Trajectory scaling for a manipulator inverse dynamics control subject to generalized force derivative constraints

The behaviour of robotic manipulators is affected by the actuators dynamic limits. When such limits are not explicitly considered, manipulators performances rapidly decrease. In this paper, dynamic saturations are handled by means of a real-time technique based on a trajectory scaling method: whenever saturations occur, trajectories are automatically scaled by means of a dynamic filter in order to preserve an accurate path tracking. Commonly known scaling algorithms only consider the existence of torque saturations. In this paper, the strategy is enriched by also accounting for torque derivatives constraints. The solution proposed is suited to be used in conjunction with standard inverse dynamics controllers. The adopted methodology explicitly requires the realtime evaluation of the derivative of the manipulator inertia matrix. To this purpose, a novel efficient procedure is proposed.