Control of A New Type of Undulatory Wheeled Locomotor: A Trident Steering Walker Based on Chained Form

Hiroaki Yamaguchi

doi:10.20965/jrm.2009.p0541

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JRM Vol.21 No.4 pp. 541-553

doi: 10.20965/jrm.2009.p0541

(2009)

Paper:

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Control of A New Type of Undulatory Wheeled Locomotor: A Trident Steering Walker Based on Chained Form

Hiroaki Yamaguchi

Department of Integrated Information Technology
College of Science and Engineering, Aoyama Gakuin University
5-10-1 Fuchinobe, Sagamihara-shi, Kanagawa 229-8558, Japan

Received:

June 3, 2008

Accepted:

March 5, 2009

Published:

August 20, 2009

Keywords:

nonholonomic system, wheeled locomotor, undulatory locomotion, differential geometry, chained form

Abstract

This paper introduces and describes a new type of undulatory wheeled locomotor, which we refer to as a “trident steering walker.” The wheeled locomotor is a nonholonomic mechanical system, which consists of an equilateral triangular base, three joints, three links and four steering systems. The equilateral triangular base has a steering system at its center of mass. At each apex of the base is a joint which connects the base and a link. The link has a steering system at its midpoint. The wheeled locomotor transforms driving the three joints into its movement by operating the four steering systems. This means that the wheeled locomotor achieves undulatory locomotion in which changes in its own shape are transformed into its net displacement. We assume that there is a virtual joint at the end of the first link. The virtual joint connects the first link and a virtual link which has a virtual axle at its midpoint and a virtual steering system at its end. We prove that, by assuming the presence of such virtual mechanical elements, it is possible to convert the kinematical equation of the trident steering walker into five-chain, single-generator chained form in a mathematical framework, differential geometry. Based on chained form, we derive a path following feedback control method which causes the trident steering walker to follow a straight path. We also define a performance index of propulsion of the trident steering walker to design its control parameters. The validity of the mechanical design of the trident steering walker, the conversion of its kinematical equation into chained form, the straight path following feedback control method, and the design of the control parameters reflecting the performance index of propulsion has been verified by computer simulations.

Cite this article as:

H. Yamaguchi, “Control of A New Type of Undulatory Wheeled Locomotor: A Trident Steering Walker Based on Chained Form,” J. Robot. Mechatron., Vol.21 No.4, pp. 541-553, 2009.

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References

[1] S. Hirose, “Biologically Inspired Robots (Snake-like Locomotor and Manipulator),” Oxford University Press, 1993.
[2] J.P. Ostrowski and J.W. Burdick, “The Geometric Mechanics of Undulatory Robotic Locomotion,” Int. Journal of Robotics Research, Vol.17, No.7, pp. 683-701, 1998.
[3] S. Hirose and H. Takeuchi, “Study on Roller-Walk (Basic Characteristics and Its Control),” Proc. of the 1996 IEEE Int. Conf. on Robotics and Automation, pp. 3265-3270, 1996.
[4] P.S. Krishnaprasad and D.P. Tsakiris, “Oscillations, SE(2)-Snakes and Motion Control: A Study of the Roller Racer,” Dynamical Systems, Vol.16, No.4, pp. 347-397, 2001.
[5] S. Chitta, F.W. Heger, and V. Kumar, “Design and Gait Control of a Rollerblading Robot,” Proc. of the 2004 IEEE Int. Conf. on Robotics and Automation, pp. 3944-3949, 2004.
[6] S. Chitta, P. Cheng, E. Frazzoli, and V. Kumar, “RoboTrikke: A Novel Undulatory Locomotion System,” Proc. of the 2005 IEEE Int. Conf. on Robotics and Automation, pp. 1597-1602, 2005.
[7] C. Samson, “Control of Chained Systems: Application to Path Following and Time-Varying Point-Stabilization of Mobile Robots,” IEEE Transactions on Automatic Control, Vol.40, No.1, pp. 64-77, 1995.
[8] D.M. Tilbury, O.J. Sordalen, L.G. Bushnell, and S.S. Sastry, “A Multisteering Trailer System: Conversion into Chained Form using Dynamic Feedback,” IEEE Transactions on Robotics and Automation, Vol.11, No.6, pp. 807-818, 1995.
[9] D.M. Tilbury and S.S. Sastry, “The Multi-Steering N-Trailer System: A Case Study of Goursat Normal Forms and Prolongations,” Int. Journal of Robust and Nonlinear Control, Vol.5, No.4, pp. 343-364, 1995.
[10] H. Yamaguchi and T. Arai, “A Path Following Feedback Control Method for A Cooperative Transportation System with Two Car-Like Mobile Robots,” Transactions on Society of Instruments and Control Engineers (SICE in Japanese), Vol.39, No.6, pp. 575-584, 2003.
[11] A. Isidori, “Nonlinear Control Systems,” Second Edition, Springer-Verlag, New York, 1989.
[12] A. Ghasempoor and N. Sepehri, “A Measure of Machine Stability for Moving Base Manipulators,” Proc. of the 1995 IEEE Int. Conf. on Robotics and Automation, pp. 2249-2254, 1995.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] S. Hirose, “Biologically Inspired Robots (Snake-like Locomotor and Manipulator),” Oxford University Press, 1993.

