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Safe Aerial Manipulator Maneuvering and Force Exertion via Control Barrier Functions

Dimitris Chaikalis, Vinicius Goncalves, Nikolaos Evangeliou, Anthony Tzes, Farshad Khorrami

Abstract

This article introduces a safe control strategy for application of forces to an external object using a dexterous robotic arm mounted on an unmanned Aerial Vehicle (UAV). A hybrid force-motion controller has been developed for this purpose. This controller employs a Control Barrier Function (CBF) constraint within an optimization framework based on Quadratic Programming (QP). The objective is to enforce a predefined relationship between the end-effector's approach motion and its alignment with the surface, thereby ensuring safe operational dynamics. No compliance model for the environment is necessary to implement the controller, provided end-effector force feedback exists. Furthermore, the paper provides formal results, like guarantees of feasibility for the optimization problem, continuity of the controller input as a function of the configuration, and Lyapunov stability. In addition, it presents experimental results in various situations to demonstrate its practical applicability on an aerial manipulator platform.

Safe Aerial Manipulator Maneuvering and Force Exertion via Control Barrier Functions

Abstract

This article introduces a safe control strategy for application of forces to an external object using a dexterous robotic arm mounted on an unmanned Aerial Vehicle (UAV). A hybrid force-motion controller has been developed for this purpose. This controller employs a Control Barrier Function (CBF) constraint within an optimization framework based on Quadratic Programming (QP). The objective is to enforce a predefined relationship between the end-effector's approach motion and its alignment with the surface, thereby ensuring safe operational dynamics. No compliance model for the environment is necessary to implement the controller, provided end-effector force feedback exists. Furthermore, the paper provides formal results, like guarantees of feasibility for the optimization problem, continuity of the controller input as a function of the configuration, and Lyapunov stability. In addition, it presents experimental results in various situations to demonstrate its practical applicability on an aerial manipulator platform.
Paper Structure (21 sections, 14 theorems, 35 equations, 18 figures)

This paper contains 21 sections, 14 theorems, 35 equations, 18 figures.

Table of Contents

  1. Introduction
  2. Related Work and Contribution
  3. Mathematical notation
  4. Problem Statement & Assumptions
  5. Controller synthesis
  6. Basic definitions
  7. The force exertion subtask
  8. The alignment subtask
  9. Joint and configuration velocity limits
  10. Optimization-based controller
  11. Controller Analysis
  12. Feasibility, uniqueness and continuity of the controller
  13. Stability results and equilibrium point analysis
  14. Experimental Results
  15. Experiment 1: Above the $B=0$ curve
  16. ...and 6 more sections

Key Result

Lemma 1

The function $V_F$ is Lyapunov-like. $\qedsymbol$

Figures (18)

  • Figure 1: (a) Starting position, (b) intermediate position, and (c) final position of UAM for force exertion task.
  • Figure 2: Example of Unmanned Aerial Manipulator (UAM) system .
  • Figure 3: Coordinate frames of an example UAM system
  • Figure 4: Alignment error ($A$) vs. distance ($Z$) function diagram for UAM. Any safe trajectory $q(t)$ should be such that $(A(q(t)),Z(q(t)))$ should be in the green region (i.e., $B(q(t)) > 0$). This will be enforced by the controller.
  • Figure 5: UAM during hard contact (top) and inclined force exertion (bottom), with annotated components.
  • ...and 13 more figures

Theorems & Definitions (27)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Lemma 1
  • Definition 6
  • Definition 7
  • Definition 8
  • Definition 9
  • ...and 17 more