Safe Learning-Based Control of Elastic Joint Robots via Control Barrier Functions

TL;DR

This paper presents a method combining Gaussian process learning and control barrier functions to ensure safety in elastic joint robots, addressing unmodeled dynamics and enabling real-time safety enforcement.

Contribution

It introduces a novel approach that robustifies safety constraints using learned dynamics within a feedback linearizing control framework for elastic joint robots.

Findings

Successfully enforces safety constraints in simulations

Robustifies control barrier functions against model errors

Enables real-time safety enforcement via second-order cone programming

Abstract

Ensuring safety is of paramount importance in physical human-robot interaction applications. This requires both adherence to safety constraints defined on the system state, as well as guaranteeing compliant behavior of the robot. If the underlying dynamical system is known exactly, the former can be addressed with the help of control barrier functions. The incorporation of elastic actuators in the robot's mechanical design can address the latter requirement. However, this elasticity can increase the complexity of the resulting system, leading to unmodeled dynamics, such that control barrier functions cannot directly ensure safety. In this paper, we mitigate this issue by learning the unknown dynamics using Gaussian process regression. By employing the model in a feedback linearizing control law, the safety conditions resulting from control barrier functions can be robustified to take into account model errors, while remaining feasible. In order to enforce them on-line, we formulate the derived safety conditions in the form of a second-order cone program. We demonstrate our proposed approach with simulations on a two-degree-of-freedom planar robot with elastic joints.