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Passive Realizations of Series Elastic Actuation: Effects of Plant and Controller Dynamics on Haptic Rendering Performance

Celal Umut Kenanoglu, Volkan Patoglu

TL;DR

It is demonstrated that passive physical equivalents make the effect of controller gains explicit and establish a natural means for effective impedance analysis and promote co-design thinking by enforcing simultaneous and unbiased consideration of (possibly negative) controller gains and plant parameters.

Abstract

We introduce minimal passive physical equivalents of series (damped) elastic actuation (S(D)EA) under closed-loop control to determine the effect of different plant parameters and controller gains on the closed-loop performance of the system and to help establish an intuitive understanding of the passivity bounds. Furthermore, we explicitly derive the feasibility conditions for these passive physical equivalents and compare them to the necessary and sufficient conditions for the passivity of S(D)EA under velocity sourced impedance control (VSIC) to establish their relationship. Through the passive physical equivalents, we rigorously compare the effect of different plant dynamics (e.g., SEA and SDEA) on the system performance. We demonstrate that passive physical equivalents make the effect of controller gains explicit and establish a natural means for effective impedance analysis. We also show that passive physical equivalents promote co-design thinking by enforcing simultaneous and unbiased consideration of (possibly negative) controller gains and plant parameters. We demonstrate the usefulness of negative controller gains when coupled to properly designed plant dynamics. Finally, we provide experimental validations of our theoretical results and characterizations of the haptic rendering performance of S(D)EA under VSIC.

Passive Realizations of Series Elastic Actuation: Effects of Plant and Controller Dynamics on Haptic Rendering Performance

TL;DR

It is demonstrated that passive physical equivalents make the effect of controller gains explicit and establish a natural means for effective impedance analysis and promote co-design thinking by enforcing simultaneous and unbiased consideration of (possibly negative) controller gains and plant parameters.

Abstract

We introduce minimal passive physical equivalents of series (damped) elastic actuation (S(D)EA) under closed-loop control to determine the effect of different plant parameters and controller gains on the closed-loop performance of the system and to help establish an intuitive understanding of the passivity bounds. Furthermore, we explicitly derive the feasibility conditions for these passive physical equivalents and compare them to the necessary and sufficient conditions for the passivity of S(D)EA under velocity sourced impedance control (VSIC) to establish their relationship. Through the passive physical equivalents, we rigorously compare the effect of different plant dynamics (e.g., SEA and SDEA) on the system performance. We demonstrate that passive physical equivalents make the effect of controller gains explicit and establish a natural means for effective impedance analysis. We also show that passive physical equivalents promote co-design thinking by enforcing simultaneous and unbiased consideration of (possibly negative) controller gains and plant parameters. We demonstrate the usefulness of negative controller gains when coupled to properly designed plant dynamics. Finally, we provide experimental validations of our theoretical results and characterizations of the haptic rendering performance of S(D)EA under VSIC.
Paper Structure (23 sections, 6 theorems, 16 equations, 4 figures, 2 tables)

This paper contains 23 sections, 6 theorems, 16 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Passivity Analysis of SEA
  4. Passivity Analysis of SDEA
  5. Realization of Passive Physical Equivalents
  6. Rendering Performance
  7. Preliminaries
  8. System Description
  9. Passivity Theorems
  10. Passive Physical Equivalents and Inerter
  11. Passive Physical Equivalents of S(D)EA
  12. Voigt Model Rendering
  13. Series Damped Elastic Actuation (SDEA)
  14. Series Elastic Actuation (SEA)
  15. Spring Rendering
  16. ...and 8 more sections

Key Result

Theorem 1

A rational LTI impedance transfer function $Z(s)$ with real coefficients is passive if and only if: (1) Z(s) has no poles in the right half plane, and (2) $Re[Z(jw)] \ge 0$ for $w \in (-\infty,\infty)$, and (3) Any poles of Z(s) on the imaginary axis are simple with positive and real residues.

Figures (4)

  • Figure 1: Block diagram of S(D)EA under VSIC
  • Figure 2: Spring rendering performance and K-B plot comparison during Voigt model rendering between S(D)EA under VSIC
  • Figure 3: Passivity bounds vs experimental coupled stability for SDEA/SEA during Voigt model and spring rendering
  • Figure 4: (a) Null impedance rendering performance (potato chip) test for $G_t$ = 20, 25 and 30 rad/(s N-m), (b) Virtual stiffness rendering for $K_{ref}$ = 50 and 100 N-m/rad when $G_t$ =30 rad/(s N-m), and (c) Tracking performance of SEA during virtual spring rendering with $K_{ref}$ = 100 N-m/rad and $G_t$ = 30 rad/(s N-m).

Theorems & Definitions (13)

  • Theorem 1: colgate_hogan_1988Haykin70
  • Lemma 1
  • Lemma 2
  • Lemma 3: Mengilli2020
  • Definition 1
  • Definition 2
  • Remark : 2
  • Remark : 3
  • Proposition 1
  • Remark : 1
  • ...and 3 more