Real-time motion planning for multibody systems

The solution of constrained motion planning is an important task in a wide number of application fields. The real-time solution of such a problem, formulated in the frame- work of optimal control theory, is a challenging issue. We prove that a real-time solution of the constrained motion planning problem for multibody systems is possible for practical real-life applications on standard personal computers. The proposed method is based on an indirect approach that eliminates the inequalities via penalty formulation and solves the boundary value problem by a combination of finite differ- ences and Newton–Broyden algorithm. Two application examples are presented to validate the method and for performance comparisons. Numerical results show that the approach is real-time capable if the correct penalty formulation and settings are chosen.