A group-theoretic approach to the computation of symbolic part relations

When a set of constraints is imposed on the degrees of freedom between several rigid bodies, finding the configuration or configurations that satisfy all these constraints is a matter of special interest. The problem is not new and has been discussed, not only in kinematics, but also more recently in the design of object-level robot programming languages. In this last domain, several languages have been developed, from different points of view, that are able to partially solve the problem. A more general method is derived than those previously proposed that were based on the symbolic manipulation of chains of matrix products, using the theory of continuous groups