Abstract
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.
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References
Dierks T, Jagannathan S. Control of nonholonomic mobile robot formations: backstepping kinematics into dynamics. In: Proceedings of IEEE International Conference on Control Applications, Singapore, 2007. 94–99
Dimarogonas D V, Johansson K H. Stability analysis for multi-agent systems using the incidence matrix: quantized communication and formation control. Automatica, 2010, 46: 695–700
Zhang F M. Geometric cooperative control of particle formations. IEEE Trans Automat Contr, 2010, 55: 800–804
Orqueda O A A, Zhang X T, Fierro R. An output feedback nonlinear decentralized controller for unmanned vehicle co-ordination. Int J Robust Nonlinear Contr, 2007, 17: 1106–1128
Desai J P, Ostrowski J, Kumar V. Controlling formations of multiple mobile robots. In: Proceedings of the IEEE Intemational Conference on Robotics and Automation, Leuven, 1998. 2864–2869
Das A K, Fierro R, Kumar W, et al. A vision-based formation control framework. IEEE Trans Robot Automat, 2002, 18: 813–825
Levant A. Robust exact differentiantion via sliding mode technique. Automatica, 1998, 34: 379–384
Levant A. Universal single-input-single output (SISO) sliding-mode controllers with finite-time. IEEE Trans Automat Contr, 2001, 46: 1447–1451
Yang J M, Kim J H. Sliding mode control for trajectory tracking of nonholonomic wheeled mobile robots. IEEE Trans Robot Automat, 1999, 15: 578–587
Lim H, Kang Y, Kim J, et al. Formation control of leader following unmanned ground vehicles using nonlinear model predictive control. In: Proceedings of the IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Singapore, 2009. 945–950
Morbidi F, Mariottini G L, Prattichizzo D. Observer design via immersion and invariance for vision-based leaderfollower formation control. Automatica, 2009, 46: 148–154
Chowdhary G, Jategaonkar R. Aerodynamic parameter estimation from flight data applying extended and unscented Kalman filter. Aerosp Sci Technol, 2010, 14: 106–117
van der Merwe R, Wan E A. The unscented Kalman filter for nonlinear estimation. In: Proceedings of Adaptive Systems for Signal Processing, Communications, and Control Symposium, Lake Louise, Alta, 2000. 153–158
Abdessameud A, Tayebi A. On consensus algorithms for double-integrator dynamics without velocity measurements and with input constraints. Syst Contr Lett, 2010, 59: 812–821
Krstic M, Kanellakopoulos I, Kokotovic P. Nonlinear and Adaptive Control Design. New York: John Wiley & Sons Inc., 1995
Karagiannis D, Astolfi A. Observer design for a class of nonlinear systems using dynamic scaling with appplication to adaptive control. In: Proceedings of the IEEE Conference on Decision and Control, Cancun, 2008. 2314–2319
Choi K, Yoo S J, Park J B, et al. Adaptive formation control in absence of leader’s velocity information. IET Control Theory Appl, 2010, 4: 521–528
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Shen, D., Sun, Z. & Sun, W. Leader-follower formation control without leader’s velocity information. Sci. China Inf. Sci. 57, 1–12 (2014). https://doi.org/10.1007/s11432-013-4965-8
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DOI: https://doi.org/10.1007/s11432-013-4965-8