Today’s humanoid robots are complex mechanical systems with many degrees of freedom that are built to achieve locomotion skills comparable to humans. In order to synthesize whole-body motions, real-tme capable direct methods of optimal control are a subject of contemporary research. To this end, Nonlinear Model Predictive Control is the method of choice to realize motions on the physical robot using model-based optimal control. However, the complexity of the problem results in a high computational time that falls short of the expectations of robotic experimenters and control engineers. In this article, we show how advanced NMPC methods can be applied to improve the control rate by a factor of 10–16 up to 190Hz. This is achieved by thread-based parallelization of two controllers and by efficiently reusing control problem linearizations of the last iteration to provide fast feedback by one controller while the other controller prepares the next nonlinear step including the evaluation of the multi-body dynamics and the respective sensitivities. This way, the bottleneck of the roll-out of up to 130 ms can partly be side-stepped by repeated calls of the much faster feedback phase of ~5ms. This enables a realization of a squatting task on the actual 2D-robot Leo of Delft University of Technology, which was not possible using a conventional Nonlinear Model Predictive Control scheme. @en

Model-free reinforcement learning and nonlinear model predictive control are two different approaches for controlling a dynamic system in an optimal way according to a prescribed cost function. Reinforcement learning acquires a control policy through exploratory interaction with the system, while nonlinear model predictive control exploits an explicitly given mathematical model of the system. In this article, we provide a comprehensive comparison of the performance of reinforcement learning and nonlinear model predictive control for an ideal system as well as for a system with parametric and structural uncertainties. The comparison is based on two different criteria, namely the similarity of trajectories and the resulting rewards. The evaluation of both methods is performed on a standard benchmark problem: a cart–pendulum swing-up and balance task. We first find suitable mathematical formulations and discuss the effect of the differences in the problem formulations. Then, we investigate the robustness of reinforcement learning and nonlinear model predictive control against uncertainties. The results demonstrate that nonlinear model predictive control has advantages over reinforcement learning if uncertainties can be eliminated through identification of the system parameters. Otherwise, there exists a break-even point after which model-free reinforcement learning performs better than nonlinear model predictive control with an inaccurate model. These findings suggest that benefits can be obtained by combining these methods for real systems being subject to such uncertainties. In the future, we plan to develop a hybrid controller and evaluate its performance on a real seven-degree-of-freedom walking robot.

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