Numerical quantification of controllability in the null space for redundant manipulators

Seonwoo Kim, Seongseop Yun, Dongjun Shin

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Redundant motion, which is possible when robotic manipulators are over-actuated, can be used to control robot arms for a wide range of tasks. One of the best known methods for controlling redundancy is the null space projection, which assigns a priority while executing desired tasks. However, when the manipulator is projected into null space, its motion would be limited, since the motion is only permitted in the direction that does not interfere with the primary task. In this study, we have analyzed the null space projector matrix to derive the appropriate direction of the redundant motion by quantifying the allowed motion in each direction. As a result, we have found an ellipsoidal boundary, in which the redundant motion is permitted to move. We have named this ellipsoidal boundary as ’null space quality’ in directions. The proposed null space quality shows similar aspects with that of the robot manipulability, but it reveals a decisively different value when the manipulator operates within the null space. The experimental results showed that the robotic manipulator tracked the sinusoidal input trajectory with reduced root mean square (RMS) error by 33.84%. Furthermore, we have demonstrated the obstacle avoidance of a robotic arm utilizing the null space projector while considering the null space quality.

Original languageEnglish
Article number6190
JournalApplied Sciences (Switzerland)
Issue number13
Publication statusPublished - 2021 Jul 1

Bibliographical note

Funding Information:
Funding: This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government. (MSIT) (NRF-2021R1A2C2008379). Furthermore, this study was supported by the Chung-Ang University Graduate Research Scholarship in 2019.

Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.

All Science Journal Classification (ASJC) codes

  • Materials Science(all)
  • Instrumentation
  • Engineering(all)
  • Process Chemistry and Technology
  • Computer Science Applications
  • Fluid Flow and Transfer Processes


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