A combined stochastic and greedy hybrid estimation capability for concurrent hybrid models with autonomous mode transitions

Probabilistic hybrid discrete/continuous models, such as Concurrent Probabilistic Hybrid Automata (CPHA) are convenient tools for modeling complex robotic systems. In this paper, we present a novel method for estimating the hybrid state of CPHA that achieves robustness by balancing greedy and stochastic search. To accomplish this, we (1) develop an efficient stochastic sampling approach for CPHA based on Rao-Blackwellised Particle Filtering, (2) perform an empirical comparison of the greedy and stochastic approaches to hybrid estimation and (3) propose a strategy for mixing stochastic and greedy search. The resulting method handles nonlinear dynamics, concurrently operating components and autonomous mode transitions. We demonstrate the robustness of the mixed method empirically.

[1]  Brian C. Williams,et al.  Hybrid estimation of complex systems , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[2]  Keiji Kanazawa,et al.  A model for reasoning about persistence and causation , 1989 .

[3]  B. Buchberger,et al.  Gröbner bases and applications , 1998 .

[4]  John Langford,et al.  Risk Sensitive Particle Filters , 2001, NIPS.

[5]  Bart Selman,et al.  Boosting Combinatorial Search Through Randomization , 1998, AAAI/IAAI.

[6]  Simon J. Godsill,et al.  On sequential simulation-based methods for Bayesian filtering , 1998 .

[7]  Gabor Karsai,et al.  Building observers to address fault isolation and control problems in hybrid dynamic systems , 2000, Smc 2000 conference proceedings. 2000 ieee international conference on systems, man and cybernetics. 'cybernetics evolving to systems, humans, organizations, and their complex interactions' (cat. no.0.

[8]  B. Williams,et al.  Multi-Modal Particle Filtering for Hybrid Systems with Autonomous Mode Transitions , 2003 .

[9]  Peter S. Maybeck,et al.  Reconfigurable flight control via multiple model adaptive control methods , 1990, 29th IEEE Conference on Decision and Control.

[10]  H. Balakrishnan,et al.  State estimation for hybrid systems: applications to aircraft tracking , 2006 .

[11]  P. Pandurang Nayak,et al.  A Model-Based Approach to Reactive Self-Configuring Systems , 1996, AAAI/IAAI, Vol. 2.

[12]  Nando de Freitas,et al.  Diagnosis by a waiter and a Mars explorer , 2004, Proceedings of the IEEE.

[13]  Hiromitsu Kumamoto,et al.  Random sampling approach to state estimation in switching environments , 1977, Autom..

[14]  G. Kitagawa.  Monte Carlo Filter and Smoother for Non-Gaussian Nonlinear State Space Models , 1996 .

[15]  Nando de Freitas,et al.  Real-Time Monitoring of Complex Industrial Processes with Particle Filters , 2002, NIPS.

[16]  Sheila A. McIlraith.  Diagnosing Hybrid Systems: a Bayesian Model Selection Approach , 2005 .

[17]  Richard Dearden,et al.  Particle Filters for Real-Time Fault Detection in Planetary Rovers , 2001 .

[18]  Brian C. Williams,et al.  Mode Estimation of Probabilistic Hybrid Systems , 2002, HSCC.

[19]  Leonid Peshkin,et al.  Factored Particles for Scalable Monitoring , 2002, UAI.

[20]  D. Avitzour.  Stochastic simulation Bayesian approach to multitarget tracking , 1995 .

[21]  Gautam Biswas,et al.  Bayesian Fault Detection and Diagnosis in Dynamic Systems , 2000, AAAI/IAAI.

[22]  B. Anderson,et al.  Optimal Filtering , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[23]  Brian C. Williams,et al.  Diagnosis as Semiring-Based Constraint Optimization , 2004, ECAI.

[24]  Feng Zhao,et al.  Monitoring and Diagnosis of Hybrid Systems Using Particle Filtering Methods , 2002 .

[25]  A. Rollett,et al.  The Monte Carlo Method , 2004 .

[26]  Inseok Hwang,et al.  Hybrid Estimation Algorithm using State-Dependent Mode Transition Matrix for Aircraft Tracking , 2006 .

[27]  Frank Hutter,et al.  The Gaussian Particle Filter for Diagnosis of Non-Linear Systems , 2003 .