[2] [2] J.P. Ostrowski and J.W. Burdick, “The Geometric Mechanics of Undulatory Robotic Locomotion,” Int. Journal of Robotics Research, Vol.17, No.7, pp. 683-701, 1998.

[3] [3] S. Hirose and H. Takeuchi, “Study on Roller-Walk (Basic Characteristics and Its Control),” Proc. of the 1996 IEEE Int. Conf. on Robotics and Automation, pp. 3265-3270, 1996.

[4] [4] P.S. Krishnaprasad and D.P. Tsakiris, “Oscillations, SE(2)-Snakes and Motion Control: A Study of the Roller Racer,” Dynamical Systems, Vol.16, No.4, pp. 347-397, 2001.

[5] [5] S. Chitta, F.W. Heger, and V. Kumar, “Design and Gait Control of a Rollerblading Robot,” Proc. of the 2004 IEEE Int. Conf. on Robotics and Automation, pp. 3944-3949, 2004.

[6] [6] S. Chitta, P. Cheng, E. Frazzoli, and V. Kumar, “RoboTrikke: A Novel Undulatory Locomotion System,” Proc. of the 2005 IEEE Int. Conf. on Robotics and Automation, pp. 1597-1602, 2005.

[7] [7] C. Samson, “Control of Chained Systems: Application to Path Following and Time-Varying Point-Stabilization of Mobile Robots,” IEEE Transactions on Automatic Control, Vol.40, No.1, pp. 64-77, 1995.

[8] [8] D.M. Tilbury, O.J. Sordalen, L.G. Bushnell, and S.S. Sastry, “A Multisteering Trailer System: Conversion into Chained Form using Dynamic Feedback,” IEEE Transactions on Robotics and Automation, Vol.11, No.6, pp. 807-818, 1995.

[9] [9] D.M. Tilbury and S.S. Sastry, “The Multi-Steering N-Trailer System: A Case Study of Goursat Normal Forms and Prolongations,” Int. Journal of Robust and Nonlinear Control, Vol.5, No.4, pp. 343-364, 1995.

[10] [10] H. Yamaguchi and T. Arai, “A Path Following Feedback Control Method for A Cooperative Transportation System with Two Car-Like Mobile Robots,” Transactions on Society of Instruments and Control Engineers (SICE in Japanese), Vol.39, No.6, pp. 575-584, 2003.

[11] [11] A. Isidori, “Nonlinear Control Systems,” Second Edition, Springer-Verlag, New York, 1989.

[12] [12] A. Ghasempoor and N. Sepehri, “A Measure of Machine Stability for Moving Base Manipulators,” Proc. of the 1995 IEEE Int. Conf. on Robotics and Automation, pp. 2249-2254, 1995.