Correct-by-Design Control Barrier Functions for Euler-Lagrange Systems with Input Constraints

Cortez, Wenceslao Shaw; Dimarogonas, Dimos V.

doi:10.23919/acc45564.2020.9147367

Cited by 32 publications

(25 citation statements)

References 13 publications

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“…Ensuring safety via quadratic programming based control laws were popularized by [4], where safety constraints were incorporated via control barrier functions (CBFs). This was first applied to adaptive cruise control, and has since been utilized in a variety of application domains: automotive safety [5], robotics [6], [7], [8] and multi-agent systems [9], [10]. See [11] for a recent survey.…”

Section: Introductionmentioning

confidence: 99%

Safety-Critical Kinematic Control of Robotic Systems

Singletary

Kolathaya

Ames

2022

IEEE Control Syst. Lett.

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Over the decades, kinematic controllers have proven to be practically useful for applications like set-point and trajectory tracking in robotic systems. To this end, we formulate a novel safety-critical paradigm for kinematic control in this paper. In particular, we extend the methodology of control barrier functions (CBFs) to kinematic equations governing robotic systems. We demonstrate a purely kinematic implementation of a velocity-based CBF, and subsequently introduce a formulation that guarantees safety at the level of dynamics. This is achieved through a new form CBFs that incorporate kinetic energy with the classical forms, thereby minimizing model dependence and conservativeness. The approach is then extended to underactuated systems. This method and the purely kinematic implementation are demonstrated in simulation on two robotic platforms: a 6-DOF robotic manipulator, and a cart-pole system.

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Section: Introductionmentioning

confidence: 99%

Safety-Critical Kinematic Control of Robotic Systems

Singletary

Kolathaya

Ames

2022

IEEE Control Syst. Lett.

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“…where ḣ(q, q) = J µ q, ḧ(q, q, q) = J µ q + Jµ q, and K α satisfies the conditions of [25, Theorem 2] (closedloop system matrix Hurwitz and total negative). This h(q) is a true ECBF, meaning (23) always has a solution for any q, q such that h(q) ≥ 0, as shown in the following proposition:…”

Section: A Control Barrier Functions For Singularity Avoidancementioning

confidence: 97%

“…where f des are desired task-space forces given by (12) and "Additional Constraints" might include contact, joint limit, or other constraints [6], [7], [23]. If J T τ = f des (i.e., the additional constraints are not active), then all of the passivity properties outlined above hold.…”

Section: Task-space Passivity-based Controlmentioning

confidence: 99%

Control Barrier Functions for Singularity Avoidance in Passivity-Based Manipulator Control

Kurtz¹,

Wensing²,

Lin³

2021

Preprint

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Task-space Passivity-Based Control (PBC) for manipulation has numerous appealing properties, including robustness to modeling error and safety for human-robot interaction. Existing methods perform poorly in singular configurations, however, such as when all the robot's joints are fully extended. Additionally, standard methods for constrained taskspace PBC guarantee passivity only when constraints are not active. We propose a convex-optimization-based control scheme that provides guarantees of singularity avoidance, passivity, and feasibility. This work paves the way for PBC with passivity guarantees under other types of constraints as well, including joint limits and contact/friction constraints. The proposed methods are validated in simulation experiments on a 7 degreeof-freedom manipulator.

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“…This challenge is similarly present when addressing stability using control Lyapunov functions [28]. For certain types of mechanical systems under input constraints, analytic CBFs can be constructed [29]. The construction of polynomial barrier functions towards certifying safety for polynomial systems by using sum-ofsquares (SOS) programming was proposed in [30].…”

Section: Related Workmentioning

confidence: 99%

Learning Robust Output Control Barrier Functions from Safe Expert Demonstrations

Lindemann¹,

Robey²,

Jiang³

et al. 2021

Preprint

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This paper addresses learning safe control laws from expert demonstrations. We assume that appropriate models of the system dynamics and the output measurement map are available, along with corresponding error bounds. We first propose robust output control barrier functions (ROCBFs) as a means to guarantee safety, as defined through controlled forward invariance of a safe set. We then present an optimization problem to learn ROCBFs from expert demonstrations that exhibit safe system behavior, e.g., data collected from a human operator. Along with the optimization problem, we provide verifiable conditions that guarantee validity of the obtained ROCBF. These conditions are stated in terms of the density of the data and on Lipschitz and boundedness constants of the learned function and the models of the system dynamics and the output measurement map. When the parametrization of the ROCBF is linear, then, under mild assumptions, the optimization problem is convex. We validate our findings in the autonomous driving simulator CARLA and show how to learn safe control laws from RGB camera images.

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Correct-by-Design Control Barrier Functions for Euler-Lagrange Systems with Input Constraints

Cited by 32 publications

References 13 publications

Safety-Critical Kinematic Control of Robotic Systems

Safety-Critical Kinematic Control of Robotic Systems

Control Barrier Functions for Singularity Avoidance in Passivity-Based Manipulator Control

Learning Robust Output Control Barrier Functions from Safe Expert Demonstrations

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