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Linear controllability of two multi-link robotic systems with multiple unactuated joints.

Xin Xin1, Yannian Liu2, Kanjian Zhang2

  • 1Faculty of Computer Science and Systems Engineering, Okayama Prefectural University, 111 Kuboki, Soja, Okayama 719-1197, Japan.

ISA Transactions
|June 9, 2022
PubMed
Summary

Actuating the primary joint is essential for the linear controllability of underactuated robotic systems. This study proves this for both inverted pendulums and planar robots, regardless of their physical parameters.

Keywords:
Inverted pendulum–cart systemLinearly controllableMulti-link pendulumStrong structural controllabilityUnderactuation

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Area of Science:

  • Robotics
  • Control Theory
  • Mechanical Engineering

Background:

  • Underactuated robotic systems present unique control challenges.
  • Linear controllability is crucial for precise motion control and stability analysis.
  • Previous research has explored controllability but often with specific system constraints.

Purpose of the Study:

  • To determine the necessary conditions for linear controllability in two distinct underactuated multi-link robotic systems.
  • To provide generalizable insights into the control of systems with fewer actuators than degrees of freedom.
  • To establish fundamental principles for designing and controlling complex robotic systems.

Main Methods:

  • Mathematical analysis of system dynamics.
  • Linearization of system models around equilibrium points and trajectories.
  • Derivation of necessary and sufficient conditions for linear controllability.
  • Illustrative case studies using specific robotic configurations.

Main Results:

  • For an n-link inverted pendulum on a cart, linear controllability is achieved if and only if the cart is actuated.
  • For an n-link planar robot, linear controllability is achieved if and only if its first joint is actuated.
  • These conditions hold irrespective of physical parameters and the actuation status of other joints.

Conclusions:

  • The actuation of specific joints is a critical determinant of linear controllability in underactuated robotic systems.
  • This research offers a foundational understanding for controlling complex robotic manipulators and pendulums.
  • The findings provide valuable insights for future robotic system design and control strategy development.