Abstract
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.