Non-Prehensile Object Transportation via Model Predictive Non-Sliding Manipulation Control

This article proposes a model predictive non-sliding manipulation (MPNSM) control approach to safely transport an object on a tray-like end-effector of a robotic manipulator. For the considered non-prehensile transportation task to succeed, both non-sliding manipulation and the robotic system constraints must always be satisfied. To tackle this problem, we devise a model predictive controller enforcing sticking contacts, i.e., preventing sliding between the object and the tray, and assuring that physical limits such as extreme joint positions, velocities, and input torques are never exceeded. The combined dynamic model of the physical system, comprising the manipulator and the object in contact, is derived in a compact form. The associated non-sliding manipulation constraint is formulated such that the parametrized contact forces belong to a conservatively approximated friction cone space. This constraint is enforced by the proposed MPNSM controller, formulated as an optimal control problem that optimizes the objective of tracking the desired trajectory while always satisfying both manipulation and robotic system constraints. We validate our approach by showing extensive dynamic simulations using a torque-controlled 7-degree-of-freedom (DoF) KUKA LBR IIWA robotic manipulator. Finally, demonstrative results from real experiments conducted on a 21-DoF humanoid robotic platform are shown.