Sequence-to-Sequence model for trajectory planning of nonprehensile manipulation including contact model

Nonprehensile manipulation is necessary for robots to operate in humans' daily lives. As nonprehensile manipulation should satisfy both kinematics and dynamics requirements simultaneously, it is difficult to manipulate objects along given paths. Previous studies have considered the problems with sequence-to-sequence models, which are neural networks for time-series conversion. However, they did not consider nonlinear contact models, such as friction models. When we train the seq2seq models using end-to-end backpropagation, training losses vanish owing to static friction. In this letter, we realize sequence-to-sequence models for trajectory planning of nonprehensile manipulation including contact models between the robots and target objects. This letter proposes a training curriculum that commences training without contact models to bring the seq2seq models outside of the gradient-vanishing zone. This letter discusses sliding manipulation, which includes a friction model between objects and tools, such as frying pans fixed onto the robots. We validated the proposed curriculum through a simulation. In addition, we observed that the trained seq2seq models could handle parameter fluctuations that did not exist during training.