Legs interference checking of parallel robots over a given workspace or trajectory

We are considering a 6 d.o.f. Gough platform that has to move within a given workspace or on a trajectory. The legs of the robot are assumed to be constituted of a set of finite cylindrical elements and we address the problem of determining if any pair of such element would intersect during the robot motion. Collision conditions may be written mathematically according to various equivalent formulations. We show however that these formulations are not numerically equivalent and exhibit an efficient interference checking algorithm based on interval analysis that allows to check 6D workspace or arbitrary time-function trajectories for interference