The number of saturated actuators and constraint forces during time-optimal movement of a general robotic system

It is proved that if the dynamics of a general robot system are defined by n coordinates, m differential constraint equations, and p actuators, then some combination of at least L=m+p+1-n of the actuators and internal constraint forces are saturated during a time-optimal movement of the system along a prescribed path. The result applies to a general class of dynamic systems with both holonomic and nonholonomic constraints.>