Math Simulation of Contact Interaction During Spacecraft Docking and Robotic Assembly Operations

Abstract eng:
Contact interaction math models can be split into two classes depending on the character of the relative motion of assembly interface contacting elements. In the first-class models, one of contacting elements has several degrees of relative motion freedom. Therefore contact reaction forces must be taken into account in relative motion dynamics equations of a mechanical system. In this case the most efficient method of calculating such forces is based on the assumption of a contact penetration counteracted by contact stiffness. The penetration value is controlled; its maximal value determines the geometric contact simulation error. For the first-class contact models, basic principles of development and a classification of main pairs of interacting elements are presented; algorithms for calculation of penetration values, reaction unit vectors at contact points and contact forces are described. In the second-class models, one of contacting elements has only one degree of freedom, and its relative displacement is counteracted by a spring. Here, a slight inertia of such an element does not influence the motion dynamics of mating interfaces, but it is only the spring force that is taken into account. Therefore contact reaction forces in the second-class models are calculated based on spring deformation only, without using contact penetration. In this case the geometric place of contact, which determines the spring deformation, is calculated by the iterative method with any given accuracy. This feature is particularly useful for simulating contact mechanisms that provide a stiff interface joint and have very small displacements. Models of this class are also used for describing the motion of capture latches. Surfaces of the second and forth order (cone, torus) are approximated by more simple geometric elements of the first and third order respectively (segment, sphere) in contact models of both classes. As a result, a multiple use of simple analytical relations replaces a solution of a complex geometric problem. Calculation efficiency is ensured by the dichotomy method, as well as by a preliminary generation of the highest possible number of parameters that are just transformed during simulation into the coordinate system of the geometric problem solution. The described algorithms provide a real-time simulation of contact interaction of different mating interfaces i.e. probe-cone type and androgynous peripheral docking units, specialized berthing devices.

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