Quasi-Static Modeling and Controlling for Planar Pushing of Deformable Objects

Pushing is an essential nonprehensile manipulation for robots to achieve complex tasks. Until now, object rigidity remains one of the common assumptions in robotic pushing. To endow robots with the advanced capability of pushing deformable objects, we propose a mathematical model and control method for the planar pushing of deformable objects. Given the robotic end-effector velocity or position input, the model predicts the motion and deformation of the pushed object, which is developed based on the quasi-static finite element analysis with reasonable simplification, considering the contact conditions of nodes with both the operator and the contact surface. By combining the designed model to estimate the state of the object and interactions with the environment, we further propose a method based on model predictive control to realize the pushing control. With a specialized simplified model to accelerate prediction, the controller is solved by iterative linear quadratic regulator with a dynamic weight, which balances the object motion and pushing area adjustment. The accuracy and efficiency of the proposed deformable model are validated by comparing the theoretical results with the experimental ones under different conditions, and the controller is verified by simulation and experiments.