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Stitching Dynamic Movement Primitives and Image-based Visual Servo Control

Ghananeel Rotithor, Iman Salehi, Edward Tunstel, Ashwin P. Dani

TL;DR

A generalized control scheme that switches between motion generation using DMP and IBVS control and stability analysis of the switched system using multiple Lyapunov functions shows that the state trajectories converge to a bound asymptotically.

Abstract

Utilizing perception for feedback control in combination with Dynamic Movement Primitive (DMP)-based motion generation for a robot's end-effector control is a useful solution for many robotic manufacturing tasks. For instance, while performing an insertion task when the hole or the recipient part is not visible in the eye-in-hand camera, a learning-based movement primitive method can be used to generate the end-effector path. Once the recipient part is in the field of view (FOV), Image-based Visual Servo (IBVS) can be used to control the motion of the robot. Inspired by such applications, this paper presents a generalized control scheme that switches between motion generation using DMPs and IBVS control. To facilitate the design, a common state space representation for the DMP and the IBVS systems is first established. Stability analysis of the switched system using multiple Lyapunov functions shows that the state trajectories converge to a bound asymptotically. The developed method is validated by two real world experiments using the eye-in-hand configuration on a Baxter research robot.

Stitching Dynamic Movement Primitives and Image-based Visual Servo Control

TL;DR

A generalized control scheme that switches between motion generation using DMP and IBVS control and stability analysis of the switched system using multiple Lyapunov functions shows that the state trajectories converge to a bound asymptotically.

Abstract

Utilizing perception for feedback control in combination with Dynamic Movement Primitive (DMP)-based motion generation for a robot's end-effector control is a useful solution for many robotic manufacturing tasks. For instance, while performing an insertion task when the hole or the recipient part is not visible in the eye-in-hand camera, a learning-based movement primitive method can be used to generate the end-effector path. Once the recipient part is in the field of view (FOV), Image-based Visual Servo (IBVS) can be used to control the motion of the robot. Inspired by such applications, this paper presents a generalized control scheme that switches between motion generation using DMPs and IBVS control. To facilitate the design, a common state space representation for the DMP and the IBVS systems is first established. Stability analysis of the switched system using multiple Lyapunov functions shows that the state trajectories converge to a bound asymptotically. The developed method is validated by two real world experiments using the eye-in-hand configuration on a Baxter research robot.

Paper Structure

This paper contains 14 sections, 3 theorems, 37 equations, 6 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Image-Based Visual Servo Control
  4. Task Space Dynamic Movement Primitives
  5. Combined Position and Orientation DMPs
  6. Learning DMP Parameters
  7. Stability Analysis of DMPs
  8. Stability Analysis of the Switched System
  9. Experiments
  10. Experimental Setup
  11. Experiment 1
  12. Experiment 2
  13. Experiment 3
  14. Conclusion

Key Result

Theorem 1

If Assumptions 1 - 3 hold, then the dynamics in (eq:VS_error_dyn) are uniformly ultimately bounded in the sense that for an initial time $t_{0}\geq 0$ if where $x_{0}= x(t_{0})$, provided that $\delta_{1}>\sqrt{\overline{\gamma_{v}}\eta/\underline{\gamma_{v}}\beta_{1}}$, and the controller gains $k_{p}$ and $k_{v}$ satisfy the sufficient condition where $k^{\star}=-\frac{\bar{l}}{2}-\frac{\bar{k

Figures (6)

  • Figure 1: Reference frames attached to the camera, the goal location and the inertial reference frame.
  • Figure 2: Block diagram of the DMP-IBVS switched system.
  • Figure 3: The experimental setup showing Baxter's end-effector with an eye-in-hand configuration observing the ArUco marker.
  • Figure 4: Experimental results for the DMP and IBVS for a single switching instance at $16.4\:\mathrm{s}$. (a) Camera acceleration generated by DMP controller till $16.4\:\mathrm{s}$ and camera acceleration generated by IBVS controller after $16.4\:\mathrm{s}$ (b) Pose error $e_{p}(t)$ converges to a bound. (c) Image feature errors $e_{i}(t)$ computed after $16.4\:\mathrm{s}$. (d) Value of Lyapunov function $V_{\sigma(x,t)}(x(t),t)$, with left y-axis showing the scale for $V_{d}(x(t))$ and right y-axis showing the scale for $V_{v}(x(t),t)$.
  • Figure 5: Experimental results for the DMP and IBVS with frequent feature occlusion (a) Camera acceleration generated by DMP controller and the IBVS controller in the presence of occlusion with grey dashed-dotted lines showing the switching instances. (b) Pose error $e_{p}(t)$ converges to a bound in the presence of multiple switching instances. (c) Image feature errors $e_{i}(t)$ computed when all the features are visible and satisfy the threshold condition in Algorithm 1. (d) Value of Lyapunov function $V_{\sigma(x,t)}(x(t),t)$ during multiple switching instances, with left y-axis showing the scale for $V_{d}(x(t))$ and right y-axis showing the scale for $V_{v}(x(t),t)$.
  • ...and 1 more figures

Theorems & Definitions (12)

  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Theorem 1
  • Remark 5
  • Theorem 2
  • Remark 6
  • Definition 1
  • Theorem 3
  • ...and 2 more