Structure preserving optimal control of 2D-Spider Crane

In this paper we present a new approach for optimal control of 2D-Spider Crane, which is based on structure preserving numerical integrators derived from discrete mechanics. The discrete framework is developed for Lagrangian optimal control problems. The method is based on a direct discretization of the Lagrange-dAlembert principle for the mechanical system. The resulting forced discrete Euler-Lagrange equations then serve as constraints for the optimization of a given cost functional. This optimization method is known as DMOC, Discrete Mechanics Optimal Control, which inherits the special properties like symmetries and integrals of motion exhibited by variational integrators. Cranes are all pervasive in the heavy engineering industry. Precise payload positioning by an overhead crane is difficult due to the fact that the payload may exhibit a pendulum-like swinging motion. This demands truly efficient control strategies. Motivated by this desire to achieve fast and precise payload positioning while minimizing forces. In this paper, we consider a planar version of the Spider-Crane. Our objective is: Point-to-point transfer of the payload with minimum force.