Complex Mission Planning in Uncertain Adversarial Environment

Transcription

1 Complex Mission Planning in Uncertain Adversarial Environment Andrzej Banaszuk United Technologies Research Center ASEAS Workshop, March 23-24, 2009 Supported in part by DARPA DSO under AFOSR contract FA C-0024

2 Thomas Frewen Amit Surana Harshad Sane Greg Hagen Satish Narayanan Sean Meyn George Mathew Vladimir Fonoberov Igor Mezic Marin Kobilarow Philip DuToit Jerry Marsden Acknowledgements

3 Outline DyNARUM overview Efficient Search Algorithms Scalable Uncertainty Quantification Challenge Problem: Mission Planning in Adversarial Urban Environment Detection of Anomalous Behavior

4 UT Power Pratt & Whitney Carrier Sikorsky Building Systems Aerospace Systems Power Systems Otis Hamilton-Sundstrand UT Fire & Security Products affected by complex dynamic interactions, uncertainty and adversarial behavior

5 Dynamic Network Analysis for Robust Uncertainty Management Objectives: Barriers Large Scale Multiscale Uncertainty Nontrivial Dynamics Uncertainty Propagation Intractable With Current Methods Large Surveillance Network Uncertainty: vehicles, sensors, communications models Enablers: Variational Integrators Geometric Dynamics Network Decomposition Graph Theory Model Reduction Uncertainty Propagation Tools Network Design Tools Optimal Control Tractable Description Distribution of target detection time Efficient Measure Propagation Asynchronous Computations Operator Theory DYNARUM methods and tools 1.Develop analysis and design tools for Robust Uncertainty Management 2.Demonstrate analysis tools in a Molecular Dynamics problem with 10,000 particles and design tools in surveillance networks with 100 agents Approach : 1.Decompose networks into components using Spectral Graph Theory. 2.Propagate uncertainty through components using Operator Theory and Geometric Dynamics Optimal/Robust Algorithm Baseline Algorithm 3.Iteratively aggregate component uncertainty

6 DyNARUM Team Igor Mezic Simeon Grivopoulos Bryan Eisenhower Marko Budisic Gunjan Thakur Lan Yueheng Ryan Mohr Alice Hubenko Jerry Marsden Houman Owhadi Phillip Du Toit Katalin Grubits Sujit Nair Sigrid Leyendecker Sina Ober-Blobaum Nawaf Bou-Rabee Raphy Coifman Yoel Shkolnisky Amit Singer Fred Wagner Sanjay Lall Matt West SunHwan Lee Tsu-Chien Liang Laurent Lessard Jong-Han Kim Andrzej Banaszuk Marco Arienti Sorin Costiner George Mathew Jose Miguel Pasini Konda Reddy Tuhin Sahai Amit Surana Yannis Kevrekidis Vladimir Fonoberov Caroline Cardonne Sophie Loire Eric Johnson Suresh Kannan University Thomas Frewen UTRC Gleb Oshanin (Univ. P&MCurie) Sean Meyn (UIUC) Michael Dellnitz (Paderborn) George Karniadakis (Brown/MIT) Basic Research: Long range technology development Applied Research: Integrate, mature, and transfer technology to market opportunities Mark Lutian

7 DyNARUM scope results highlighted in this talk 2000x faster than Monte-Carlo in a Phase Diagram Uncertainty Quantification: Polynomial Chaos Response Surface Dynamical System Sampling Temporal acceleration tools: Network Decomposition Asynchronous Variational Integrators Markov Chain Model learning Coarse Projective Integrators Uncertain Parameters Search Algorithms: Spectral Multiscale Search Greedy Probabilistic Design Variables 10000x faster than Monte-Carlo in an aircraft electric power network example Complex Dynamic Network Optimization Algorithm Estimators: Bayesian Consensus-based Metrics of performance Optimization Tools: Adaptive Coarse Trend Based Roadmap methods DMOC primitives 2.2x faster than lawnmover

8 Phase 2 Surveillance Milestone Met Achieved 2.2x faster Median Search Time than Baseline Baseline: lawnmower prior target density foliage 1 Target, 5000 realizations drawn from prior 50 Searchers Single sensor: p d = 0.8; p fa = 0.2 Requirements: P D,group > 0.9; P FA,group < 0.1 Greedy Spirals (Caltech) 1.9x faster Spectral Multiscale Search (UCSB/Aimdyn) Dynamic Greedy Search (Caltech) 2.2x faster 1.7x faster

