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.

翻译：通用化操作要求机器人能够与新颖物体和环境进行交互。这一需求使得操作极具挑战性，因为机器人必须考虑复杂的摩擦相互作用，同时应对物体和环境的物理特性不确定性。本文研究了存在不确定性情况下枢轴操作规划的鲁棒优化问题。我们提出了关于如何利用摩擦来补偿操作过程中物理属性估计不准确性的见解。在特定假设下，我们推导出枢轴操作中摩擦提供的稳定性裕度的解析表达式。该裕度随后被用于接触隐式双层优化（CIBO）框架中，以优化轨迹最大化该稳定性裕度，从而针对物体多个物理参数的不确定性提供鲁棒性。我们分析了稳定性裕度与底层双层优化问题中多个参数的关系。通过使用六自由度机械臂操作多个不同物体，演示了所提出的方法。