Retrieving rich contact information from robotic tactile sensing has been a challenging, yet significant task for the effective perception of object properties that the robot interacts with. This work is dedicated to developing an algorithm to estimate contact force and torque for vision-based tactile sensors. We first introduce the observation of the contact deformation patterns of hyperelastic materials under ideal single-axial loads in simulation. Then based on the observation, we propose a method of estimating surface forces and torque from the contact deformation vector field with the Helmholtz-Hodge Decomposition (HHD) algorithm. Extensive experiments of calibration and baseline comparison are followed to verify the effectiveness of the proposed method in terms of prediction error and variance. The proposed algorithm is further integrated into a contact force visualization module as well as a closed-loop adaptive grasp force control framework and is shown to be useful in both visualization of contact stability and minimum force grasping task.
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