A Family of Iterative Gauss-Newton Shooting Methods for Nonlinear Optimal Control
This work addresses nonlinear model predictive control applications, offering improved algorithms for robotics and control systems, but it is incremental as it builds upon existing iLQR methods.
The paper tackles nonlinear optimal control by introducing a family of iterative Gauss-Newton shooting methods that generalize iLQR to multiple-shooting variants, achieving faster convergence, better local contraction rates, and much shorter runtimes than classical iLQR in simulations, including on a high-dimensional underactuated robot.
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 have similar computational complexity, i.e. linear complexity in the time horizon, and can be derived in the same computational framework. 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.