An online algorithm for simultaneously learning forward and inverse kinematics

This paper proposes a supervised algorithm for online learning of input-output relations that is particularly suitable to simultaneously learn the forward and inverse kinematics of general manipulators — the multi-valued nature of the inverse kinematics of serial chains and forward kinematics of parallel manipulators makes it infeasible to apply state-of-the-art learning techniques to these problems, as they typically assume a single-valued function to be learned. The proposed algorithm is based on a generalized expectation maximization approach to fit an infinite mixture of linear experts to an online stream of data samples, together with an outlier probabilistic model that dynamically grows the number of linear experts allocated to the mixture, this way controlling the complexity of the resulting model. The result is an incremental, online and localized learning algorithm that performs nonlinear, multivariate regression on multivariate outputs by approximating the target function by a linear relation within each expert input domain, which can directly provide forward and inverse multi-valued estimates. The experiments presented in this paper show that it can achieve, for single-valued functions, a performance directly comparable to state-of-the-art online function approximation algorithms, while additionally providing inverse predictions and the capability to learn multi-valued functions in a natural manner. To our knowledge this is a distinctive property of the algorithm presented in this paper.