Gordon A. Dakin, Robin J. Popplestone
A methodology is presented whereby a nominal trajectory for an assembly operation, computed from kinematic constraints alone, is augmented with a fine-motion strategy synthesized through uncertainty and force analyses. Insertion clearances and size tolerances are introduced into the assembly part models in parallel with the manual selection of a perturbed nominal trajectory in contact space. The selection of small clearances, and in turn, small insertion angles allows us to linearize contact space about discrete points in the nominal trajectory. Contact states are represented as affine spaces in a generalized C-space of model error and pose variables. The feasibility of proposed command velocities to be executed in the presence of position, control, and model error is determined through an uncertainty analysis technique based on the forward-projection of convex polytopes in contact space. Our approach further the automates the so-called "manual" methods of motion planning with uncertainty.