Managing Multiple Moving Vehicles with Patch Models

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Managing Multiple Moving Vehicles with Patch
Models
Venkatesh G. RaoPostdoctoral Associate Cornell
University

• Raffaello DAndrea
• Associate Professor
• Cornell University

Four Year MURI Research Review
UCLA, January 28, 2005 With inputs from Tichak
orn Wongpiromsarn and Thientu Ho
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What Next?
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Outline
Focus missing elements symbolic-subsymbolic
interface, functional integration, abstraction
and hierarchies, open systems, expressive
coordination mechanisms

• Motivation combat operations and wide-area
  disaster relief
  
• Region Connection Calculus (RCC)
• Patch models for abstraction
• Implementation overview
• Ongoing work

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Air Combat Operations

• Vast amounts of spatio-temporal information
• 200-plus aircraft, dozen types, service, mission
  hierarchies
  
• 24-hour cycle of planned missions/sorties, plus
  reactive and opportunistic missions
  
• Main bottleneck mission coordination and
  resource allocation
  
• Opposed architectural tensions centralized,
  human-in-loop information sharing versus autonomy
  for agents (Rob Murphey, circa last week)

(Based on discussions with Lt. Col. Fred Zeitz,
USAF (retd).)
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Future of Air Combat (OSD)
Air Combat
CAS
AEW
Nonlethal SEAD
Armed Recce
Reactive SEAD
Stand-Out AEA
Mission Complexity
Strike
Stand-In AEA
Information Operations
High Value Strike
Non-Pene ISR
Deep Strike
Penetrating ISR
TAC Recce
Lethal SEAD
Directed Energy
Comm Relay
BDA
Slide Taken from OSD UCAV Missions Briefing,
10/7/03 Presented at UCAVs, Armed UAVs and LAMs C
onference by Mr. James Durham, Lead, Deputy Secre
tary of Defense UCAV Options Study, Office of
the Secretary of Defense, Programs, Analysis and
Evaluation, TACAIR Division
Likelihood of Encounter
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Tsunami Relief

• Dozen countries
• Dozen navies and air forces
• Political constraints on resource movement

• Last Mile distribution network overloaded
• Poor coordination too much material in some
  districts, too little in others
  
• HUNDREDS of organizations working bottom-up,
  THOUSANDS of individuals participating randomly
  
• Relief material traffic jams in frontline cities

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The System Design Problem

• Problem 1 A ground unit in a combat theater
  requests a strike mission for a target of
  opportunity that will be vulnerable for 30
  minutes.
• ANALYSIS Can C2 system achieve 30-minute WC
  reactivity?
  
• SYNTHESIS Given a dozen such process performance
  parameters, design a C2
  
• Problem 2 A businessman in Colombo, Sri Lanka,
  wants to volunteer his fleet of 6 trucks for
  tsunami relief work logistics.
  
• ANALYSIS Can the combination of local, national,
  inter-governmental and non-government agencies
  deliver 90 utilization of these trucks over the
  next week?
• SYNTHESIS Design a distributed disaster-relief
  coordination website that permits this level of
  efficiency of utilization

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Problem Characteristics

• Kill-chain is interesting because it crosses
  functional boundaries
  
• What is the right ontology?
• What information is pertinent and how do you
  represent it?
  
• How do you reason about this information?
• What problem solving processes need to be
  engineered?
  
• How do you design a system that realizes the
  representations and problem solving processes
  using agents as building blocks?
  
• GOAL Sufficiently simple system models to
  support distributed planning, scheduling,
  control, learning and human interaction. Models
  must also facilitate posing of global-scope
  questions such as kill-chain reaction time.

