An Input Observer-Based Stiffness Estimation Approach for Flexible Robot Joints

This letter addresses the stiffness estimation problem for flexible robot joints, driven by variable stiffness actuators in antagonistic setups. Due to the difficulties of achieving consistent production of these actuators and the time-varying nature of their internal flexible elements, which are subject to plastic deformation over time, it is currently a challenge to precisely determine the total flexibility torque applied to a robot's joint and the corresponding joint stiffness. Herein, by considering the flexibility torque acting on each motor as an unknown signal and building upon Unknown Input Observer theory, a solution for electrically-driven actuators is proposed, which consists of a linear estimator requiring only knowledge about the positions of the joints and the motors as well as the drive's dynamic parameters. Beyond its linearity advantage, another appealing feature of the solution is the lack of need for torque and velocity sensors. The presented approach is first verified via simulations and then successfully tested on an experimental setup, comprising bidirectional antagonistic variable stiffness actuators.

I. Introduction

Soft robots have been brought into the limelight as cutting-edge technology, primarily with the vision of enabling humans a harmless physical interaction with robots [1]. Practically divided into soft-bodied and articulated soft robots, whose dynamics have just recently been shown to match under suitable assumptions [2], they are intrinsically endowed with the capacity of dynamically modulating elasticity while moving, which opens many opportunities for the amelioration of various life aspects [3], [4]. For articulated soft robots, i.e., robots with elasticity concentrated mostly at their joints, the achievement of human-like abilities, such as dexterity and robustness, relies on the availability of so-called Variable Stiffness Actuators (VSA). Most attention is nowadays turned to electrically-driven VSAs, that enable accurate position and velocity control, while also allowing online compliance adjustment [5]. These actuators are generally preferred to their pneumatic and hydraulic counterparts for their greater compactness, for being more silent, and not requiring external devices, such as air compressors. Systems such as Kuka's lightweight robot, endowed with active compliance control [6], and other novel cost-effective, open-source solutions, including e.g., the products by Natural Machine Motion Initiative [7], are now emerging on the market, all sharing the common aspiration to empower faster development of this field.