Optimal trajectory generation for generalization of discrete movements with boundary conditions

Trajectory generation methods play an important role in robotics since they are essential for the execution of actions. In this paper we present a novel trajectory generation method for generalization of accurate movements with boundary conditions. Our approach originates from optimal control theory and is based on a second order dynamic system. We evaluate our method and compare it to state-of-the-art movement generation methods in both simulations and a real robot experiment. We show that the new method is very compact in its representation and can reproduce demonstrated trajectories with zero error. Moreover, it has most of the properties of the state-of-the-art trajectory generation methods such as robustness to perturbations and generalisation to new boundary position and velocity conditions. We believe that, due to these features, our method has great potential for various robotic applications, especially, where high accuracy is required, for example, in industrial and medical robotics.