The performances of feedback control systems change depending on the characteristics of the reference signals. For this reason, robot trajectories have always been designed by paying attention to their smoothness. Originally, trajectories were only synthesized offline, and the smoothness requirement was achieved by exclusively taking care of some continuity aspects (velocity and acceleration continuity). Planners have evolved along the years, so that, still in an offline context, the subsequent generations were also able to account for the existence of physical limits concerning the system kinematics/dynamics, while, in more recent approaches, trajectories are also planned by optimizing some given performance indexes.

A relevant limitation of the aforementioned approaches is represented by their intrinsic offline nature: trajectories cannot be modified online, so that control systems cannot suddenly react to possible environmental changes. This has originated an increasing interest on planners that are able to generate, in an online context, optimal constrained trajectories.

The seminar will propose an overview on some known online planning techniques, by describing their main characteristics and by providing some possible classifications. The attention will then be addressed to a planner that has been recently designed in the Robotic Lab of the University of Parma. It is based on a variable structure sliding mode control scheme, which behavior will be analyzed with the aid of some simulation experiments. The proposed generator can also be used in contexts that are totally different from those for which it was originally conceived. For example, it has been recently used to solve several online trajectory scaling problems for systems subject to physical constraints. Some videos will show the performances that have been achieved on some actual manipulators.