[28]  Brian C. Williams,et al.  Mode Estimation of Model-based Programs: Monitoring Systems with Complex Behavior , 2001, IJCAI.

[29]  Richard S. Sutton,et al.  Reinforcement Learning , 1992, Handbook of Machine Learning.

[30]  Nando de Freitas,et al.  Rao-Blackwellised Particle Filtering for Dynamic Bayesian Networks , 2000, UAI.

[31]  Michael W. Hofbaur,et al.  Hybrid Diagnosis with Unknown Behavioral Modes , 2002 .

[32]  John Langford,et al.  Non-Parametric Fault Identification for Space R overs , 2001 .

[33]  N. de Freitas.  Rao-Blackwellised particle filtering for fault diagnosis , 2002, Proceedings, IEEE Aerospace Conference.

[34]  Patrick Brézillon,et al.  Lecture Notes in Artificial Intelligence , 1999 .

[35]  Brian C. Williams,et al.  Model-Based Monitoring and Diagnosis of Systems with Software-Extended Behavior , 2005, AAAI.

[36]  Brian C. Williams,et al.  Diagnosis as Approximate Belief State Enumeration for Probabilistic Concurrent Constraint Automata , 2005, AAAI.

[37]  Arnaud Doucet,et al.  Particle filters for state estimation of jump Markov linear systems , 2001, IEEE Trans. Signal Process..

[38]  N. Gordon,et al.  Novel approach to nonlinear/non-Gaussian Bayesian state estimation , 1993 .

[39]  H. Joe.  Approximations to Multivariate Normal Rectangle Probabilities Based on Conditional Expectations , 1995 .

[40]  Michael K. Ewert,et al.  Advanced Life Support--Baseline Values and Assumptions Document , 2005 .

[41]  Inseok Hwang,et al.  An Estimation Algorithm for Stochastic Linear Hybrid Systems with Continuous-State-Dependent Mode Transitions , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[42]  Richard S. Sutton,et al.  Reinforcement Learning: An Introduction , 1998, IEEE Trans. Neural Networks.

[43]  Peter S. Maybeck,et al.  Multiple-model adaptive estimation using a residual correlation Kalman filter bank , 2000, IEEE Trans. Aerosp. Electron. Syst..

[44]  P. Pandurang Nayak.  Automated Modelling of Physical Systems , 1995 .

[45]  Jonathan C. McDowell.  Jupiter Icy Moons Orbiter , 2004 .

[46]  Joelle Pineau,et al.  Experiences with a mobile robotic guide for the elderly , 2002, AAAI/IAAI.

[47]  A. Genz,et al.  Numerical evaluation of singular multivariate normal distributions , 2000 .

[48]  K. Ito,et al.  On State Estimation in Switching Environments , 1970 .

[49]  Alan Genz,et al.  Numerical computation of rectangular bivariate and trivariate normal and t probabilities , 2004, Stat. Comput..

[50]  Jeffrey K. Uhlmann,et al.  New extension of the Kalman filter to nonlinear systems , 1997, Defense, Security, and Sensing.

[51]  Vladimir Pavlovic,et al.  A dynamic Bayesian network approach to figure tracking using learned dynamic models , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[52]  G. Casella,et al.  Rao-Blackwellisation of sampling schemes , 1996 .

[53]  Uri Lerner,et al.  Inference in Hybrid Networks: Theoretical Limits and Practical Algorithms , 2001, UAI.

[54]  Gautam Biswas,et al.  Hybrid Systems Diagnosis , 2000, HSCC.

[55]  Timothy J. Robinson,et al.  Sequential Monte Carlo Methods in Practice , 2003 .

[56]  P. Pandurang Nayak,et al.  Fast Context Switching in Real-Time Propositional Reasoning , 1997, AAAI/IAAI.

[57]  Uri Lerner,et al.  Hybrid Bayesian networks for reasoning about complex systems , 2002 .

[58]  Jitendra K. Tugnait,et al.  Detection and estimation for abruptly changing systems , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[59]  Y. Bar-Shalom,et al.  The interacting multiple model algorithm for systems with Markovian switching coefficients , 1988 .

[60]  Christian Smith,et al.  Robot manipulators , 2009, IEEE Robotics & Automation Magazine.