In this article, we present the mechanics and algorithms to compute the set of feasible motions of an object pushed in a plane. This set is known as the motion cone and was previously described for non-prehensile manipulation tasks in the horizontal plane. We generalize its construction to a broader set of planar tasks, such as those where external forces including gravity influence the dynamics of pushing, or prehensile tasks, where there are complex frictional interactions between the gripper, object, and pusher. We show that the motion cone is defined by a set of low-curvature surfaces and approximate it by a polyhedral cone. We verify its validity with thousands of pushing experiments recorded with a motion tracking system. Motion cones abstract the algebra involved in the dynamics of frictional pushing and can be used for simulation, planning, and control. In this article, we demonstrate their use for the dynamic propagation step in a sampling-based planning algorithm. By constraining the planner to explore only through the interior of motion cones, we obtain manipulation strategies that are robust against bounded uncertainties in the frictional parameters of the system. Our planner generates in-hand manipulation trajectories that involve sequences of continuous pushes, from different sides of the object when necessary, with 5–1,000 times speed improvements to equivalent algorithms.

中文翻译：

---

通过运动锥进行平面手动操作

在本文中，我们介绍了计算被推入平面的物体的可行运动集的机制和算法。这组被称为运动锥，之前描述过用于水平平面中的非抓握操作任务。我们将其构造推广到更广泛的平面任务，例如包括重力在内的外力影响推动动力学的任务，或抓握任务，其中抓手、物体和推动器之间存在复杂的摩擦相互作用。我们表明运动锥由一组低曲率表面定义，并由多面体锥体近似。我们通过运动跟踪系统记录的数千次推动实验来验证其有效性。运动锥抽象了摩擦推动动力学中涉及的代数，可用于模拟、规划、和控制。在本文中，我们展示了它们在基于采样的规划算法中动态传播步骤的使用。通过限制规划器仅通过运动锥的内部进行探索，我们获得了对系统摩擦参数中的有界不确定性具有鲁棒性的操纵策略。我们的规划器生成手内操作轨迹，其中包括在必要时从对象的不同侧面连续推动的序列，与等效算法相比，速度提高了 5-1,000 倍。我们获得了对系统摩擦参数中的有界不确定性具有鲁棒性的操纵策略。我们的规划器生成手内操作轨迹，其中包括在必要时从对象的不同侧面连续推动的序列，与等效算法相比，速度提高了 5-1000 倍。我们获得了对系统摩擦参数中的有界不确定性具有鲁棒性的操纵策略。我们的规划器生成手内操作轨迹，其中包括在必要时从对象的不同侧面连续推动的序列，与等效算法相比，速度提高了 5-1000 倍。