Nonlinear Model Predictive Control of Robotic Systems with Control Lyapunov Functions

Ruben Grandia (ETH Zurich); Andrew Taylor (Caltech); Andrew Singletary (Caltech); Marco Hutter (ETHZ); Aaron Ames (Caltech)


The theoretical unification of Nonlinear Model Predictive Control (NMPC) with Control Lyapunov Functions (CLFs) provides a framework for achieving optimal control performance while ensuring stability guarantees. In this paper we present the first real-time realization of a unified NMPC and CLF controller on a robotic system with limited computational resources. These limitations motivate a set of approaches for efficiently incorporating CLF stability constraints into a general NMPC formulation. We evaluate the performance of the proposed methods compared to baseline CLF and NMPC controllers with a robotic Segway platform both in simulation and on hardware. The addition of a prediction horizon provides a performance advantage over CLF based controllers, which operate optimally point-wise in time. Moreover, the explicitly imposed stability constraints remove the need for difficult cost function and parameter tuning required by NMPC. Therefore the unified controller improves the performance of each isolated controller and simplifies the overall design process.

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The paper is clearly written and, despite having to invoke a fair amount of techniques and results, does a good job at providing a coherent exposition. Minor improvements to the exposition: in Section III.A, it's confusing to call something "a stabilizing control input" (because it satisfies the CLF eq at a particular point in time) while at the same time acknowledging that it is in general not stabilizing (because it should satisfy the CLF equation everywhere in time). A better wording convention should be used here; the subindex LLS is never defined (although one can deduce it corresponds to Lyapunov level set?); in Section III.C, the reference output should be y_d, not y. Finally, I was expecting the conclusions to mention the incorporation of safety constraints (a la CBF) into the proposed design.