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Tool Region Connection Calculus

• Randell, Cui and Cohn, 1992, based on Allen,
  1983
  
• Main application to do Weather and GIS

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Representing Combat Theaters
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Representing Disaster Relief Operations
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Reasoning and Computation

• RCC is NOT set theory ( regular sets of T3
  spaces)
  
• RCC is undecidable decidable subsets exist
• For AB, AB, A, many sorted logic called LLAMA
  is needed
  
• Need extra machinery for time, orientation,
  shape, variety
  
• Reasoning with any of these individually is NP
  hard
  
• All can be formulated as standard CSPs
• Poverty Conjecture There is no
  problem-independent, purely qualitative
  representation of space or shape (Forbus et.
  al., 1987)
• OUR GOAL is representational computational
  processes will be function dependent and include
  quantitative data

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Abstraction for motion domains

• Can support (semi/) automated reasoning with
  abstract models
  
• Cut down information overload for humans in loop
• Insulate efficient computation
• Protect symbolic technology from numbers and
  calculus

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Patch Models
Let G be the set of regions in the plane
satisfying RCC axioms. A patch p(t) is a region
of the plane, defined for the instant t.
Given a domain (D, E), and a function E (t, e),
(D is in G, and E is a set of entities),
satisfying
a scene history S (t0, tf) is a triple (D,
E,E(t)) defined on t0, tf. A view history V(t0
, tf) is a pair (P (t), R (t)) where P (t) is a
set of patches and R is a partial representation
function
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Patch Models (contd.)
A view history is said to correctly represent a
scene history if
Restricting S (t0, tf) and V(t0, tf) to an
instant yields views and scenes. Continuity for
scene and view histories is defined by
where the term represents the measure of the
set difference between the regions denoted.
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Illustration
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Patch Models (contd.)
A view history is strongly continuous if the
cardinality, n, of P(t) remains constant in t0,
tf. For a strongly continuous view history,
define the region connection state X(V(t)) of the
view history
A patch model is a scene history and a set of one
or more view histories that represent it.
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Continuity illustrated

• Formation and breakup two patches created and
  destroyed? One patch dormant?
  
• Did the patch at t become the patch at t- by
  moving or is it a new patch?
  
• Cause of subtleties patches do not have physical
  identities

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Example Entry-and-Exit
Basic mission template for hostage rescue, covert
operations, rush plays in football
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Entry-Exit (contd.)
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Entry-Exit (contd.)
Region connection history
Sample portion of realization
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Sensing and Command

• Any correct view history that can be uniquely
  constructed from a scene history is a legal
  observer view history Vo(t).
  
• Any (possibly incorrect) view history is a legal
  command view history Vc(t) for the domain (D,E)
  it represents for the period t0, tf that it is
  defined.
• A view history error Vc(t)-Vo(t) is defined if
  R(t, e) and E(t,e) induce the same partition on
  E.
  
• Vc-Vo can be computed from X(Vc(t)) and
  X(Vo(t))
  
• Control problem achieve Vc(t)-Vo(t) 0

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Remarks

• The definitions define legal dynamic
  abstractions
  
• Partiality of R(t,e) permits relevance-based
  abstraction
  
• R(t,e) being into allows for arbitrary
  non-representational patches in P(t)
  
• Continuity enforces RCC transition continuity
• Strong continuity captures persistence of a team
  entities
  
• Discontinuities model context shifts and
  formation and breakup phenomena (moving to a
  different induced partition of E)

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Expressivity

• Problem trivial representations
• Define expressivity e(V(t)) of a view as the
  ratio of the size of the reachable set of X(t) to
  the size of the state space, 8 n(n-1)/2 under
  arbitrary rigid translations of all patches in
  P(t).
• Expressivity is hard to compute, but bounds can
  be computed.

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Examples

• The scene itself has e (2/8) n(n-1)/2
• The trivial view n patches all equal to the
  whole domain has e (1/8) n(n-1)/2
  
• Hull expansion observer view e (3/8) n(n-1)/2
• Hula Hoop observer view has e (3/8) n(n-1)/2
  
  
• Expressivity is usefully high when the
  abstraction is neither too coarse, nor too fine.

