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

Galloway, Kevin S.; Sreenath, Koushil; Ames, Aaron D.; Grizzle, Jessy W.

doi:10.1109/access.2015.2419630

Cited by 141 publications

(121 citation statements)

References 22 publications

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“…For simplicity, suppose that 13) where h(x) : R n → R represents a safety constraint, and k(x) : R n → R is a boundary that h(x) cannot violate. In addition, we can define…”

Section: Control Barrier Functionsmentioning

confidence: 99%

“…The QP-based control method (2.7) has been applied to robotic locomotion and manipulation [5], experimental robotic walking [3,13], and adaptive cruise control [4].…”

Section: Control Lyapunov Functionsmentioning

confidence: 99%

“…In the field of bipedal robotic locomotion, the method has been applied both in simulations and experiments [5,3,13].…”

Section: Introductionmentioning

confidence: 99%

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

Hsu

Ames

2015

2015 American Control Conference (ACC)

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166

122

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This thesis 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.

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“…For simplicity, suppose that 13) where h(x) : R n → R represents a safety constraint, and k(x) : R n → R is a boundary that h(x) cannot violate. In addition, we can define…”

Section: Control Barrier Functionsmentioning

confidence: 99%

“…The QP-based control method (2.7) has been applied to robotic locomotion and manipulation [5], experimental robotic walking [3,13], and adaptive cruise control [4].…”

Section: Control Lyapunov Functionsmentioning

confidence: 99%

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

Hsu

Ames

2015

2015 American Control Conference (ACC)

Self Cite

166

122

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“…Similar to [9] for continuous-time systems, the CLF condition (4) can be enforced through a constrained optimization program:…”

Section: A Lyapunov Functions For Discrete-time Systemsmentioning

confidence: 99%

“…The discrete time CBF-CLF controller (30) can be concatenated with a continuous-time CBF-CLF controller [9,22,26] to traverse over more complex terrains such as stepping stones while avoiding obstacles.…”

Section: E Obstacle Avoidancementioning

confidence: 99%

Discrete Control Barrier Functions for Safety-Critical Control of Discrete Systems with Application to Bipedal Robot Navigation

Agrawal

Sreenath

2017

Robotics: Science and Systems XIII

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169

154

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Abstract-In this paper, we extend the concept of control barrier functions, developed initially for continuous time systems, to the discrete-time domain. We demonstrate safety-critical control for nonlinear discrete-time systems with applications to 3D bipedal robot navigation. Particularly, we mathematically analyze two different formulations of control barrier functions, based on their continuous-time counterparts, and demonstrate how these can be applied to discrete-time systems. We show that the resulting formulation is a nonlinear program in contrast to the quadratic program for continuous-time systems and under certain conditions, the nonlinear program can be formulated as a quadratically constrained quadratic program. Furthermore, using the developed concept of discrete control barrier functions, we present a novel control method to address the problem of navigation of a high-dimensional bipedal robot through environments with moving obstacles that present time-varying safety-critical constraints.

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A novel projected Fletcher‐Reeves conjugate gradient approach for finite‐time optimal robust controller of linear constraints optimization problem: Application to bipedal walking robots

Sun

Tian

Wang

2017

Optim Control Appl Methods

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SummaryFor finite-time optimal robust control problem of bipedal walking robot, a class of global and feasible projected Fletcher-Reeves conjugate gradient approach is proposed based on an online convex optimization algorithm. The optimal robust controllers are solved by projected Fletcher-Reeves conjugate gradient approach.The approach can rapidly converge to a stable gait cycle by selecting an initial gait. Under some suitable conditions, we provide a rigorous proof of global convergence and well-defined properties for projected Fletcher-Reeves conjugate gradient approach. To demonstrate the effectiveness of the bipedal walking robot, we will conduct numerical simulations on the model of 3-link robot with nonlinear, impulsive, and underactuated dynamics. Furthermore, to indicate the availability of high-dimensional robotic system, the main result is illustrated on a nonlinear impulsive model of a bipedal walking robot through simulations via finite-time optimal robust controller. Numerical results show that the projected Fletcher-Reeves conjugate gradient approach is feasible and effective for bipedal walking robots. Therefore, it is reasonable to infer that the optimal robust control approach can be used in practical systems.

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

Cited by 141 publications

References 22 publications

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

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

Discrete Control Barrier Functions for Safety-Critical Control of Discrete Systems with Application to Bipedal Robot Navigation

A novel projected Fletcher‐Reeves conjugate gradient approach for finite‐time optimal robust controller of linear constraints optimization problem: Application to bipedal walking robots

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