Control barrier function based quadratic programs with application to bipedal robotic walking. Hsu, S., Xu, X., & Ames, A. D. In 2015 American Control Conference (ACC), pages 4542–4548, July, 2015. ISSN: 2378-5861
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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.
@inproceedings{hsu_control_2015,
	title = {Control barrier function based quadratic programs with application to bipedal robotic walking},
	copyright = {10/10},
	doi = {10.1109/ACC.2015.7172044},
	abstract = {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.},
	booktitle = {2015 {American} {Control} {Conference} ({ACC})},
	author = {Hsu, Shao-Chen and Xu, Xiangru and Ames, Aaron D.},
	month = jul,
	year = {2015},
	note = {ISSN: 2378-5861},
	keywords = {Backstepping, CBF, CLF, Context, Foot, Legged locomotion, Lyapunov methods, Mathematical model, QP based controllers, backstepping inspired approach, bipedal robot AMBER2, bipedal robotic walking, control Lyapunov functions, control barrier function, control nonlinearities, forward invariance, higher order derivatives, invariance, iterative methodology, iterative methods, joint limits, legged locomotion, physical realizability constraints, quadratic programming, quadratic programs, stable walking},
	pages = {4542--4548},
}
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