Control of Underactuated Mechanical Systems

A mechanical system is called underactuated if the number of actuating inputs (applied forces or torques) is smaller than the number of mechanical degrees of freedom. If, on the other hand, the number of actuating interventions corresponds to the number of mechanical degrees of freedom, we speak of fully actuated systems. While the modeling of both system classes (underactuated or fully actuated) can be done in the same way with the common methods of rigid body mechanics (e.g. Newton, Euler-Langrange, Hamilton), underactuated systems are usually much more difficult to control than fully actuated systems. From a technical point of view, the transition to an underactuated system would correspond to the deliberate reduction of actuators and thus opens up an opportunity for material or cost savings. For special applications (e.g., in space technology), weight reduction could also be relevant. Likewise, it may be necessary to still be able to specifically influence certain systems in the event of an actuator defect.

Example: Planar Underactuated Manipulator