Learning Robust Point-to-Point Motions Adversarially: A Stochastic Differential Equation Approach

This paper proposes a robust stochastic differential equation approach for learning point-to-point motions in an adversarial way. The proposed stochastic dynamical model combines the advantages of the stochastic differential equation and the transformer-like function together to achieve both robustness and accuracy of the learning. The adversarial training method is proposed to simplify the way of updating the parameters of the model. The state of the proposed stochastic dynamical system is mathematically proved to converge asymptotically in the mean square sense, and it has been experimentally validated on the LASA dataset and by the trajectory-programming task of the Franka Emika robot. The experimental results show that: (1) the adversarial training method helps the model to achieve higher reproduction accuracy; (2) the trajectories generated by the proposed model achieve higher accuracy in both the noise-free condition (by approximately 14.9\%) and the noisy condition (by approximately 17.8\%) compared with the state-of-the-art methods in terms of the similarity to the demonstration; and (3) the proposed approach can learn smoother trajectories even if the observations are contaminated by noises.