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Generalized Flexible Hybrid Cable-Driven Robot (HCDR): Modeling, Control, and Analysis

Ronghuai Qi, Amir Khajepour, William W. Melek

TL;DR

Results show that the fully integrated control strategy can improve significantly the tracking performance of the end-effector and address the limitations of existing stiffness optimization approaches.

Abstract

This paper presents a generalized flexible Hybrid Cable-Driven Robot (HCDR). For the proposed HCDR, the derivation of the equations of motion and proof provide a very effective way to find items for generalized system modeling. The proposed dynamic modeling approach avoids the drawback of traditional methods and can be easily extended to other types of hybrid robots, such as a robot arm mounted on an aircraft platform. Additionally, another goal of this paper is to develop integrated control systems to reduce vibrations and improve the accuracy and performance of the HCDR. To achieve this goal, redundancy resolution, stiffness optimization, and control strategies are studied. The proposed optimization problem and algorithm address the limitations of existing stiffness optimization approaches. Three types of control architecture are proposed, and their performances (i.e., reducing undesirable vibrations and trajectory tracking errors, especially for the end-effector) are evaluated using several well-designed case studies. Results show that the fully integrated control strategy can improve the tracking performance of the end-effector significantly.

Generalized Flexible Hybrid Cable-Driven Robot (HCDR): Modeling, Control, and Analysis

TL;DR

Results show that the fully integrated control strategy can improve significantly the tracking performance of the end-effector and address the limitations of existing stiffness optimization approaches.

Abstract

This paper presents a generalized flexible Hybrid Cable-Driven Robot (HCDR). For the proposed HCDR, the derivation of the equations of motion and proof provide a very effective way to find items for generalized system modeling. The proposed dynamic modeling approach avoids the drawback of traditional methods and can be easily extended to other types of hybrid robots, such as a robot arm mounted on an aircraft platform. Additionally, another goal of this paper is to develop integrated control systems to reduce vibrations and improve the accuracy and performance of the HCDR. To achieve this goal, redundancy resolution, stiffness optimization, and control strategies are studied. The proposed optimization problem and algorithm address the limitations of existing stiffness optimization approaches. Three types of control architecture are proposed, and their performances (i.e., reducing undesirable vibrations and trajectory tracking errors, especially for the end-effector) are evaluated using several well-designed case studies. Results show that the fully integrated control strategy can improve the tracking performance of the end-effector significantly.

Paper Structure

This paper contains 17 sections, 2 theorems, 40 equations, 8 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Generalized System Modeling
  3. Equations of Motion of the CDPR
  4. Equations of Motion of the HCDR
  5. Redundancy Resolution
  6. Stiffness Optimization
  7. HCDR Example for Analysis
  8. HCDR Configuration and Kinematic Constraints
  9. Dynamics of the 9-DOF HCDR
  10. Vibration Control Design
  11. Independent Control
  12. Integrated Control-I
  13. Integrated Control-II (Fully Integrated Control)
  14. Control Performance and Evaluation
  15. Case Study--Comparison of Three Control Structures
  16. ...and 2 more sections

Key Result

Lemma 1

Let ${{\vec{\dot \theta}}_{ak}} \in {\mathbb{R}^3}$ be the vector of joint velocity about its body-fixed axis. Then the $j$th angle velocity vector is equal to ${\omega _{acj}} = {[R_m^{a0}R_{a0}^{aj}]^T}{\omega _m} + \sum\limits_{k = 0}^j {\left\{ {{{[R_{ak}^{aj}]}^T}{{\vec{\dot \theta}}_{ak}}} \ri

Figures (8)

  • Figure 1: Configuration of a generalized $(n+m)$-DOF HCDR with an $n$-DOF CDPR and an $m$-DOF robot arm, where the robot arm is mounted on the CDPR.
  • Figure 2: Configuration of the 9-DOF HCDR. The CDPR is driven by four actuators with 12 cables; the robot arm has three joints with the first, second, and third joints rotating about $Z_{a0}$-, $Y_{a1}$-, and $Y_{a2}$-axis (i.e., the corresponding moving frames), respectively.
  • Figure 3: Three types of control architecture of the HCDR. (a) Independent control with the CDPR and the robot arm are decoupled; (b) Integrated control-I with the CDPR and the robot arm are coupled; and (c) Integrated control-II with the CDPR and the robot arm are coupled.
  • Figure 4: An stiffness optimization example using \ref{['algorithm:J1_optimalRefInput']}, where the mobile platform is stationary (i.e., position-holding at $[p_{mx},p_{mz}]^T=[0,0]^T$) and the upper unstretched cable lengths are equal to $L_{01}=L_{02}=1.005 \; \rm{m}$. (a) $X$-$Y$ view, (b) 3D view, and (c) eigenvalues of the stiffness matrix $K$.
  • Figure 5: End-effector trajectory in Cartesian coordinates.
  • ...and 3 more figures

Theorems & Definitions (4)

  • Definition 1
  • Lemma 1
  • proof
  • Proposition 1