Datta Godbole

1
Safety and Capacity Analysis of Automated Highway
Systems

• Datta Godbole
• California PATH,
• University of California, Berkeley
• November 5, 1998

2
Emergency Operation of Platoons Collisions,
Emergency Deceleration Platoon Lane Change(MOU
319)

• Research Focus
• Detailed design and analysis of regulation and
  coordination level controllers for emergency
  platoon operation
• obstacle avoidance is used as an illustrative
  example.
• Background
• Under normal operations, a platooning system can
  be designed to completely exclude possibility of
  collisions
• perfect lateral control
• Swaroop-Hedrick, Varaiya et. al.,
  Lygeros-Godbole-Sastry
• Under degraded conditions, intra-platoon
  collisions may be inevitable and may limit system
  performance
• Hitchcock, Godbole-Lygeros

3
Emergency Platoon Operation

• Tasks
• Investigate the effect of coordinated and
  uncoordinated emergency braking on platoon safety
• Design emergency platoon maneuvers to maximize
  safety
• emergency deceleration platoon lane change
• Analyze the effect of different control
  operating strategies on system capacity
• Investigators Projects
• Profs. Sastry, Lynch (MIT) Swaroop (Texas AM)
• Drs. Lygeros Godbole (MOUs 319, 238-310)
• Jianghai Hu, Jun Zhang (UCB), S. M. Yoon (Texas
  AM), Carl Livadas (MIT)
• Veit Hagenmeyer, Dr. Raja Sengupta (NAHSC Task
  C3, B5)

4
Emergency Deceleration Modeling

• Scenario
• First vehicle decelerates as hard as possible
• Safety
• Collisions (if any) at low relative velocity
• Assumptions
• All following vehicles respond by braking only
• Vehicle longitudinal dynamics
• point-mass model with delays and first order lags
• collisions modeled by conservation of
• momentum and coefficient of restitution

5
Emergency DecelerationProblem Formulation

• Analysis Problem
• Given a deceleration strategy for a vehicle
  string, establish conditions on parameters such
  that system is safe
• Synthesis Problem
• Given system parameters, design a safety
  maximizing controller.
• Parameters
• Acceleration capabilities, operating speed,
  control system delays, coefficients of
  restitution, vehicle masses

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Emergency Deceleration

• Analysis of a default deceleration strategy for
  platooning
• Each vehicle decelerates as hard as it can
  immediately after realizing emergency situation
• Necessary and sufficient conditions on parameter
  variations
• Probabilistic analysis with parameter variations
  matching current vehicle-highway system
• Question How does coordinated braking compare
  with this strategy

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Emergency Deceleration and Coordinated Braking

• string stability is achieved
• using coordinated braking
• at the cost of braking amplification
• in platoon follower controller

• We are currently working on analyzing effect of
• emergency deceleration of the platoon leader
• using SMARTAHS (Texas AM)

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Emergency Deceleration Theoretical Analysis
(Lygeros, Lynch _at_ MIT)

• Formalism
• Each vehicle is modeled as an I-O Hybrid
  automaton with
• continuous variables Dxi, vi, ai
• discrete actions collision, touching, separate
• Derive conditions for safety (all collision
  speeds lt vA) using deductive verification methods
• Results (vA3 m/s, no delays, near-equal masses)
• e variation in braking capability
• Sufficient condition e lt 1.08 m/s2 (0.9) at v0
  25m/s (30)
• Necessary condition (v025 m/s, elastic
  collisions)

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Braking Capability Distribution(Bret Michael _at_
PATH)
Dry Pavement (LDPV)
Wet Pavement(LDPV)
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Emergency Deceleration Probabilistic Analysis
(Godbole, Lygeros _at_ UCB)

• Given
• probability distribution of braking capabilities
  of vehicles
• communication actuation delays,
• initial speeds and spacings
• coefficient of restitution as a function of
  impact speed
• calculate collision statistics
• frequency and severity of collisions
• Parameter sensitivity
• safety increases with
• decreasing elasticity, decreasing intra-platoon
  spacing, narrower braking distribution
• safety insensitive to
• operating speeds, communication delays and
• communication architectures

