Key result
Gauss-Newton Multiple Shooting algorithms achieved faster convergence, better local contraction rates, and shorter runtimes than classical iLQR for nonlinear model predictive control applications.
The proposed Gauss-Newton Multiple Shooting algorithms offer faster convergence and better local contraction rates than classical iLQR for nonlinear model predictive control applications.
May speed NMPC deployment in engineering; leaves open real-world validation before broader use.
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 straightforward 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.
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Giftthaler et al. (2018) studied this question. Gauss-Newton Multiple Shooting (GNMS) algorithms vs. Iterative Linear-Quadratic Regulator (iLQR) and Single Shooting was evaluated on Convergence rate and computational runtime. Gauss-Newton Multiple Shooting algorithms achieved faster convergence, better local contraction rates, and shorter runtimes than classical iLQR for nonlinear model predictive control applications.
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