We propose a framework for optimizing a planar parallel-jaw gripper for use with multiple objects. While optimizing general-purpose grippers and contact locations for grasps are both well studied, co-optimizing grasps and the gripper geometry to execute them receives less attention. As such, our framework synthesizes grippers optimized to stably grasp sets of polygonal objects. Given a fixed number of contacts and their assignments to object faces and gripper jaws, our framework optimizes contact locations along these faces, gripper pose for each grasp, and gripper shape. Our key insights are to pose shape and contact constraints in frames fixed to the gripper jaws, and to leverage the linearity of constraints in our grasp stability and gripper shape models via an augmented Lagrangian formulation. Together, these enable a tractable nonlinear program implementation. We apply our method to several examples. The first illustrative problem shows the discovery of a geometrically simple solution where possible. In another, space is constrained, forcing multiple objects to be contacted by the same features as each other. Finally a toolset-grasping example shows that our framework applies to complex, real-world objects. We provide a physical experiment of the toolset grasps.

翻译：我们提出一个框架，用于优化面向多物体操作的平面平行夹爪。虽然通用夹爪的优化以及抓取接触位置的选取均已得到充分研究，但抓取动作与夹爪几何结构的协同优化却鲜有关注。为此，我们的框架合成了能够稳定抓取多边形物体集合的优化夹爪。在给定接触点数量及其与物体表面和夹爪指面的对应关系前提下，该框架优化了沿物体表面的接触位置、每个抓取姿态对应的夹爪位姿以及夹爪形状。我们的关键思路是将形状约束与接触约束定义在夹爪指面的固连坐标系中，并利用增广拉格朗日方法将抓取稳定性与夹爪形状模型中的线性约束特性相结合。这些措施共同实现了可解的的非线性规划求解。我们将该方法应用于多个实例：第一个示例问题展示了在可行条件下几何简化解的自动发现；第二个示例中，受空间限制，多个物体被迫采用相同特征作为接触面；最后的工具组抓取示例表明该框架可适用于复杂真实物体。我们给出了工具组抓取的物理实验验证。