Geodesic Tracing-Based Kinematic Integration of Rolling and Sliding Contact on Manifold Meshes for Dexterous In-Hand Manipulation

Figure 1: Snapshots of a robotic hand performing dexterous in-hand manipulation tasks using the integration scheme we developed. Tasks from left to right: 1) horizontally turning a screwdriver, 2) vertically turning the screwdriver, 3) turning an M2 threaded rod, 4) pressing down a knurled hobby knife, 5) pressing down a dining knife, 6) closing tweezers. Abstract -- Reasoning about rolling and sliding contact, or roll-slide contact for short, is critical for dexterous manipulation tasks that involve intricate geometries. But existing works on roll-slide contact mostly focus on continuous shapes with differentiable parametrizations. This work extends roll-slide contact modeling to manifold meshes. Specifically, we present an integration scheme based on geodesic tracing to first-order time-integrate roll-slide contact directly on meshes, enabling dexterous manipulation to reason over high-fidelity discrete representations of an object's true geometry. Using our method, we planned dexterous motions of a multi-finger robotic hand manipulating five objects in-hand in simulation. The planning was achieved with a least-squares optimizer that strives to maintain the most stable instantaneous grasp by minimizing contact sliding and spinning. Then, we evaluated our method against a baseline using collision detection and a baseline using primitive shapes.