Design and control of the nonholonomic manipulator

Yoshihiko Nakamura, Woojin Chung, Ole Jacob Sordalen

Research output: Contribution to journalArticlepeer-review

70 Citations (Scopus)


Nonholonomic constraints are exploited to design a controllable n-joint manipulator with only two inputs. Gears subject to nonholonomic constraints are designed to transmit velocities from the inputs to the passive joints. The system possesses a triangular structure for which a conversion into chained form is presented. The nonholonomic manipulator can, therefore, be controlled with an open loop or a closed loop using existing controllers for chained form. Mechanical design is established, and experimental results proved the usefulness of design of the nonholonomic manipulator and applied control schemes. While previous publications have assumed that the nonholonomic systems are given and have developed theory for these systems, this paper points out a new direction where the nonholonomic theory is used to design controllable and stabilizable systems.

Original languageEnglish
Pages (from-to)48-59
Number of pages12
JournalIEEE Transactions on Robotics and Automation
Issue number1
Publication statusPublished - 2001 Feb

Bibliographical note

Funding Information:
The authors would like to acknowledge the reviewers of this paper for their valuable comments. W. Chung acknowledges the Pohang Steel Company Scholarship Society.

Funding Information:
Manuscript received December 4, 1999; revised August 11, 2000. This paper was recommended for publication by Associate Editor A. Bicchi and Editor A. De Luca upon evaluation of the reviewers’ comments. This work was supported in part by NTT Company, Ltd., Japan Society of the Promotion of Science, the Center of Maritime Control Systems at NTH/SINTEF, and Ministry of Culture, Sports and Education under the Grant in Aid of Scientific Research (General Research (b)04452153). This paper was presented in part at the 1994 IEEE International Conference on Robotics and Automation, San Diego, CA, May 1994.


  • Chained form
  • Nonholonomic constraint
  • Nonlinear control
  • Robot manipulator
  • Underactuated system

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering


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