On the Generality and Application of Mason's Voting Theorem to Center of Mass Estimation for Pure Translational Motion

Object rearrangement is widely demanded in many of the manipulation tasks performed by industrial and service robots. Rearranging an object through planar pushing is deemed energy efficient and safer compared with the pick-and-place operation. However, due to the unknown physical properties of the object, re-arranging an object toward the target position is difficult to accomplish. Even though robots can benefit from multi-modal sensory data for estimating novel object dynamics, the exact estimation error bound is still unknown. In this work, firstly, we demonstrate a way to obtain an error bound on the center of mass (CoM) estimation for the novel object only using a position-controlled robot arm and a vision sensor. Specifically, we extend Mason's Voting Theorem (MVT) to object CoM estimation in the absence of accurate information on friction and object shape. The probable CoM locations are monotonously narrowed down to a convex region, and the Extended Voting Theorems (EVT's) guarantee that the convex region contains the CoM ground truth in the presence of contact normal estimation error and pushing execution error. For the object translation task, existing methods generally assume that the pusher-object system's physical properties and full-state feedback are available, or utilize iterative pushing executions, which limits the application of planar pushing to real-world settings. In this work, assuming a nominal friction coefficient between the pusher and object through contact normal error bound analysis, we leverage the estimated convex region and the Zero Moment Two Edge Pushing (ZMTEP) method [1] to select the contact configurations for object pure translation. It is ensured that the selected contact configurations are capable of tolerating the CoM estimation error. The experimental results show that the object can be accurately translated to the target position with only two controlled pushes at most.