Optimal trajectory planning of a 3R SCARA manipulator using geodesic

Abstract

This paper proposes an optimal planning technique using geodesic to achieve accurate as well as smooth trajectory for industrial robot manipulators. The shortest path connecting any two points on a Riemannian manifold along itself is called as the geodesic. The work volume of manipulator end-effector is divided into position and orientation space. A Riemannian metric is assigned to both the spaces in order to attain geodesic conditions for intended motion of the end-effector. Cartesian trajectories are shown by joint trajectories in which joint variables are treated as local coordinates of the position space and the orientation space. Then the obtained geodesic equations for each space are evaluated for initial conditions of the trajectory and the results are plotted. To validate the effectiveness of the geodesic method, numerical computations are performed using data taken from the Quest SCARA robot. For simplicity vertical motion of link 3 of the 3R SCARA manipulator is restricted.