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

"A Family of Iterative Gauss-Newton Shooting Methods for Nonlinear Optimal Control". Markus Giftthaler, Michael Neunert, Markus Stäuble, Jonas Buchli and Moritz Diehl.

"This paper introduces a family of iterative algorithms for unconstrained nonlinear optimal control. We generalize the well-known iLQR algorithm to different multiple-shooting variants, combining advantages like straight-forward initialization and a closed-loop forward integration. All algorithms feature similar computational complexity, i.e. linear complexity in the time horizon, and can be easily transformed into each other. We compare the full-step variants of our algorithms and present several simulation examples, including a high-dimensional underactuated robot subject to contact switches. Simulation results show that our multiple-shooting algorithms can achieve faster convergence, better local contraction rates and much shorter runtimes than classical iLQR, which makes them a superior choice for nonlinear model predictive control applications."

Agile & Dexterous Robotics Lab, ETH Zürich, Switzerland;
Systems Control and Optimization Laboratory, Department of Microsystems Engineering (IMTEK), University of Freiburg, Germany.