Planning of Underactuated Differentially Flat Robot Trajectories with a via Point

Underactuated robots usually perform point-to-point motions exploiting the differential flatness property. This paper aims to extend the capabilities of this class of robots considering a via point in the workspace. A method for trajectory planning in the space of flat variables is presented. Flat variables are described by means of polynomials and have to guarantee the continuity of motor torques. Numerical results and experimental tests carried out on a 2 degree of freedom prototype show the validity of the method, which allows the robot to avoid an obstacle in the workspace.