Numerical Solution for Manipulator Forward Dynamics BVPs
Abstract A new algorithm is presented for iterative solution of systems of nonlinear ordinary differential equations (ODEs) with any order for multibody dynamics and control problems. The collocation technique (based on the explicit fixed-point iteration scheme) may be used for solving both initial value problems (IVPs) and boundary value problems (BVPs). The BVP is solved by first transforming it into the IVP. If the Lipschitz constant is large and the algorithm diverges in a single (‘long’) domain, the domain is partitioned into a number of subdomains and the local solutions of the corresponding BVPs are matched either locally (in parallel) or globally. The technique is general and may be applied to general systems of ODEs in any field. As an illustration, the forward dynamics problem of a manipulator is solved as an IVP and then as a BVP.