Generation of movements with boundary conditions based on optimal control theory

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 the state of the art movement generation methods in both simulations and real robot experiments. We show that the new method is very compact in its representation and can reproduce reference trajectories with zero error. Moreover, it has most of the features of the state of the art movement generation methods such as robustness to perturbations and generalization to new position and velocity boundary conditions. We believe that, due to these features, our method may have potential for robotic applications where high accuracy is required paired with flexibility, for example, in modern industrial robotic applications, where more flexibility will be demanded as well as in medical robotics.