Contact-rich manipulation often requires strategic interactions with objects, such as pushing to accomplish specific tasks. We propose a novel scenario where a robot inserts a book into a crowded shelf by pushing aside neighboring books to create space before slotting the new book into place. Classical planning algorithms fail in this context due to limited space and their tendency to avoid contact. Additionally, they do not handle indirectly manipulable objects or consider force interactions. Our key contributions are: i) re-framing quasi-static manipulation as a planning problem on an implicit manifold derived from equilibrium conditions; ii) utilizing an intrinsic haptic metric instead of ad-hoc cost functions; and iii) proposing an adaptive algorithm that simultaneously updates robot states, object positions, contact points, and haptic distances. We evaluate our method on such crowded bookshelf insertion task but it is a general formulation to rigid bodies manipulation tasks. We propose proxies to capture contact point and force, with superellipse to represent objects. This simplified model guarantee the differentiablity. Our framework autonomously discovers strategic wedging-in policies while our simplified contact model achieves behavior similar to real world scenarios. We also vary the stiffness and initial positions to analysis our framework comprehensively. The video can be found at https://youtu.be/eab8umZ3AQ0.

翻译：接触密集型操作通常需要与物体进行策略性交互，例如通过推动完成特定任务。本文提出一种新颖场景：机器人在将新书插入拥挤书架时，首先通过推开相邻书籍创造空间，再将新书归位。经典规划算法在此场景下会失效，原因在于空间受限及其回避接触的倾向。此外，这些算法无法处理间接可操作物体，也未考虑力相互作用。我们的核心贡献在于：i) 将准静态操作重新构建为基于平衡条件推导的隐式流形上的规划问题；ii) 采用内在触觉度量替代临时成本函数；iii) 提出能同步更新机器人状态、物体位置、接触点及触觉距离的自适应算法。我们在拥挤书架插入任务中评估了该方法，但该框架适用于刚体操作任务的通用表述。我们提出通过代理变量捕捉接触点与作用力，并使用超椭圆表征物体。该简化模型保证了可微性。我们的框架能自主发现策略性楔入策略，简化接触模型所实现的行为与现实场景高度相似。我们还通过改变刚度和初始位置对框架进行全面分析。演示视频可见：https://youtu.be/eab8umZ3AQ0。