DMOC approach of real-time trajectory generation for mechanical systems

Discrete mechanics and optimal control (DMOC) is newly developed methodology to solve the optimal control problems of mechanical systems. It is based on a direct discretization of the Lagrange-d´Alembert principle. The constraints are modeled as Euler-Langrange equations for discrete states. With the application of DMOC, a new real-time trajectory generation approach is proposed. The formulated problem is solved in the open source free nonlinear programming solver IPOPT (interior point optimizer). Superior performance of DMOC is verified through a standard forced VanDerPol oscillator example. It is shown DMOC is much faster than NTG (nonlinear trajectory generation) in computation time, it is 1.31% of the CPU time. Finally, for real-time trajectory generation, a dynamical glider example is shown as one of its possible application fields.