This paper proposes a novel Hamiltonian servo system , a combined modeling framework for control and estimation of a large team/fleet of autonomous robotic vehicles. The Hamiltonian servo framework represents high-dimensional, nonlinear and non-Gaussian generalization of the classical Kalman servo system . After defining the Kalman servo as a motivation, we define the affine Hamiltonian neural network for adaptive nonlinear control of a team of UGVs in continuous time. We then define a high-dimensional Bayesian particle filter for estimation of a team of UGVs in discrete time. Finally, we formulate a hybrid Hamiltonian servo system by combining the continuous-time control and the discrete-time estimation into a coherent framework that works like a predictor-corrector system.
KeywordsTeam of UGVsKalman ServoHamiltonian ControlBayesian Estimation
Hui, K.-P. and Pourbeik, P. (2011) OPAL—A Survivability-Oriented Approach to Management of Tactical Military Networks. IEEE MILCOM, 7-10 November 2011.
Nicholas, P., et al. (2016) Measuring the Operational Impact of Military SATCOM Degradation. Winter Simulation Conference (WSC), 11-14 December 2016.
Jormakha, J., et al. (2011) UAV-Based Sensor Networks for Future Force Warriors. International Journal of Advances in Telecommunications, 4, 58-71.
Vukobratovic, M. and Potkonjak, V. (1982) Scientific Fundamentals of Robotics, Vol. 1, Dynamics of Manipulation Robots: Theory and Application. Springer, Berlin.
Vukobratovic, M. and Stokic, D. (1982) Scientific Fundamentals of Robotics, Vol. 2, Control of Manipulation Robots: Theory and Application. Springer, Berlin.
Vukobratovic, M. and Kircanski, M. (1985) Scientific Fundamentals of Robotics, Vol. 3, Kinematics and Trajectories Synthesis of Manipulation Robots. Springer, Berlin.
Vukobratovic, M. and Kircanski, N. (1985) Scientific Fundamentals of Robotics, Vol. 4, Real-Time Dynamics of Manipulation Robots. Springer, Berlin.
Vukobratovic, M., Stokic, D. and Kircanski, N. (1985) Scientific Fundamentals of Robotics, Vol. 5, Non-Adaptive and Adaptive Control of Manipulation Robots. Springer, Berlin.
Vukobratovic, M. and Potkonjak, V. (1985) Scientific Fundamentals of Robotics, Vol. 6, Applied Dynamics and CAD of Manipulation Robots. Springer, Berlin.
Ivancevic, V. and Ivancevic, T. (2006) Human-Like Biomechanics. Springer, Dordrecht.
ASIMO (2016) The Honda Humanoid Robot. http://world.honda.com/ASIMO/
Ivancevic, V.G. (2010) Nonlinear Complexity of Human Biodynamics Engine, Nonlin. Dynamics, 61, 123-139.
Durrant-Whyte, H. and Bailey, T. (2006) Simultaneous Localization and Mapping (SLAM): Part I. IEEE Robotics & Automation Magazine, 13, 99-110. https://doi.org/10.1109/MRA.2006.1638022
Wikipedia (2016) Simultaneous Localization and Mapping.
Montemerlo, M., Thrun, S., Koller, D. and Wegbreit, B. (2002) FastSLAM: A Factored Solution to the Simultaneous Localization and Mapping Problem.
Montemerlo, M., Thrun, S., Koller, D. and Wegbreit, B. (2003) FastSLAM 2.0: An Improved Particle Filtering Algorithm for Simultaneous Localization and Mapping That Provably Converges. Proceedings of IJCAI, 1151-1156.
Thrun, S., Montemerlo, M., Koller, D., Wegbreit, B., Nieto, J. and Nebot, E. (2004) FastSLAM: An Efficient Solution to the Simultaneous Localization and Mapping Problem with Unknown Data Association. Journal of Machine Learning Research, 1-48.
