Safety-Critical Kinematic Control of Robotic Systems

Abstract

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.

Model-Free Safety-Critical Control for Robotic Systems

“…Thus, this approach is a manifestation of control based on reducedorder models. While h is a CBF for the reduced-order model, h V is a CBF for the full system (13) as a dynamic extension of h, similar to the energy-based extension in [16]. Other reduced-order models of the form q = A(q)µ s with control input µ s ∈ R k and transformation A(q) ∈ R n×k can also be used.…”

“…Following [15], [16], we seek to maintain safety by synthesizing and tracking a safe velocity. This reduces the complexity of safety-critical control significantly, while velocity tracking controllers are widely used [17].…”

“…problem in a model-free fashion, without relying on the fullorder dynamics of the robot. We follow the approach of [15], [16], where a safe velocity was designed based on reducedorder kinematics -i.e., without the full dynamical model -and this safe velocity was tracked by a velocity tracking controller. This approach is agnostic to the application domain, although the underlying tracking controllers depend on the system and their synthesis or tuning may require knowledge about the full model.…”

Model-Free Safety-Critical Control for Robotic Systems

“…Following [14], [15], we seek to maintain safety by designing a safe velocity and tracking this velocity. This method reduces the complexity of safety-critical control significantly, while velocity tracking controllers are widely used [16].…”

“…In this paper, we rely on CBFs to synthesize safe controllers for robotic systems, while handling the safety-critical aspect of this problem in a model-free fashion, i.e., without relying on the full-order dynamics of the robot. Namely, we follow the approach of [14], [15], where a safe velocity was designed based on reduced-order kinematics -i.e., without the full dynamic model -and this safe velocity was tracked by a velocity tracking controller. We emphasize that this Fig.…”