Learning of Surgical Gestures for Robotic Minimally Invasive Surgery Using Dynamic Movement Primitives and Latent Variable Models

Full and partial automation of Robotic Minimally Invasive Surgery holds significant promise to improve patient treatment, reduce recovery time, and reduce the fatigue of the surgeons. However, to accomplish this ambitious goal, a mathematical model of the intervention is needed. In this thesis, we propose to use Dynamic Movement Primitives (DMPs) to encode the gestures a surgeon has to perform to achieve a task. DMPs allow to learn a trajectory, thus imitating the dexterity of the surgeon, and to execute it while allowing to generalize it both spatially (to new starting and goal positions) and temporally (to different speeds of executions). Moreover, they have other desirable properties that make them well suited for surgical applications, such as online adaptability, robustness to perturbations, and the possibility to implement obstacle avoidance. We propose various modifications to improve the state-of-the-art of the framework, as well as novel methods to handle obstacles. Moreover, we validate the usage of DMPs to model gestures by automating a surgical-related task and using DMPs as the low-level trajectory generator. In the second part of the thesis, we introduce the problem of unsupervised segmentation of tasks' execution in gestures. We will introduce latent variable models to tackle the problem, proposing further developments to combine such models with the DMP theory. We will review the Auto-Regressive Hidden Markov Model (AR-HMM) and test it on surgical-related datasets. Then, we will propose a generalization of the AR-HMM to general, non-linear, dynamics, showing that this results in a more accurate segmentation, with a less severe over-segmentation. Finally, we propose a further generalization of the AR-HMM that aims at integrating a DMP-like dynamic into the latent variable model.