  This study presents a whole-body model predictive control (MPC) of robotic
systems with rigid contacts, under a given contact sequence using online
switching time optimization (STO). We treat robot dynamics with rigid contacts
as a switched system and formulate an optimal control problem of switched
systems to implement the MPC. We utilize an efficient solution algorithm for
the MPC problem that optimizes the switching times and trajectory
simultaneously. The present efficient algorithm, unlike inefficient existing
methods, enables online optimization as well as switching times. The proposed
MPC with online STO is compared over the conventional MPC with fixed switching
times, through numerical simulations of dynamic jumping motions of a quadruped
robot. In the simulation comparison, the proposed MPC successfully controls the
dynamic jumping motions in twice as many cases as the conventional MPC, which
indicates that the proposed method extends the ability of the whole-body MPC.
We further conduct hardware experiments on the quadrupedal robot Unitree A1 and
prove that the proposed method achieves dynamic motions on the real robot.