OpenSLAM (2016). https://www.openslam.org/
Kalman, R.E. (1960) A New Approach to Linear Filtering and Prediction Problems. Journal of Basic Engineering, 82, 34-45. https://doi.org/10.1115/1.3662552
Kalman, R.E. and Bucy, R.S. (1961) New Results in Linear Filtering and Prediction Theory. Journal of Basic Engineering, 96, 95-108. https://doi.org/10.1115/1.3658902
Kalman, R.E., Falb, P. and Arbib, M.A. (1969) Topics in Mathematical System Theory. McGraw Hill, New York.
Ivancevic, V. and Yue, Y. (2016) Hamiltonian Dynamics and Control of a Joint Autonomous Land-Air Operation. Nonlinear Dynamics, 84, 1853-1865. https://doi.org/10.1007/s11071-016-2610-y
Ivancevic, V. and Ivancevic, T. (2006) Geometrical Dynamics of Complex Systems. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4545-X
Ivancevic, V. and Ivancevic, T. (2007) Neuro-Fuzzy Associative Machinery for Comprehensive Brain and Cognition Modelling. Springer, Berlin. https://doi.org/10.1007/978-3-540-48396-0
Kosko, B. (1992) Neural Networks and Fuzzy Systems, A Dynamical Systems Approach to Machine Intelligence. Prentice-Hall, New York.
Arulampalam, S., Maskell, S., Gordon, N. and Clapp, T. (2002) A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking. IEEE Transactions on Signal Processing, 50, 174-188. https://doi.org/10.1109/78.978374
Ristic, B., Arulampalam, S. and Gordon, N. (2004) Beyond the Kalman Filter. Artech House.
Schön, T.B., Gustafsson, F. and Nordlund, P.-J. (2005) Marginalized Particle Filters for Mixed Linear/Nonlinear State-Space Models. IEEE Transactions on Signal Processing, 53, 2279-2289. https://doi.org/10.1109/TSP.2005.849151
Schön, T.B., Lindsten, F., Dahlin, J., et al. (2015) Sequential Monte Carlo Methods for System Identification. IFAC-PapersOnLine, 48, 775-786.
Gordon, N.J., Salmond, D.J. and Smith, A.F.M. (1993) Novel Approach to Nonlinear/Non-Gaussian Bayesian State Estimation. I Radar and Signal Processing, 140, 107-113.
Casella, G. and Robert, C.P. (1996) Rao-Blackwellisation of Sampling Schemes. Biometrika, 83, 81-94. https://doi.org/10.1093/biomet/83.1.81
Chen, R. and Liu, J.S. (2000) Mixture Kalman Filters. Journal of the Royal Statistical Society, 62, 493-508. https://doi.org/10.1111/1467-9868.00246
Doucet, A., Godsill, S.J. and Andrieu, C. (2000) On Sequential Monte Carlo Sampling Methods for Bayesian Filtering. Statistics and Computing, 10, 197-208. https://doi.org/10.1023/A:1008935410038
Doucet, A., Gordon, N. and Krishnamurthy, V. (2001) Particle Filters for State Estimation of Jump Markov Linear Systems. IEEE Transactions on Signal Processing, 49, 613-624. https://doi.org/10.1109/78.905890
Andrieu, C. and Doucet, A. (2002) Particle Filtering for Partially Observed Gaussian State Space Models. Journal of the Royal Statistical Society, 64, 827-836. https://doi.org/10.1111/1467-9868.00363
Schön, T., Gustafsson, F. and Nordlund, P.-J. (2003) Marginalized Particle Filters for Nonlinear State-Space Models. Tec. Report LiTH-ISY-R-2548, Linköping Univ.
Schön, T., Gustafsson, F. and Nordlund, P.-J. (2005) Marginalized Particle Filters for Mixed Linear/Nonlinear State-Space Models. IEEE Transactions on Signal Processing, 53, 2279-2289. https://doi.org/10.1109/TSP.2005.849151
Karlsson, R., Schön, T. and Gustafsson, F. (2005) Complexity Analysis of the Marginalized Particle Filter. IEEE Transactions on Signal Processing, 53, 4408-4411. https://doi.org/10.1109/TSP.2005.857061
Schön, T., Karlsson, R. and Gustafsson, F. (2006) The Marginalized Particle Filter in Practice. Aerospace Conference, 4-11 March 2006. https://doi.org/10.1109/AERO.2006.1655922