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

TL;DR

This paper develops a family of iterative multiple-shooting algorithms extending iLQR for nonlinear optimal control, demonstrating faster convergence and shorter runtimes in simulations, suitable for nonlinear model predictive control.

Contribution

It generalizes iLQR to multiple-shooting variants, offering improved convergence and efficiency for nonlinear optimal control problems.

Findings

Multiple-shooting algorithms outperform classical iLQR in convergence speed.

Algorithms achieve linear complexity in the time horizon.

Simulation on high-dimensional robot shows practical advantages.

Abstract

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.