A Family of Iterative Gauss-Newton Shooting Methods for Nonlinear\n Optimal Control

This paper introduces a family of iterative algorithms for unconstrained\nnonlinear optimal control. We generalize the well-known iLQR algorithm to\ndifferent multiple-shooting variants, combining advantages like\nstraight-forward initialization and a closed-loop forward integration. All\nalgorithms have similar computational complexity, i.e. linear complexity in the\ntime horizon, and can be derived in the same computational framework. We\ncompare the full-step variants of our algorithms and present several simulation\nexamples, including a high-dimensional underactuated robot subject to contact\nswitches. Simulation results show that our multiple-shooting algorithms can\nachieve faster convergence, better local contraction rates and much shorter\nruntimes than classical iLQR, which makes them a superior choice for nonlinear\nmodel predictive control applications.\n