Kuka youBot arm shortest path planning based on geodesics

The state-of-the-art Kuka youBot is an open-source robot platform. In order to improve youBot arm manipulation performance, a novel robotic trajectory planning method based on geodesics is used for Kuka youBot arm shortest path trajectory planning in this paper. Geodesic is the necessary condition of the shortest length between two points on the Riemannian surface in which the covariant derivative of the geodesic´s tangent vector is zero. The Riemannian metric is constructed according to the distance metric by arc length of the youBot arm trajectory to achieve shortest path. Once the Riemannian metric is obtained, the corresponding Riemannian surface is solely determined. Then the geodesic equations on this surface can be determined and calculated. For the given initial conditions of the trajectory, the geodesic equations can be solved and the results are the optimal trajectory of the youBot arm in the joint space for the given metric. The planned trajectories in the joint space can also be mapped into the workspace. A simple trajectory planning example on Kuka youBot arm from camera pose ready point to object grasping point is given to demonstrate the feasibility of the proposed approach.