A Gaussian Mixture Model for Probabilistic Workspace Generation of Multibody Systems

In this paper, a computationally efficient method is presented for probabilistic workspace analysis of multibody systems. Growing interest in robotically assembled space structures has introduced a demand for analyzing all end-to-end configurations of large multibody systems as they are expanded and articulated in outer space. This paper develops a computationally efficient approach for workspace analysis in which the system's workspace is approximated by a Gaussian mixture model. The independence of inputs for each link is exploited to propagate the bounds on relative rotation of one link with respect to the other through forward kinematics. Furthermore, a non-product quadrature method known as Conjugate Un-scented Transformation is used to compute statistical moments with a minimum number of samples. The trade-off between accuracy of the Gaussian mixture model in representing the workspace distribution and computational time is performed by increasing or decreasing the number of batches in the mixture model. To showcase the newly developed algorithm, several numerical experiments are conducted emphasizing its utility in design and trajectory planning applications. By revealing low and high probability regions of the workspace, the algorithm can be utilized in applications such as stochastic design and fail-safe trajectory planning.