Differentially Flat Robots with Compliance in Actuated Joints

Most robots and mechanisms are fully actuated, i.e., the number of actuators is equal to the number of degrees of freedom (DOFs). Thus, the robot’s configuration is fully determined by imposing the position of the actuators. However, a class of robots exists, the under-actuated robots, in which the number of actuators is smaller than the number of degrees of freedom. In this case, the non-actuated joints cannot be directly controlled. When an under-actuated robot with n-DOFs and n-1 actuators is designed with specific inertial properties of the links, it becomes differentially flat. In this case, the non-actuated joint, which is equipped with a torsion spring, can be controlled by the motion of the actuated joints. In the previous works dealing with differentially flat underactuated robots the compliance of the actuated joints was neglected. In this paper, the effect of actuated joint compliance in differentially flat underactuated robots is investigated. A mathematical model is proposed and numerical simulations are carried out to highlight the effect of joint compliance in the precision of point-to-point motions.