Influence of Joint Stiffness and Motion Time on the Trajectories of Underactuated Robots

Underactuated robots have fewer actuators than degrees of freedom (DOF). Nonactuated joints can be equipped with torsional springs. Underactuated robots can be controlled in a point-to-point motion if they have a particular mass distribution that makes them differentially flat. The trajectory described by the robot moving from the start point to the end point largely depends on the torsional stiffness of the nonactuated joints and on motion time. Thus, the same point-to-point motion can be obtained by sweeping different parts of the workspace. This property increases the dexterity of the robot. This paper focuses on the trajectories of a 3-DOF robot moving in the horizontal plane with two actuators and a torsional spring. Parametric analyses showing the effect of torsional stiffness and motion time are presented. The existence of combinations of torsional stiffness and motion time that minimize the motion torques or the swept area is discussed. The area swept by the underactuated robot is compared with the one swept by an equivalent actuated robot performing the same task. Reductions in the swept area of up to 36% are obtained. Finally, numerical results are validated by means of experimental tests on a simplified prototype.