In-Hand Manipulation via Motion Cones (1810.00219v2)

Abstract: In this paper, 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 geometric construction to a broader set of planar tasks, where external forces such as gravity influence the dynamics of pushing, and prehensile tasks, where there are complex interactions between the gripper, object, and pusher. We show that the motion cone is defined by a set of low-curvature surfaces and provide a polyhedral cone approximation to it. We verify its validity with 2000 pushing experiments recorded with motion tracking system. Motion cones abstract the algebra involved in simulating frictional pushing by providing bounds on the set of feasible motions and by characterizing which pushes will stick or slip. We demonstrate their use for the dynamic propagation step in a sampling-based planning algorithm for in-hand manipulation. The planner generates trajectories that involve sequences of continuous pushes with 5-1000x speed improvements to equivalent algorithms. Video Summary -- https://youtu.be/tVDO8QMuYhc

• The paper generalizes motion cones for in-hand manipulation tasks under external forces like gravity, offering an efficient polyhedral approximation.
• Leveraging motion cones in a sampling-based planning framework significantly accelerates dynamics propagation, achieving performance gains of 5x to 1000x.
• This approach enables faster, more reliable planning for complex in-hand manipulation through contact, potentially improving robotic systems for dynamic environments.

In-Hand Manipulation via Motion Cones

The paper presents a novel extension and application of the motion cone concept to the domain of in-hand manipulation, focusing on tasks involving external forces such as gravity. Originally introduced by Mason for frictional pushing on a horizontal plane, motion cones abstract the algebra of frictional contact dynamics by characterizing feasible object motions produced by sticking pushes. This research extends these concepts to handle planar tasks where forces such as gravity play a critical role, thus broadening the application scope of motion cones. The authors define the motion cones as sets determined by low-curvature surfaces intersecting at a point, and offer a polyhedral approximation for efficient computation.

The significance of this work is underscored by their experimental validation comprising 2000 pushing experiments that confirm the validity of these extended motion cones. The authors propose a computational approach that combines motion cones with a sampling-based planning algorithm, yielding substantial performance improvements ranging from 5x to 1000x. This acceleration is primarily attributed to the improved efficiency in planning dynamics propagation, reducing the complexity inherent in traditional methods that employ complementarity formulations of contact dynamics.

From a methodological standpoint, the paper tackles two essential objectives:

1. Generalization of Motion Cones: The motion cone is generalized to encompass tasks influenced by gravity, extending its utility beyond plane surfaces to include interactions in arbitrary planes. This involves a precise characterization of the motion cone contours as consisting of intersecting low-curvature surfaces, a novel perspective distinct from the conventional polyhedral view.
2. Application in Planning Algorithms: Motion cones are leveraged to expedite the dynamics propagation step in a sampling-based in-hand manipulation planning framework. This framework strategically integrates T-RRT$^*$ algorithm techniques with motion cone computations to efficiently generate pushing strategies within a fraction of a second.

The practical implications of this work are quite profound. In-hand manipulation through contact, a staple challenge in robotics, benefits substantially from the motion cone approach by enabling faster and more reliable planning of trajectories that accommodate the compliant and variable nature of contacts. This methodological advance has the potential to aid in developing efficient robotic systems capable of handling complex manipulation tasks in dynamic environments.

Theoretically, the extension of motion cones into variable force domains such as those influenced by gravity introduces a new dimension to the understanding of friction-induced motions, which could inspire future research on optimizing contact-based manipulation strategies. This innovation presents opportunities for enhancing the robustness of robotic systems, not only in in-hand manipulation but also in broader applications necessitating precision and adaptability.

Moving forward, the utilization of motion cones could be further explored in conjunction with trajectory optimization methods which inherently benefit from the direct constraints provided by motion cones on feasible object motions and control inputs. This integration could unlock novel applications in automated systems, allowing for more intricate manipulation sequences that are both efficient and adaptable to varying environmental conditions.

In summary, this paper enriches the landscape of robotic manipulation by elevating the concept of motion cones to address a wider array of challenges, laying the groundwork for continued exploration in AI and robotics with regard to handling and manipulating objects with extrinsic and gravity-influenced dexterity.