  Generalizable manipulation requires that robots be able to interact with
novel objects and environment. This requirement makes manipulation extremely
challenging as a robot has to reason about complex frictional interactions with
uncertainty in physical properties of the object and the environment. In this
paper, we study robust optimization for planning of pivoting manipulation in
the presence of uncertainties. We present insights about how friction can be
exploited to compensate for inaccuracies in the estimates of the physical
properties during manipulation. Under certain assumptions, we derive analytical
expressions for stability margin provided by friction during pivoting
manipulation. This margin is then used in a Contact Implicit Bilevel
Optimization (CIBO) framework to optimize a trajectory that maximizes this
stability margin to provide robustness against uncertainty in several physical
parameters of the object. We present analysis of the stability margin with
respect to several parameters involved in the underlying bilevel optimization
problem. We demonstrate our proposed method using a 6 DoF manipulator for
manipulating several different objects. We also design and validate an MPC
controller using the proposed algorithm which can track and regulate the
position of the object during manipulation.
