQR MPC is compared against methods that utilize centroidal dynamic
assumptions on a quadruped robot (Unitree A1). HiLQR MPC outperforms the
centroidal methods in both simulation and hardware tests.
