This paper presents a parametrization of a feed-forward control based on structures of subspaces for a non-interacting regulation. With advances in technological development, robotics is increasingly being used in many industrial sectors, including medical applications (e. g., micro-manipulation of internal tissues or laparoscopy). Typical problems in robotics and general mechanisms may be mathematically formalized and analyzed, resulting in outcomes so general that it is possible to speak of structural properties in robotic manipulation and mechanisms. This work shows an explicit formula for the reachable internal contact forces of a general manipulation system. The main contribution of the paper consists of investigating the design of a feed-forward force-motion control which, together with a feedback structure, realizes a decoupling force-motion control. A generalized linear model is used to perform a careful analysis, resulting in the proposed general geometric structure for the study of mechanisms. In particular, a lemma and a theorem are presented which offer a parametrization of a feed-forward control for a task-oriented choice of input subspaces. The existence of these input subspaces is a necessary condition for the structural non-interaction property. A simulation example in which the subspaces and the control structure are explicitly calculated is shown and widely explicated.
A graph is called distance integral (or D-integral) if all eigenvalues of its distance matrix are integers. In their study of D-integral complete multipartite graphs, Yang and Wang (2015) posed two questions on the existence of such graphs. We resolve these questions and present some further results on D-integral complete multipartite graphs. We give the first known distance integral complete multipartite graphs {K_{{p_1},{p_2},{p_3}}} with p1 < p2 < p3, and {K_{{p_1},{p_2},{p_3},{p_4}}} with p1 < p2 < p3 < p4, as well as the infinite classes of distance integral complete multipartite graphs {K_{{a_1}{p_1},{a_2}{p_2},...,{a_s}{p_s}}} with s = 5, 6., Pavel Híc, Milan Pokorný., and Obsahuje seznam literatury