Algorithms for contact parameters determination during math simulation of spacecraft docking and berthing

Spacecraft docking and berthing are realized using active and passive docking units, whose guiding surfaces provide decreasing of relative lateral and angular misalignments during approach. Complex shapes of these surfaces decrease the number of degrees of freedom and a relative motion volume of joining units during approach. Theses surfaces are not arbitrary, they are presented as a combination of geometrical elements described by first up to fourth order equations. This feature is taken into account when developing methods for describing surfaces and algorithms for calculation of contact parameters. Elements of guiding surfaces are presented by geometrical primitives or theirs ordered sets. An algorithm for contact possibility estimation and for calculation of contact parameters is developed for each pair of such primitives on the base of simple analytical formulas. Such surface elements as a truncated cone, cylinder, torus or theirs fragment are presented by ordered sets of geometrical primitives of a lower order, and a dichotomy algorithm, with these analytical formulas at each iteration step, is used for theirs contact possibility estimation. All above mentioned provide a real time simulation of docking and berthing.