This paper introduces a family of iterative algorithms for unconstrainednonlinear optimal control. We generalize the well-known iLQR algorithm todifferent multiple-shooting variants, combining advantages likestraight-forward initialization and a closed-loop forward integration. Allalgorithms have similar computational complexity, i.e. linear complexity in thetime horizon, and can be derived in the same computational framework. Wecompare the full-step variants of our algorithms and present several simulationexamples, including a high-dimensional underactuated robot subject to contactswitches. Simulation results show that our multiple-shooting algorithms canachieve faster convergence, better local contraction rates and much shorterruntimes than classical iLQR, which makes them a superior choice for nonlinearmodel predictive control applications.
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