Reliable and Failure-Free Workspaces for Motion Planning Algorithms for Parallel Manipulators Under Geometrical Uncertainties

Abstract

Manufacturing tolerances and other uncertainties may play an important role in the performance of parallel manipulators since they can affect the distance to a singular configuration. Motion planning strategies for parallel manipulators under uncertainty require decision making approaches for classifying reliable regions within the workspace. In this paper, we address fail free and reliable motion planning for parallel manipulators. Failure is related to parallel kinematic singularities in the motion equations or to ill-conditioning of the Jacobian matrices. Monte Carlo algorithm is employed to compute failure probabilities for a dense grid of manipulator workspace configurations. The inverse condition number of the Jacobian matrix is used to compute the distance between each configuration and a singularity. For supporting motion planning strategies, not only failure maps are constructed but also reliable and failure-free workspaces are obtained. On the one hand, the reliable workspace is obtained by minimizing the failure probabilities subject to a minimal workspace area. Differently, a failure-free workspace is found by maximizing the workspace area subject to a probability of failure equal to zero. A 3RRR manipulator is used as a case study. For this case study, the usage of the reliable strategy can be useful for robustifying motion planning algorithm without a significant reduction of the reliable regions within the workspace.