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.

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。这一要求使得操作任务极具挑战性，因为机器人必须在物体和环境物理属性存在不确定性的情况下，推理复杂的摩擦相互作用。本文研究了存在不确定性条件下翻转操作规划的鲁棒优化问题。我们提出了关于如何利用摩擦补偿操作过程中物理属性估计误差的见解。在特定假设下，我们推导了翻转操作期间摩擦所提供的稳定性裕度的解析表达式。随后将该裕度应用于接触隐式双层优化框架中，通过优化轨迹最大化此稳定性裕度，从而对物体多个物理参数的不确定性实现鲁棒性。我们分析了该稳定性裕度与底层双层优化问题中多个参数的关系。使用六自由度机械臂对多种不同物体进行操作，验证了所提方法。此外，我们基于该算法设计并验证了模型预测控制器，该控制器能够在操作过程中跟踪和调节物体位置。