Predictive control for trajectory tracking and decentralized navigation of multi-agent formations

Open access

This paper addresses a predictive control strategy for a particular class of multi-agent formations with a time-varying topology. The goal is to guarantee tracking capabilities with respect to a reference trajectory which is pre-specified for an agent designed as the leader. Then, the remaining agents, designed as followers, track the position and orientation of the leader. In real-time, a predictive control strategy enhanced with the potential field methodology is used in order to derive a feedback control action based only on local information within the group of agents. The main concern is that the interconnections between the agents are time-varying, affecting the neighborhood around each agent. The proposed method exhibits effective performance validated through some illustrative examples.

Baskar, L., De Schutter, B. and Hellendoorn, H. (2006). Decentralized traffic control and management with intelligent vehicles, Proceedings of the 9th TRAILCongress, Delft, The Netherlands, (CD-ROM).

Bemporad, A. and Morari, M. (1999). Control of systems integrating logic, dynamics, and constraints, Automatica35(3): 407-427.

Blanchini, F. (1995). Nonquadratic Lyapunov functions for robust control, Automatica 31(3): 451-461.

Camacho, E. and Bordons, C. (2004). Model Predictive Control, Springer-Verlag, London.

De Doná, J., Suryawan, F., Seron, M. and Lévine, J. (2009). A flatness-based iterative method for reference trajectory generation in constrained NMPC, in L. Magni, D.M. Raimondo and F. Allgöwer (Eds.), Nonlinear Model PredictiveControl, Springer-Verlag, pp. 325-333.

Dunbar, W. and Murray, R. (2006). Distributed receding horizon control for multi-vehicle formation stabilization, Automatica42(4): 549-558.

Fang, Z., Song, W., Zhang, J. and Wu, H. (2010). Experiment and modeling of exit-selecting behaviors during a building evacuation, Statistical Mechanics and Its Applications389(4): 815-824.

Fliess, M., Lévine, J., Martin, P. and Rouchon, P. (1995). Flatness and defect of non-linear systems: Introductory theory and examples, International Journal of Control61(6): 1327-1361.

Garey, M. and Johnson, D. (1979). Computers and Intractability. A Guide to the Theory of NP-completeness, WH Freeman and Company, San Francisco, CA.

Gielen, R., Olaru, S., Lazar, M., Heemels, W., Van de Wouw, N. and Niculescu, S. (2010). On polytopic inclusions as a modeling framework for systems with time-varying delays, Automatica 46(3): 615-619.

Girard, A., de Sousa, J. and Hedrick, J. (2001). Coordinated control of agent formations in uncertain, dynamic environments, Proceedings of the European Control Conference,Porto, Portugal, pp. 121-127.

Goodwin, G., Seron, M., Middleton, R., Zhang, M., Hennessy, B., Stone, P. and Menabde, M. (2006). Receding horizon control applied to optimal mine planning, Automatica42(8): 1337-1342.

Heemels,W., Van DeWouw, N., Gielen, R., Donkers, M., Hetel, L., Olaru, S., Lazar, M., Daafouz, J. and Niculescu, S. (2010). Comparison of overapproximation methods for stability analysis of networked control systems, Proceedingsof the 13th ACM International Conference on HybridSystems: Computation and Control, Stockholm, Sweden, pp. 181-190.

Helbing, D., Farkas, I. and Vicsek, T. (2000). Simulating dynamical features of escape panic, Nature407(6803): 487-490.

Jadbabaie, A., Lin, J. and Morse, A. (2003). Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Transactions on Automatic Control48(6): 988-1001.

Khatib, O. (1986). Real-time obstacle avoidance for manipulators and mobile robots, International Journal ofRobotics Research 5(1): 90.

Maciejowski, J. (2002). Predictive Control with Constraints, Pearson Education, Harlow.

Massion, I., Keviczky, T. and Verhaegen, M. (2008). New approaches to distributed control of satellite formation flying, Proceedings of the 3rd International Symposium onFormation Flying, Missions and Technologies, Noordwijk,The Netherlands, pp. 22-27.

Mayne, D., Rawlings, J., Rao, C. and Scokaert, P. O. (2000). Constrained model predictive control: Stability and optimality, Automatica 36(6): 789-814.

Mazur, A. and Szakiel, D. (2009). On path following control of nonholonomic mobile manipulators, InternationalJournal of Applied Mathematics and Computer Science19(4): 561-574, DOI: 10.2478/v10006-009-0044-0.

