Situational Planning for the MIT DARPA Challenge Vehicle

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Situational Planning for the MIT DARPA Challenge
Vehicle

• Thomas Coffee

Image Credit David Moore et al.
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Problem Statement

• Inputs
• Vehicle path position-space waypoint sequence ?
  Mission Planner
• Vehicle state state-space configuration ?
  Perceptual State Estimator
• Obstruction environment position-space regions,
  current velocities, and types (lanes, static
  obstacles, vehicles, unknowns) ? Perceptual State
  Estimator
• Law constraints lane corridors and speed limits
  ? RNDF
• Sensor model ? ???
• Output (10 Hz)
• Status reports success/failure of each
  constraint on vehicle trajectory plan
• Vehicle trajectory high-resolution state-space
  curve
• Open-space-realizable by vehicle control system
• Avoids input obstacles current-velocity-bounded
  subspace
• Avoids input unknown regions zero-velocity
  subspace
• Consistent with law constraints
• Prioritizes inconsistent constraints by type
  static gt vehicle gt unknown gt lane gt law
• Attempts to achieve sensor coverage of unknown
  regions
• Time estimate to first waypoint in sequence

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Overview of Past Approaches

• Exact solutions
• Dynamic programming state-space grid search
• Holonomic configuration-space planning with
  steering control for admissible path fitting
• Adaptive exploration and searching with maximally
  spaced landmarks (Ariadnes Clew)
• Probabilistic roadmaps with learning by adaptive
  sampling query by graph search
• Rapidly exploring random trees (bidirectional)

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Exact Solutions

• Limited to special cases
• Canny J, Rege A, Reif J (1990)
• Point masses only
• lt 2-D position space
• Static bounds on velocity and acceleration
• Souères P, Boissonnat JD (1998)
• Specific to forward-backward simple car geometry
  and dynamics
• Does not handle obstacles
• Constructs distance-optimal solution
  (time-optimal only with decoupled steering and
  accelerator dynamics)

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State-Space Grid Search

• Donald B, Xavier P, Canny J, Reif J (1993)
• Advantages
• Provably polynomial running time (first such
  algorithm)
• Provably near-optimal (1 e), can trade run time
  vs. e
• Uses bang-control steps often corresponding to
  optimal paths
• Disadvantages
• Handles only simple magnitude bounds on state
  variables
• Does not scale well to larger dof problems

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Holonomic Steering Control

• Variety of holonomic planning techniques with
  domain-specific steering control
• Advantages
• Holonomic/non-holonomic decision problems
  equivalent for small-time controllable systems
• Fast path planning in lower-dimensional spaces
• Disadvantages
• Path planning separated from vehicle dynamics
  (Lozano-Perez configuration space) inefficient
  use of resources
• Paths found may be topologically distant from
  dynamically optimal paths
• Incomplete for non-small-time controllable
  systems
• Steering control must be specialized for each
  application

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Ariadnes Clew

• Bessière P, Ahuactzin J-M, Talbi E-G, Mazer E
  (1993)
• Advantages
• Landmarks adaptively sample widely over the
  configuration space
• Fast optimization step based on genetic
  algorithms
• Signficantly faster still with massively parallel
  implementation
• Disadvantages
• Produces rather suboptimal path results
  regardless of c-space difficulty
• Extremely messy implementation with many free
  parameters

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Probabilistic Roadmaps

• Kavraki LE, Svestka P, Latombe J-C, Overmars MH
  (1996)
• Advantages
• Roadmaps adaptively sample widely over the
  configuration space
• Fast roadmap forest expansion based on
  semi-complete planning
• Learning and query phases resize appropriately to
  resource constraints
• Disadvantages
• Produces somewhat suboptimal path results
  regardless of c-space difficulty
• Somewhat messy implementation with many free
  parameters
• Requires additional smoothing to fully respect
  dynamic constraints

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Rapidly Exploring Random Trees

• LaValle SM, Kuffner JJ (2001)
• Advantages
• Fast adaptive sampling of configuration space
  using Voronoi randomization bias
• Scales well to higher-dimensional configuration
  spaces
• Disadvantages
• Produces somewhat suboptimal path results
  regardless of c-space difficulty
• Bidirectional approach requires additional
  smoothing at tree intersection

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Baseline Approach

• Deterministic (single) tree exploration in
  unobstructed configuration spacetime
• Tree maintenance/expansion based on D
• Heuristic using modified Reeds-Shepp metric
• Node expansion using hard and level steer,
  accelerator/brake for optimality
• Reverse gear dynamics included by default
• Moderate aggressiveness model dynamic obstacles
  as bounded by current velocity

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Justification for Baseline Approach

• Simple essential configuration space (3-D), hence
  high-dof performance not required
• Highly dynamic obstacle map, hence building up
  map information less valuable
• D approach provides a candidate path regardless
  of search completion
• Computational resources expended only on strong
  candidate paths
• Node expansion strategy can be tailored to
  obstacle and law constraints to produce
  near-optimal paths
• Guaranteed approximate optimality, can be traded
  vs. node expansion parameters

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Test Plan Success Criteria

• Test Plan
• Software testing with simulated splinter and
  vehicle dynamics
• Hardware testing on splinter with added dynamic
  constraint layer
• Hardware testing on DGC vehicle?
• Success Criteria
• Consistent path generation meeting constraints
  for reasonable driving environments
• Behavioral appropriateness of paths generated
• Sufficient plan frequency to maintain intended
  course and avoid dynamic obstacles in
  non-emergency scenarios

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Project Timeline

• Nov 17 Initial software implementation
• Nov 24 Simulation testing complete
• Dec 01 Splinter testing complete
• Dec 08 Initial DGC vehicle testing complete
• Dec 13 Final code/documentation delivered
• ?