Modeling, analysis and control of robot–object nonsmooth underactuated Lagrangian systems: A tutorial overview and perspectives

So-called robot–object Lagrangian systems consist of a class nonsmooth underactuated complementarity systems, with specific structure: an “object” and “robot”. Only the robot is actuated. The object dynamics can thus be controlled only through action contact Lagrange multipliers, which represent interaction forces between object. Juggling, walking, running, hopping machines, robotic that manipulate objects, tapping, pushing kinematic chains joint clearance, crawling, climbing robots, some cable-driven manipulators, circuits set-valued components, belong this class. This article aims at presenting their main features, then many application examples to class, reviewing tools control strategies have been proposed in Automatic Control Robotics literature. Some comments open issues conclude article.