11
Emergency DecelerationSimulation Results
12
Emergency DecelerationCollision Statistics
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Relationship Between Safety and Capacity
Accel to Merge

• What should be the baseline minimum safety?
• Number of crashes per hazard, hard braking, ... ?
• Approach
• Eliminate propagation of collisions from one
  platoon to another using appropriate
  inter-platoon spacing
• only collisions in the system are intra-platoon
  collisions
• Additional parameters
• inter-platoon communication (continuous or
  emergency)
• Real-time knowledge of braking capability

i1
i2
i
Obstacle
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Pipeline Capacity

• N Platoon size
• braking capability known
• within 0.5 m/s/s
• Loss of capacity due to
• platoon join split
• not considered
• spacing designed for
• no inter-platoon collisions
• in worst-case

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Summary of Emergency Deceleration

• Question To Platoon or Not to Platoon?
• Ans No
• with current state of the technology current
  vehicle fleet
• Ans Yes
• with narrower braking distribution (entry
  control), inelastic bumper designs real-time
  braking capability estimation
• Issues for further investigation
• braking capability estimation
• elimination of merging by accelerating (merging
  by lane changing?) to improve safety
• elimination of splitting before lane changing for
  improving capacity
• infrastructure assisted merge/entry to improve
  traffic flow
• design of optimal emergency platoon controller

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Emergency Lane Change1 vehicle platoons

• Lane change Maneuver involves
• Gap selection/creation, Alignment, Lateral
  move-over
• Safe Lane Change
• Vehicle pairs (1,2), (3,1) satisfy safe vehicle
  following requirements from the beginning of
  lateral motion.
• Safe efficient control coordination design
• Hagenmeyer,Godbole,Sengupta,Swaroop (CDC97,CDC98)

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Platoon Lane Change(Swaroop Yoon _at_ Texas AM)

• Lateral control is facilitated by obtaining
• absolute position of vehicle w.r.t. specified
  trajectory
• preview information of the trajectory
• improved ride comfort and tracking performance
• Lane changing task
• trajectory is designed in real time gt absolute
  deviation from the trajectory is difficult to
  sense for the followers
• Problem Statement
• Consider 2 vehicle platoon.
• Design a controller for the follower to track the
  trajectory traced by the leader while maintaining
  desired distance from the leader

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Platoon Lane Change(Work in Progress)

• Control Design
• Information used by the control law
• range, range rate, relative yaw angle
• lateral, longitudinal, yaw velocity
  acceleration of follower
• lateral, longitudinal, yaw velocity
  acceleration of leader
• instantaneous curvature of the trajectory traced
  by leader
• Assumption
• both vehicles traverse same curvature at any
  given time
• Solution Methodology
• consider the motion of 3 rigid links in a
  horizontal plane such that the center of mass of
  1st 3rd link are always on the same circular
  arc
• Status
• controller developed for 2 vehicle platoon

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Summary Future Work(MOU 319)

• Analyzed inter-vehicle collisions in a vehicle
  string due to emergency deceleration
• necessary sufficient conditions for safe
  platooning
• parameter sensitivity analysis
• Developed a combined safety and capacity analysis
• Current work
• Platoon lane change and lateral string stability
• Optimal control law for platoon emergency
  deceleration
• Probabilistic analysis of collision propagation
  in a string of platoons.

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Reports Publications(MOU 319)

• John Lygeros Nancy Lynch, Strings of vehicles
  Modeling and Control, In Hybrid Systems
  Computation and Control, LNCS No. 1386, pp.
  273-288, Springer 1998
• Datta N. Godbole John Lygeros, Safety and
  Capacity analysis of Automated Highway Systems,
  Accepted to appear in Transportation Research -
  Part C
• D. Swaroop S. M. Yoon, The Design of a
  Controller for a following vehicle in an
  Emergency Lane Change Maneuver, Preprint, Texas
  AM University