  Contact-rich manipulation is challenging due to dynamically-changing physical
constraints by the contact mode changes undergone during manipulation. This
paper proposes a versatile local planning and control framework for
contact-rich manipulation that determines the continuous control action under
variable contact modes online. We model the physical characteristics of
contact-rich manipulation by quasistatic dynamics and complementarity
constraints. We then propose a linear complementarity quadratic program (LCQP)
to efficiently determine the control action that implicitly includes the
decisions on the contact modes under these constraints. In the LCQP, we relax
the complementarity constraints to alleviate ill-conditioned problems that are
typically caused by measure noises or model miss-matches. We conduct dynamical
simulations on a 3D physical simulator and demonstrate that the proposed method
can achieve various contact-rich manipulation tasks by determining the control
action including the contact modes in real-time.
