Learning robustly stable open-loop motions for robotic manipulation

Robotic arms have been shown to be able to perform cyclic tasks with an open-loop stable controller. However, model errors make it hard to predict in simulation what cycle the real arm will perform. This makes it difficult to accurately perform pick and place tasks using an open-loop stable controller. This paper presents an approach to make open-loop controllers follow the desired cycles more accurately. First, we check if the desired cycle is robustly open-loop stable, meaning that it is stable even when the model is not accurate. A novel robustness test using linear matrix inequalities is introduced for this purpose. Second, using repetitive control we learn the open loop controller that tracks the desired cycle. Hardware experiments show that using this method, the accuracy of the task execution is improved to a precision of 2.5 cm, which suffices for many pick and place tasks.