Mesbahi, M. and Hadaegh, F. (2001). Formation flying control of multiple spacecraft via graphs, matrix inequalities, and switching, Journal of Guidance, Control, and Dynamics24(2): 369-377.

Michałek, M., Dutkiewicz, P., Kiełczewski, M. and Pazderski, D. (2009). Trajectory tracking for a mobile robot with skid-slip compensation in the vector-field-orientation control system, International Journal of Applied Mathematicsand Computer Science 19(4): 547-559, DOI: 10.2478/v10006-009-0043-1.

Negenborn, R., van Overloop, P., Keviczky, T. and De Schutter, B. (2009). Distributed model predictive control of irrigation canals, Networks and Heterogeneous Media4(2): 359-380.

Osiadacz, A., Nemhauser, G.L. and Wolsey, L.A. (1990). Integer and combinatorial optimization, International Journal ofAdaptive Control and Signal Processing 4(4): 333-334.

Overloop, P., Negenborn, R., Schutter, B. and Giesen, N. (2010). Predictive control for national water flow optimization in the Netherlands, in R.R. Negenborn, Z. Lukszo and H. Hellendoorn (Eds.), Intelligent Infrastructures, Springer, pp. 439-461.

Prodan, I., Bencatel, R., Olaru, S., Sousa, J., Stoica, C. and Niculescu, S. (2012). Predictive control for autonomous aerial vehicles trajectory tracking, Proceedings of the NonlinearModel Predictive Control Conference, Noordwijkerhout,The Netherlands, pp. 508-513.

Prodan, I., Olaru, S., Stoica, C. and Niculescu, S. (2010). Collision avoidance and path following for multi-agent dynamical systems, 2010 International Conference onControl Automation and Systems (ICCAS), Gyeonggi-do,Seoul, Korea, pp. 1930-1935.

Prodan, I., Olaru, S., Stoica, C. and Niculescu, S.-I. (2011). Predictive control for tight group formation of multi-agent systems, Proceedings of the 18th IFAC World Congress,Milano, Italy, pp. 138-143.

Richards, A. and How, J. (2002). Aircraft trajectory planning with collision avoidance using mixed integer linear programming, Proceedings of the 21st American ControlConference, Anchorage, AL, USA, pp. 1936-1941.

Rimon, E. and Koditschek, D. (1992). Exact robot navigation using artificial potential functions, IEEE Transactions onRobotics and Automation 8(5): 501-518.

Rossiter, J. (2003). Model-Based Predictive Control: A PracticalApproach, CRC Press, Boca Raton, FL.

Roussos, G. and Kyriakopoulos, K. (2010). Completely decentralised navigation of multiple unicycle agents with prioritization and fault tolerance, Proceedings of the 49thIEEE Conference on Decision and Control, Atlanta, GA,USA, pp. 1372-1377.

Stoican, F., Prodan, I. and Olaru, S. (2011). On the hyperplanes arrangements in mixed-integer techniques, Proceedings ofthe 30th American Control Conference, San Francisco, CA,USA, pp. 1898-1903.

Suryawan, F., De Dona, J. and Seron, M. (2010). Methods for trajectory generation in a magnetic-levitation system under constraints, 18thMediterranean Conference on Controland Automation, Marrakech, Morocco, pp. 945-950.

Tanner, H., Jadbabaie, A. and Pappas, G. (2007). Flocking in fixed and switching networks, IEEE Transactions on AutomaticControl 52(5): 863-868.

Van den Berg, M., Hegyi, A., De Schutter, B. and Hellendoorn, J. (2004). A macroscopic traffic flow model for integrated control of freeway and urban traffic networks, Proceedingsof the 43rd IEEE Conference on Decision and Control,Atlantis, Paradise Island, The Bahamas, Vol. 3, pp. 2774-2779.

Van Nieuwstadt, M. and Murray, R. (1998). Real-time trajectory generation for differentially flat systems, InternationalJournal of Robust and Nonlinear Control 8(11): 995-1020.

Ziegler, G.M. (1995). Lectures on Polytopes, Springer-Verlag, New York, NY.

International Journal of Applied Mathematics and Computer Science

Journal of the University of Zielona Góra

Journal Information

IMPACT FACTOR 2018: 1,504
5-year IMPACT FACTOR: 1,553

CiteScore 2018: 2.09

SCImago Journal Rank (SJR) 2018: 0.493
Source Normalized Impact per Paper (SNIP) 2018: 1.361

Mathematical Citation Quotient (MCQ) 2017: 0.13

Cited By


All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 367 247 15
PDF Downloads 108 95 11