Inverse position problem in highly redundant multibody systems in environments with obstacles

This paper looks at a method for the analysis of highly redundant multibody systems (e.g. in the case of cellular adaptive structures of variable geometry) in environments with obstacles. It is sought to solve the inverse problem in successive positions of multibody systems, avoiding the obstacles in its work environment; i.e. the computation of the increment that has to be assigned to the actuators throughout the movement of the multibody system so that it does not collide with obstacles, as one or more nodes perform a pre-established function (e.g. a certain path). The multibody systems are modelled via rod-type finite elements, both deformable and rigid, and the coordinates of their nodes are chosen as variables. The obstacles are modelled via a mesh of points that exert repulsive forces on the nodes of the model of the multibody, so that interference between the two is avoided. Such forces have been chosen inversely proportional to the Nth power of the distance between the corresponding points of the obstacle and of the multibody system. The method is based on a potential function and on its minimization using the Lagrange Multiplier Method. The solution of the resulting equations is undertaken iteratively with the Newton–Raphson method. The 2D and 3D examples provided attest to the good performance of the algorithms and procedure here set forth.