Leader-follower formation control without leader’s velocity information

In this paper, we consider the mobile robots formation control problem without direct measurement of the leader robot’s linear velocity. Two decentralized nonlinear algorithms are proposed, respectively, based on adaptive dynamic feedback and immersion & invariance estimation based second order sliding mode control methodologies. The main idea is to solve formation problem by estimating the leader robots’s linear velocity, while maintaining the given predefined separation distance and bearing angle between the leader robot and the follower robot. The stability of the closed-loop system is proven by means of the Lyapunov method. The proposed controllers are smooth, continuous and robust against unknown bounded uncertainties such as sensor inaccuracy between the outputs of sensors and the true values in collision free environments. Simulation examples and physical vehicles experiments are presented to verify the effectiveness of the proposed design approaches, and the proposed designed methodologies are carefully compared to illustrate the pros and cons of the approaches.

[1]  Rudolph van der Merwe,et al.  The unscented Kalman filter for nonlinear estimation , 2000, Proceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium (Cat. No.00EX373).

[2]  Arie Levant,et al.  Universal single-input-single-output (SISO) sliding-mode controllers with finite-time convergence , 2001, IEEE Trans. Autom. Control..

[3]  Jong-Hwan Kim,et al.  Sliding mode control for trajectory tracking of nonholonomic wheeled mobile robots , 1999, IEEE Trans. Robotics Autom..

[4]  Yeonsik Kang,et al.  Formation control of leader following unmanned ground vehicles using nonlinear model predictive control , 2009, 2009 IEEE/ASME International Conference on Advanced Intelligent Mechatronics.

[5]  A. Levant.  Robust exact differentiation via sliding mode technique , 1998 .

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

[7]  Miroslav Krstic,et al.  Nonlinear and adaptive control de-sign , 1995 .

[8]  J. B. Park,et al.  Adaptive formation control in absence of leader's velocity information , 2010 .

[9]  Abdelkader Abdessameud,et al.  On consensus algorithms for double-integrator dynamics without velocity measurements and with input constraints , 2010, Syst. Control. Lett..

[10]  Rafael Fierro,et al.  An output feedback nonlinear decentralized controller for unmanned vehicle co‐ordination , 2007 .

[11]  Domenico Prattichizzo,et al.  Observer design via Immersion and Invariance for vision-based leader-follower formation control , 2010, Autom..

[12]  R. V. Jategaonkar,et al.  Aerodynamic parameter estimation from flight data applying extended and unscented Kalman filter , 2006 .

[13]  Alessandro Astolfi,et al.  Observer design for a class of nonlinear systems using dynamic scaling with application to adaptive control , 2008, 2008 47th IEEE Conference on Decision and Control.

[14]  Fumin Zhang,et al.  Geometric Cooperative Control of Particle Formations , 2010, IEEE Transactions on Automatic Control.

[15]  Karl Henrik Johansson,et al.  Stability analysis for multi-agent systems using the incidence matrix: Quantized communication and formation control , 2010, Autom..

[16]  Vijay Kumar,et al.  Controlling formations of multiple mobile robots , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).