Combining multi-level real-time iterations of Nonlinear Model Predictive Control to realize squatting motions on Leo

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