9 Speed-up over MC inversely proportional to desired error Uncertainty Quantification Methods Preferred Methods: Wrap-Around methods allow use of deterministic solver x f ( ) f ( x) N j= 1 a j v j ( x) Polynomial Chaos Methods (UTRC) #parameters ~ Use orthogonal stochastic basis, collocation points to fit coefficients (recently extended to 100+) Molecular Dynamics with 10K atoms, 4 parameters: 2000x faster than MC DSAMPLE (UCSB, Aimdyn, UTRC) #parameters >100 Utilize ergodic dynamics for efficient sampling, convergence rate independent of # parameters! Electric power system, 26 parameters: 10,000x faster than MC

10 into weakly interacting sub-networks Scalability by Network Decomposition => Fast Uncertainty Quantification utilizing parallel computations Graph Representation of Dynamical System Adjacency Matrix Degree Matrix Horizontal Vertical Decomposition (HVD) (Mezic) Identify interconnection structure using recurrent & transient states of corresponding Markov chain Spectral Graph Decomposition (Chung) Identify weak connections & strongly connected components at each sub-level using graph Laplacian Unnormalized: Normalized: Identify number of clusters k (by for e.g. by examining the spectral gap of Laplacian) Apply k-means to identify clusters HVD Spectral Decomposition Others Techniques: Diffusion Map Based Hierarchical Clustering (Coifman), Almost Invariant Sets (Dellnitz)

11 Probabilistic Waveform Relaxation Exploit Weak Interactions Scalable UQ Graph Decomposition Probabilistic Waveform Relaxation Computational Gain over full grid collocation Order of PCh expansion #uncertain parameters # Iterations Fine grid for parameters that directly affect i th subsystem Coarse grid for parameters in adjacent subsystem #subsystems

12 Example: 80 oscillators, 40 uncertain parameters Eigenvalues of graph Laplacian Gap Convergence of mean and variance at t=1 after 10 iterations 40 Subsystems

13 Challenge Problem Description Mission: High value asset (a manned rotorcraft) must reach a specific destination in an urban adversarial environment (within time of completion limits), while minimizing a probability of being exposed to small and shoulder arms fire. Threat: Complex Uncertain Urban Terrain Adversaries (~ 5) mixed with non-combatants (100+) may have an priori information about the possible paths of the high value asset. Resources High Altitude UAVs: Global coarse view Low Altitude UAVs: Local detailed view, low instantaneous coverage Motion Planning Probabilistic Description of Potential threats & Survivability Metric Sensor Tasking & Anomalous/ Adversarial Detection Prior intelligence information (Expert Knowledge, Social Network), Real time video feeds (to detect weapons), Detect threatening motion patterns

14 Detecting adversaries based on patterns of motion is a hard problem What makes it difficult Cannot distinguish combatants from short time behavior Enormous amount of possible long time behaviors SNR: few combatants many noncombatants Inability to construct complete set of models Finite time to make decision What can be exploited Sparseness of rational behaviors in space/time Long term behavior of combatants Normal behavior can be learned Anomalies can be detected by Robust Hypothesis Testing Dictionaries of known threatening behaviors Multiscale features of combatant dynamics Coordination of combatants

15 Anomalous/Adversarial Behavior Detection Expert Knowledge Model Based Simulation Simulation/Real Time data Extract Coarse Variables Markov Model Learning Model for normal behavior Robust Hypothesis Testing Meyn et. al. Anomaly Score H = z z Γ k Transition matrix for real time Markov model ( z 0, z 1 ) log 0, Q P k ( z ( z 0, z, z 1 ) ) Real-time Model Bivariate distribution for real time Markov model Transition matrix for normal Markov model Multiple Normal & Adversarial Models OR

16 Key points Model-based algorithms for complex mission planning developed under DARPA DSO Robust Uncertainty Management program Latency Models Disturbances Sensors BATTLEFIELD REMOTE COMMAND Situational Awareness Consensus Data Human Command Decision Support Data Success Probability Mission Alternatives Mission Adaptation Trajectory Generation Communication Network and Battlefield Consensus Compressed Features Positions & Mission Commands Threats Distributions Mission Commands Mission Waypoints Troop locations Search Trajectories Status Terrain & Threat Data Obstacles Search & UAV Support Network UAV Network High Mission Value Main Asset Rotorcrafts Evolving Threats Evolving Threats Cluttered Urban Terrain Troops Support/Extraction Search algorithms demonstrated in simulation of 50 UAVs 2x faster median search time than lawnmower baseline real-time trajectory planning in urban environment enabled Quantification of mission success probability enabled Challenge problem: complex mission planning including heterogeneous assets and dynamically evolving adversarial threats in urban environment including noncombatants Robust Hypothesis Testing for detection of adversaries from patterns of motion being investigated