A general algorithm for derivation and analysis of constraint for motion of polyhedra in contact

This paper presents a general algorithm for derivation and analysis of motion constraints of objects in contact. The constraints can be derived as linear inequalities for a general case, even when a vertex contacts another vertex or an edge. The solution of the inequalities is a direct sum of a nonnegative linear combination of motions which change the contact state and a linear combination of them which maintain it. From the singular value decomposition of the coefficient matrix of the inequalities it is possible to find the solution in the minimal dimensional space, where the complexity of the algorithm is also minimal. An algorithm is proposed which is not optimal as asymptotic complexity, but is fast in the practical cases and uniform for the dimension of the cone. The algorithm presented can be applied not only to the sensing and control of motion in contact, but also to the planning of it