Differential-Algebraic Equation Control Barrier Function for Flexible Link Manipulator

This paper presents a control barrier function (CBF) for systems described by differential-algebraic equations and applies the method to guarantee the safety of a two-link flexible-link manipulator. The two main contributions of the paper are: a) an extension of CBFs to systems governed by differential-algebraic equations; b) a framework for simulation of flexible-link robots in a floating frame of reference formulation (FFRF) finite element method (FEM). Numerical simulations demonstrate the minimally invasive safety control of a flexible two-link manipulator with position constraints through CBF quadratic programming without converting the differential-algebraic equations to a control-affine system.