A model-free approach to control barrier functions for higher-order systems
For control engineers working on safe operation of complex nonlinear systems, this work removes the requirement for accurate dynamic models, but it is an incremental extension of existing model-free CBF methods from relative-degree-one to higher relative degrees.
This paper extends model-free control barrier function (CBF) design to nonlinear systems of arbitrary relative degree, eliminating the need for accurate system dynamics or state measurement. The approach is validated on a seven-degree-of-freedom robotic manipulator with relative degree two.
Control barrier functions (CBFs) are a widely applied modular tool to ensure safe operation of nonlinear dynamical control systems. However, for their construction accurate knowledge of the system dynamics is typically needed. This requirement was recently alleviated for relative-degree-one systems using techniques from prescribed performance control (PPC) or funnel control (FC). This article extends the model-free CBF design to nonlinear systems of arbitrary relative degree. Moreover, we show with a simple example that a straightforward extension of existing results for relative-degree-one systems fails. Instead, we utilize novel techniques from funnel control to characterize a subset of the controls satisfying a CBF condition without requiring a dynamic model or state measurement. Finally, we demonstrate the applicability of our results on a seven degrees of freedom robotic manipulator with relative degree two.