  Pushing is a simple yet effective skill for robots to interact with and
further change the environment. Related work has been mostly focused on
utilizing it as a non-prehensile manipulation primitive for a robotic
manipulator. However, it can also be beneficial for low-cost mobile robots that
are not equipped with a manipulator. This work tackles the general problem of
controlling a team of mobile robots to push collaboratively polytopic objects
within complex obstacle-cluttered environments. It incorporates several
characteristic challenges for contact-rich tasks such as the hybrid switching
among different contact modes and under-actuation due to constrained contact
forces. The proposed method is based on hybrid optimization over a sequence of
possible modes and the associated pushing forces, where (i) a set of sufficient
modes is generated with a multi-directional feasibility estimation, based on
quasi-static analyses for general objects and any number of robots; (ii) a
hierarchical hybrid search algorithm is designed to iteratively decompose the
navigation path via arc segments and select the optimal parameterized mode; and
(iii) a nonlinear model predictive controller is proposed to track the desired
pushing velocities adaptively online for each robot. The proposed framework is
complete under mild assumptions. Its efficiency and effectiveness are validated
in high-fidelity simulations and hardware experiments. Robustness to motion and
actuation uncertainties is also demonstrated.
