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This paper presents a methodology for the development of control barrier functions (CBFs) through a backstepping inspired approach. Given a set defined as the superlevel set of a function, h, the main result is a constructive means for generating control barrier functions that guarantee forward invariance of this set. In particular, if the function defining the set has relative degree n, an iterative methodology utilizing higher order derivatives of h provably results in a control barrier function that can be explicitly derived. To demonstrate these formal results, they are applied in the context of bipedal robotic walking. Physical constraints, e.g., joint limits, are represented by control barrier functions and unified with control objectives expressed through control Lyapunov functions (CLFs) via quadratic program (QP) based controllers. The end result is the generation of stable walking satisfying physical realizability constraints for a model of the bipedal robot AMBER2.
Hsu et al. (Wed,) studied this question.