Multi-finger Manipulation via Trajectory Optimization with Differentiable Rolling and Geometric Constraints

Parameterizing finger rolling and finger-object contacts in a differentiable manner is important for formulating dexterous manipulation as a trajectory optimization problem. In contrast to previous methods which often assume simplified geometries of the robot and object or do not explicitly model finger rolling, we propose a method to further extend the capabilities of dexterous manipulation by accounting for non-trivial geometries of both the robot and the object. By integrating the object's Signed Distance Field (SDF) with a sampling method, our method estimates contact and rolling-related variables and includes those in a trajectory optimization framework. This formulation naturally allows for the emergence of finger-rolling behaviors, enabling the robot to locally adjust the contact points. Our method is tested in a peg alignment task and a screwdriver turning task, where it outperforms the baselines in terms of achieving desired object configurations and avoiding dropping the object. We also successfully apply our method to a real-world screwdriver turning task, demonstrating its robustness to the sim2real gap.