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.
References
[1]
Hui, K.-P. and Pourbeik, P. (2011) OPAL—A Survivability-Oriented Approach to Management of Tactical Military Networks. IEEE MILCOM, 7-10 November 2011.
[2]
Nicholas, P., et al. (2016) Measuring the Operational Impact of Military SATCOM Degradation. Winter Simulation Conference (WSC), 11-14 December 2016.
[3]
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.
[6]
Vukobratovic, M. and Stokic, D. (1982) Scientific Fundamentals of Robotics, Vol. 2, Control of Manipulation Robots: Theory and Application. Springer, Berlin.
[7]
Vukobratovic, M. and Kircanski, M. (1985) Scientific Fundamentals of Robotics, Vol. 3, Kinematics and Trajectories Synthesis of Manipulation Robots. Springer, Berlin.
[8]
Vukobratovic, M. and Kircanski, N. (1985) Scientific Fundamentals of Robotics, Vol. 4, Real-Time Dynamics of Manipulation Robots. Springer, Berlin.
[9]
Vukobratovic, M., Stokic, D. and Kircanski, N. (1985) Scientific Fundamentals of Robotics, Vol. 5, Non-Adaptive and Adaptive Control of Manipulation Robots. Springer, Berlin.
[10]
Vukobratovic, M. and Potkonjak, V. (1985) Scientific Fundamentals of Robotics, Vol. 6, Applied Dynamics and CAD of Manipulation Robots. Springer, Berlin.
[11]
Ivancevic, V. and Ivancevic, T. (2006) Human-Like Biomechanics. Springer, Dordrecht.
[12]
ASIMO (2016) The Honda Humanoid Robot. http://world.honda.com/ASIMO/
[13]
Ivancevic, V.G. (2010) Nonlinear Complexity of Human Biodynamics Engine, Nonlin. Dynamics, 61, 123-139.
[14]
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
[15]
Wikipedia (2016) Simultaneous Localization and Mapping.
[16]
Montemerlo, M., Thrun, S., Koller, D. and Wegbreit, B. (2002) FastSLAM: A Factored Solution to the Simultaneous Localization and Mapping Problem.
[17]
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.
[18]
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.
[19]
OpenSLAM (2016). https://www.openslam.org/
[20]
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
[21]
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
[22]
Kalman, R.E., Falb, P. and Arbib, M.A. (1969) Topics in Mathematical System Theory. McGraw Hill, New York.
[23]
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
[24]
Ivancevic, V. and Ivancevic, T. (2006) Geometrical Dynamics of Complex Systems. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4545-X
[25]
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
[26]
Kosko, B. (1992) Neural Networks and Fuzzy Systems, A Dynamical Systems Approach to Machine Intelligence. Prentice-Hall, New York.
[27]
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
[28]
Ristic, B., Arulampalam, S. and Gordon, N. (2004) Beyond the Kalman Filter. Artech House.
[29]
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
[30]
Schön, T.B., Lindsten, F., Dahlin, J., et al. (2015) Sequential Monte Carlo Methods for System Identification. IFAC-PapersOnLine, 48, 775-786.
[31]
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.
[32]
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
[33]
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
[34]
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
[35]
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
[36]
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
[37]
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.
[38]
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
[39]
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
[40]
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
