This document revises the latest results related to robotic non-prehensile object transportation. The problem consists of a robotic arm transporting an object along the desired trajectory on a tray, guaranteeing a sticking behaviour and other constraints. The solution in [1], where an optimal control problem has been devised, is revised together with the case in [2], where a quadruped/mobile robot is considered. A model predictive control approach is also described to solve the same problem.