Geodesic Approach for Trajectory Planning of Mobile Robot Manipulators

This research article offers an efficient trajectory planning approach by employing geodesic to attain a smooth and accurate trajectory for a mobile robot link mechanism. Geodesic is defined as the shortest curve joining any two loci on a Riemannian manifold. The workspace of the manipulator has been assigned with a Riemannian metric so as to achieve geodesic settings for the planned end-effector motion. The jointDH parameters for joint trajectories are chosen as local coordinates of the workspace to represent Cartesian trajectories. Boundary conditions of the trajectory are considered in order to get the geodesic equations for the Riemannian metric space. The results of the geodesic computations have been plotted in graphical form. A simple three degrees of freedom spatial manipulator fixed upon the mobile robot platform has been considered for numerical computations to validate the efficacy of the geodesic technique.