Energy Gradient-Based Graphs for Planning Within-Hand Caging Manipulation

In this work, we present a within-hand manipulation approach that leverages a simple energy model based on caging grasps made by underactuated hands. Instead of explicitly modeling the contacts and dynamics in manipulation, we can calculate a map to describe the energy states of different hand-object configurations under an actuation input. Since the system intrinsically steers towards low energy states, the object's movement is uniquely described by the gradient of the energy map if the corresponding actuation is applied. Such maps are pre-calculated for a range of actuation inputs to represent the system's energy profile. We discretize the workspace into a grid and construct an energy gradient-based graph by locally exploring the gradients of the stored energy profile. Given a goal configuration of a simple cylindrical object, a sequence of actuation inputs can be calculated to manipulate it towards the goal by exploiting the connectivity in the graph. The proposed approach is experimentally implemented on a Yale T42 hand. Our evaluation results show that parts of the graph are well connected, explaining our ability to successfully plan and execute trajectories within the gripper's workspace.