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Spatio-Temporal Realizability

• A view history is realizable if there exists at
  least one possible scene history, with initial
  scene S(t0), such that Vc(t0,tf) is a
  representation of S(t0,tf).
• Relation to expressivity highly expressive views
  lead to more realizable futures
  
• Must consider temporal realizability as well, to
  achieve desired RC vector

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Examples

• Finite hula-hoop views of finite number of
  infinitismal entities (completely realizable)
  
• Two cars at an intersection, patches defined
  relative to road edges and car front and rear
  (but not lateral position)
  
• ATC, patches defined relative to nominal
  trajectories (Tomlins ATC method)

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Patch Model Capabilities

• Planning RCC-TIC CSP (can handle dynamic
  worlds!)
  
• Observation becomes view history generation
• Execution monitoring becomes view drift
  detection
  
• Feedback control becomes view matching
• Coordination becomes view merging
• Inter-mission conflict resolution is frame patch
  constraint satisfaction
  
• Adversary intention recognition is RCC string
  recognition
  
• Resource allocation RCC plus occupancy
  distributions
  
• Uncertain information translates to
  low-expressivity views (view dilution occurs as
  pdf covariances increase)
  
• Generals have balanced resolution views, privates
  have unbalanced resolution views
  
• Multiple hierarchies (mission/service) multiple
  views at each node
  
• Humans enter the loop naturally as part of the
  plan refinement problem

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Caveats

• Poverty conjecture will always need to augment
  RCC-based information
  
• Planning is between PSPACE to EXPSPACE hard, but
  
  
• Plan adaptation and refinement is the need,
  rather than first-principles planning
  
• BIG ONE One-pass view history realization not
  enough, need convergent iterative (multipass)
  refinement architectures

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Patchworks Implementation Architecture
iteration

• Distinction from target assignment
  simulator
  
• Need light-weight representations for symbolic
  logic methods
  
• Support interleaved deliberative/reactive
  behaviors
  
• Make space/time fundamental

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Patch-Based C2 Architecture
Automate 80 of information flow via views rule
bases capture coordination protocols, command loci
Slower, coarser view histories upstream in
hierarchy, created trickle-up, trickle-down (view
filtering and fusion)

Dynamically defined command nodes autonomy locus
composed from mission and service hierarchy
views, composition rules
Wrapper-based domain interaction layer, real-time
reconfigurable
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Glimpses of Refinement
Algorithm portfolio approach for repairing broken
paths
(Thientu Ho)
Failure vs. speed tradeoff for highly aggressive
discounted horizon dynamic refinement using
circular arcs (Tichakorn Wongpiromsarn)

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Summary

• Developed theoretical basis for abstraction-based
  motion management in complex, adversarial
  environments
  
• Developed prototype abstraction-based motion
  management system (patchworks)
  
• Proof-of-concept demonstrations of support for
  centralized/decentralized planning, plan
  recognition and coordination
  
• Completed (unintegrated) components for iterative
  path refinement

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Ongoing Work

• Refine theory
• Support more processes and functions
• Support automated abstraction
• Release open source version 2.0
• STRETCH goal 1 import RCC-based primitives into
  a planning DDL, glue patch models to BDI (Joint
  Intention) theory
  
• STRETCH goal 2 Demonstrate multi-node system in
  a simulation game
  
• Publication pipeline CCO 05, GNC 05

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Optimization techniques for multi-vehicle
cooperative control
M. Earl and R. DAndrea (Cornell University)
Modeling and strategy generation
Improve MILP efficiency using intelligent time
discretization techniques

• MILP methods
• Centralized planning (using fast tree search
  techniques) with decentralized plan execution
  (using optimal trajectory primitives)

Algorithm analysis

• Tradeoff between computational complexity and
  optimality
  
• Phase transitions as a function of vehicle
  capabilities (helpful discussions with C. Gomes).

Demonstrate cooperative control methods on
adversarial missions derived from RoboFlag