# Control barrier function based quadratic programs with application to bipedal robotic walking

@article{Hsu2015ControlBF, title={Control barrier function based quadratic programs with application to bipedal robotic walking}, author={Shao-Chen Hsu and Xiangru Xu and A. Ames}, journal={2015 American Control Conference (ACC)}, year={2015}, pages={4542-4548} }

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 barrierâ€¦Â Expand

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#### References

SHOWING 1-10 OF 50 REFERENCES

Control barrier function based quadratic programs with application to adaptive cruise control

- Mathematics, Computer Science
- 53rd IEEE Conference on Decision and Control
- 2014

A control methodology that unifies control barrier functions and control Lyapunov functions through quadratic programs is developed, which allows for the simultaneous achievement of control objectives subject to conditions on the admissible states of the system. Expand

Torque Saturation in Bipedal Robotic Walking Through Control Lyapunov Function-Based Quadratic Programs

- Computer Science, Mathematics
- IEEE Access
- 2015

A framework is presented, which results in more effective handling of control saturations and provides a means for incorporating a whole family of user-defined constraints into the online computation of a CLF-based controller. Expand

Sufficient conditions for the Lipschitz continuity of QP-based multi-objective control of humanoid robots

- Mathematics, Computer Science
- 52nd IEEE Conference on Decision and Control
- 2013

A generalized QP-based control law is developed through the use of multiple control Lyapunov functions (CLFs) that provides conditions under which any number of tasks encoded as CLFs can be simultaneously exponentially stabilized. Expand

Towards the Unification of Locomotion and Manipulation through Control Lyapunov Functions and Quadratic Programs

- Mathematics, Computer Science
- CPSW@CISS
- 2013

This paper presents the first steps toward unifying locomotion controllers and algorithms with whole-body control and manipulation through the use of control Lyapunov functions presented in the form of a quadratic program. Expand

Asymptotically stable walking for biped robots: analysis via systems with impulse effects

- Engineering, Computer Science
- IEEE Trans. Autom. Control.
- 2001

The principal contribution of the present work is to show that the control strategy can be designed in a way that greatly simplifies the application of the method of Poincare to a class of biped models, and to reduce the stability assessment problem to the calculation of a continuous map from a subinterval of R to itself. Expand

HZD-based control of a five-link underactuated 3D bipedal robot

- Engineering, Computer Science
- 2008 47th IEEE Conference on Decision and Control
- 2008

This paper presents a within-stride feedback controller that achieves an exponentially stable, periodic, and fast walking gait for a 3D bipedal robot consisting of a torso, revolute knees, andâ€¦ Expand

Dynamically stable bipedal robotic walking with NAO via human-inspired hybrid zero dynamics

- Engineering, Computer Science
- HSCC '12
- 2012

This paper demonstrates the process of utilizing human locomotion data to formally design controllers that yield provably stable robotic walking and experimentally realizing these formal methods toâ€¦ Expand

Dynamic multi-domain bipedal walking with atrias through SLIP based human-inspired control

- Engineering, Computer Science
- HSCC
- 2014

This paper presents a methodology for achieving efficient multi-domain underactuated bipedal walking on compliant robots by formally emulating gaits produced by the Spring Loaded Inverted Pendulumâ€¦ Expand

Barrier Lyapunov Functions for the control of output-constrained nonlinear systems

- Mathematics, Computer Science
- Autom.
- 2009

This paper presents control designs for single-input single-output (SISO) nonlinear systems in strict feedback form with an output constraint, and explores the use of an Asymmetric Barrier Lyapunov Function as a generalized approach that relaxes the requirements on the initial conditions. Expand

Achieving bipedal locomotion on rough terrain through human-inspired control

- Computer Science
- 2012 IEEE International Symposium on Safety, Security, and Rescue Robotics (SSRR)
- 2012

Experimental results show how the walking gait morphs based upon the terrain, thereby justifying the theory applied, and the technique developed is implemented on different terrains in simulation. Expand