Mixed-Integer Programming Techniques in Distributed MPC Problems
This chapter proposes a distributed approach for the resolution of a multi-agent problem under collision and obstacle avoidance conditions. Using hyperplane arrangements and mixed integer programming, we provide an efficient description of the feasible region verifying the avoidance constraints. We exploit geometric properties of hyperplane arrangements and adapt this description to the distributed scheme in order to provide an efficient Model Predictive Control (MPC) solution. Furthermore, we prove constraint validation for a hierarchical ordering of the agents.
KeywordsFeasible Region Mixed Integer Programming Model Predictive Control Prediction Horizon Hyperplane Arrangement
The research of Ionela Prodan is financially supported by the EADS Corporate Foundation (091-AO09-1006).
- 1.D. Grundel, R. Murphey, P.M. Pardalos, Cooperative Systems, Control and Optimization, vol. 588 (Springer, New York, 2007)Google Scholar
- 2.M. Jünger, M. Junger, T.M. Liebling, D. Naddef, G. Nemhauser, W.R. Pulleyblank, 50 Years of Integer Programming 1958–2008: From the Early Years to the State-of-the-Art (Springer, New York, 2009)Google Scholar
- 4.S. Lin, B. De Schutter, Y. Xi, H. Hellendoorn, Model predictive control for urban traffic networks via milp, in Proceedings of the 29th American Control Conference, pp. 2272–2277, Baltimore, 30 June–2 July 2010Google Scholar
- 5.R. Olfati-Saber, R.M. Murray, Distributed cooperative control of multiple vehicle formations using structural potential functions, in Proceedings of the 15th IFAC World Congress, pp. 346–352, Barcelona, 21–26 July 2002Google Scholar
- 6.P.M. Pardalos, Hyperplane arrangements in optimization, in Encyclopedia of Optimization (Springer, New York, 2009), pp. 1547–1548Google Scholar
- 7.I. Prodan, S. Olaru, C. Stoica, S.-I. Niculescu, Predictive control for tight group formation of multi-agent systems, in Proceedings of the 18th IFAC World Congress, pp. 138–143, Milano, 28 Aug–2 Sept 2011Google Scholar
- 8.I. Prodan, S. Olaru, C. Stoica, S.-I. Niculescu, On the tight formation for multi-agent dynamical systems, in KES—Agents and Multi-agent Systems, Technologies and Applications, LNAI 7327. (Springer, New York, 2012), pp. 554–565Google Scholar
- 14.M.P. Vitus, V. Pradeep, G. Hoffmann, S.L. Waslander, C.J. Tomlin, Tunnel-milp: path planning with sequential convex polytopes, in Proceedings of the 26th AIAA Guidance, Navigation, and Control Conference, Honolulu, 18–21 Aug 2008Google Scholar
- 15.G.M. Ziegler, Lectures on Polytopes, vol. 152. (Springer, New York, 1995)Google Scholar