Energy based Control Barrier Functions for Robotic Systems

Abstract

<div>Control barrier function (CBF) based Quadratic Programs (QPs) were introduced in early 2014 as a means to guarantee safety in affine control systems in conjunction with stability/tracking. However, due to the presence of model-based terms, they fail to provide guarantees under model perturbations. Therefore, in this paper, we propose a new class of CBFs for robotic systems that augment kinetic energy with the traditional forms. We show that with torque limits permitting, and with the kinematic models accurately known, forward invariance of safe sets generated by kinematic constraints (position and velocity) can be guaranteed. The proposed methodology is motivated by the control Lyapunov function (CLF) based QPs that use the kinetic energy function. By the property of CBF-QPs, we show that the pointwise min-norm control laws obtained are feasible and Lipschitz continuous, and can be derived analytically via the KKT conditions. In order to include stability with safety, we also augment CLF based constraints in the CBF-QPs to realize a unified control law that allows tracking with safety irrespective of the inertial parameters of the robot. We will demonstrate the robustness of this class of CBF-QPs in two robotic platforms: a 1-DOF and a 2-DOF manipulator, by scaling the masses by up to 100, and then simulating the resulting dynamics.</div>

Safety-Critical Kinematic Control of Robotic Systems

“…We now wish to establish the main result of this paper: that guarantees safety for the dynamics of a robotic system. To do this, we first introduce an alternative formulation of the energy-based CBFs shown in [13] for robotic systems.…”

“…Recently, energy-based reciprocal control barrier functions were introduced [13] as a means to provide robust safety guarantees for fully-actuated robotic platforms with model 1 Mechanical and Civil Engineering, Caltech, Pasadena, CA, USA, 91125.…”

Safety-Critical Kinematic Control of Robotic Systems

“…This construction is similar to the augmentation of kinetic energy in [16] for reciprocal control barrier functions. While the reciprocal formulation has the advantage of having no added conservatism, due to the set remaining unchanged, it does not have well-defined behavior on the boundary of the set and outside of it, making it less popular for implementation.…”

“…We now wish to establish the main result of this paper: that guarantees safety for the dynamics of a robotic system. To do this, we first introduce an alternative formulation of the energy-based CBFs shown in [16] for robotic systems. We consider Euler-Lagrangian dynamics of the form:…”

“…Recently, energy-based reciprocal control barrier functions were introduced [16] as a means to provide robust safety 1 Mechanical and Civil Engineering, Caltech, Pasadena, CA, USA, 91125.…”