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.

本文研究在不确定性条件下，使用鲁棒优化进行支点式操作规划，并探讨摩擦力是如何被利用来补偿对象的物理属性准确性不足所带来的不确定性。通过使用分析表达式为支点式操作提供稳定性保障，并在 CIBO 框架中使用稳定边界进行优化，从而提高鲁棒性。我们还针对一些底层优化问题的参数进行了稳定性比较，并使用六自由度机械臂对多个不同的对象进行操作，证明了所提出的方法。