Asymptotic Stabilization of Nonholonomic Robots Leveraging Singularity

Due to the nonholonomic constraints as well as the constraints on torque and power resources, it is challenging to design a controller to asymptotically stabilize a nonholonomic robot at a predefined pose. In this paper, a switched controller is introduced for the asymptotic stabilization of nonholonomic robots using singularity, which is deemed undesirable due to loss of controllability. The proposed controller is inspired by a new insight on the singularity set of the nonholonomic robot, i.e., the singularity set includes a subset that can be asymptotically stabilized. The proposed controller is applicable to chained form systems that make an important class of drift-less nonholonomic systems, especially for those robots with a differential-drive mechanism. Considering its simplicity and efficiency, our method has the potential to be used in practice.

[1]  R. W. Brockett,et al.  Asymptotic stability and feedback stabilization , 1982 .

[2]  Zhong-Ping Jiang,et al.  Velocity-Scheduling Control for a Unicycle Mobile Robot: Theory and Experiments , 2009, IEEE Transactions on Robotics.

[3]  Charles E. Thorpe,et al.  Integrated mobile robot control , 1991 .

[4]  Nils J. Nilsson,et al.  A Formal Basis for the Heuristic Determination of Minimum Cost Paths , 1968, IEEE Trans. Syst. Sci. Cybern..

[5]  Henk Nijmeijer,et al.  Tracking Control of Mobile Robots: A Case Study in Backstepping , 1997, Autom..

[6]  Xi Liu,et al.  Motion-Estimation-Based Visual Servoing of Nonholonomic Mobile Robots , 2011, IEEE Transactions on Robotics.

[7]  Cheong Boon Soh,et al.  Stability of hybrid dynamic systems , 1997, Int. J. Syst. Sci..

[8]  Claude Samson,et al.  Feedback control of a nonholonomic wheeled cart in Cartesian space , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[9]  O. Khatib,et al.  Real-Time Obstacle Avoidance for Manipulators and Mobile Robots , 1985, Proceedings. 1985 IEEE International Conference on Robotics and Automation.

[10]  P. Tsiotras,et al.  Control design for chained-form systems with bounded inputs , 2000 .

[11]  Jie Chen,et al.  An overview of recent progress in high-order nonholonomic chained system control and distributed coordination , 2015 .

[12]  Zhengguo Li,et al.  Robust stability of a class of hybrid nonlinear systems , 2001, IEEE Trans. Autom. Control..

[13]  Changyun Wen,et al.  Robust stability of switched systems with arbitrarily fast switchings by generalized matrix measure , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[14]  Nicolas Marchand,et al.  Discontinuous exponential stabilization of chained form systems , 2003, Autom..

[15]  Nicole Bauer.  Switched And Impulsive Systems Analysis Design And Applications , 2016 .

[16]  Z. G. Lia,et al.  Observer-based stabilization of switching linear systems , 2003 .

[17]  Paolo Fiorini,et al.  A robotics wheelchair for crowded public environment , 2001, IEEE Robotics Autom. Mag..

[18]  Paolo Fiorini,et al.  A Robotic Wheelchair for Crowded Public Environments MAid Combines Narrow- and Wide-Area Navigation Behaviors for Traversing Varying Environments While Retaining User Independence and Preventing Fatigue , 2001 .

[19]  Fumio Miyazaki,et al.  A stable tracking control method for an autonomous mobile robot , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[20]  O. J. Sørdalen,et al.  Exponential stabilization of nonholonomic chained systems , 1995, IEEE Trans. Autom. Control..

[21]  Yu-Ping Tian,et al.  Smooth exponential stabilization of nonholonomic systems via time-varying feedback , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[22]  Zhong-Ping Jiang,et al.  A global output-feedback controller for simultaneous tracking and stabilization of unicycle-type mobile robots , 2004, IEEE Transactions on Robotics and Automation.

[23]  Marilena Vendittelli,et al.  WMR control via dynamic feedback linearization: design, implementation, and experimental validation , 2002, IEEE Trans. Control. Syst. Technol..

[24]  Camillo J. Taylor,et al.  A vision-based formation control framework , 2002, IEEE Trans. Robotics Autom..

[25]  Z. Qu,et al.  Continuous Time-Varying Pure Feedback Control for Chained Nonholonomic Systems with Exponential Convergent Rate , 2008 .

[26]  Panagiotis Tsiotras,et al.  Controllers for unicycle-type wheeled robots: Theoretical results and experimental validation , 2002, IEEE Trans. Robotics Autom..

[27]  A. Bloch,et al.  Control and stabilization of nonholonomic dynamic systems , 1992 .

[28]  Wolfram Burgard,et al.  Monte Carlo Localization: Efficient Position Estimation for Mobile Robots , 1999, AAAI/IAAI.

[29]  Wolfram Burgard,et al.  The dynamic window approach to collision avoidance , 1997, IEEE Robotics Autom. Mag..

[30]  Emilio Frazzoli,et al.  Torque efficient motion through singularity , 2017, 2017 IEEE International Conference on Robotics and Automation (ICRA).