Learning and extrapolation of robotic skills using task-parameterized equation learner networks

Imitation learning approaches achieve good generalization within the range of the training data, but tend to generate unpredictable motions when querying outside this range. We present a novel approach to imitation learning with enhanced extrapolation capabilities that exploits the so-called Equation Learner Network (EQLN). Unlike conventional approaches, EQLNs use supervised learning to fit a set of analytical expressions that allows them to extrapolate beyond the range of the training data. We augment the task demonstrations with a set of task-dependent parameters representing spatial properties of each motion and use them to train the EQLN. At run time, the features are used to query the Task-Parameterized Equation Learner Network (TP-EQLN) and generate the corresponding robot trajectory. The set of features encodes kinematic constraints of the task such as desired height or a final point to reach. We validate the results of our approach on manipulation tasks where it is important to preserve the shape of the motion in the extrapolation domain. Our approach is also compared with existing state-of-the-art approaches, in simulation and in real setups. The experimental results show that TP-EQLN can respect the constraints of the trajectory encoded in the feature parameters, even in the extrapolation domain, while preserving the overall shape of the trajectory provided in the demonstrations.