* Copyright (c) 2013-2015 Delft University of Technology, PO Box 5, 2600 AA, Delft, the Netherlands. All rights reserved.
* BSD-style license. See OpenTrafficSim License.
*
* @version $Revision: 1408 $, $LastChangedDate: 2015-09-24 15:17:25 +0200 (Thu, 24 Sep 2015) $, by $Author: pknoppers $,
* initial version 19 nov. 2014
* @author Peter Knoppers
*/
public class IDM extends AbstractGTUFollowingModel
{
/** Preferred net longitudinal distance when stopped [m]. */
private final Length.Rel s0;
/** Maximum longitudinal acceleration [m/s^2]. */
private final Acceleration a;
/** Longitudinal deceleration [m/s^2]. (Should be a positive value even though it is a deceleration.) */
private final Acceleration b;
/** Safe time headway. */
private final Time.Rel tSafe;
/**
* Time slot size used by IDM (not defined in the paper, but 0.5s is a reasonable trade-off between computational speed and
* accuracy).
*/
private final Time.Rel stepSize = new Time.Rel(0.5, TimeUnit.SECOND);
/**
* Mean speed limit adherence (1.0: mean free speed equals the speed limit; 1.1: mean speed limit equals 110% of the speed
* limit, etc.).
*/
private final double delta;
/**
* Construct a new IDM car following model with reasonable values (reasonable for passenger cars).
*/
public IDM()
{
this.a = new Acceleration(1.56, AccelerationUnit.METER_PER_SECOND_2);
this.b = new Acceleration(2.09, AccelerationUnit.METER_PER_SECOND_2);
this.s0 = new Length.Rel(3, LengthUnit.METER);
this.tSafe = new Time.Rel(1.2, TimeUnit.SECOND);
this.delta = 1d;
}
/**
* Construct a new IDM car following model.
* @param a DoubleScalar.Abs<AccelerationUnit>; the maximum acceleration of a stationary vehicle (normal value is 1
* m/s/s)
* @param b DoubleScalar.Abs<AccelerationUnit>; the maximum deemed-safe deceleration (this is a positive value).
* Normal value is 1.5 m/s/s.
* @param s0 DoubleScalar.Rel<LengthUnit>; the minimum stationary headway (normal value is 2 m)
* @param tSafe DoubleScalar.Rel<TimeUnit>; the minimum time-headway (normal value is 1s)
* @param delta double; the speed limit adherence (1.0; mean free speed equals the speed limit; 1.1: mean free speed equals
* 110% of the speed limit; etc.)
*/
public IDM(final Acceleration a, final Acceleration b, final Length.Rel s0, final Time.Rel tSafe, final double delta)
{
this.a = a;
this.b = b;
this.s0 = s0;
this.tSafe = tSafe;
this.delta = delta;
}
/**
* Desired speed (taking into account the urge to drive a little faster or slower than the posted speed limit).
* @param speedLimit DoubleScalarAbs<SpeedUnit>; the speed limit
* @param followerMaximumSpeed DoubleScalar.Abs<SpeedUnit>; the maximum speed that the follower can drive
* @return DoubleScalarRel<SpeedUnit>; the desired speed
*/
private Speed vDes(final Speed speedLimit, final Speed followerMaximumSpeed)
{
return new Speed(Math.min(this.delta * speedLimit.getSI(), followerMaximumSpeed.getSI()), SpeedUnit.SI);
}
/** {@inheritDoc} */
public final Acceleration computeAcceleration(final Speed followerSpeed, final Speed followerMaximumSpeed,
final Speed leaderSpeed, final Length.Rel headway, final Speed speedLimit)
{
// System.out.println("Applying IDM for " + follower + " headway is " + headway);
// dV is the approach speed
Speed dV = followerSpeed.minus(leaderSpeed);
Acceleration aFree =
new Acceleration(this.a.getSI()
* (1 - Math.pow(followerSpeed.getSI() / vDes(speedLimit, followerMaximumSpeed).getSI(), 4)),
AccelerationUnit.SI);
if (Double.isNaN(aFree.getSI()))
{
aFree = new Acceleration(0, AccelerationUnit.SI);
}
Acceleration logWeightedAccelerationTimes2 =
new Acceleration(Math.sqrt(this.a.getSI() * this.b.getSI()), AccelerationUnit.SI).multiplyBy(2);
// don't forget the times 2
// TODO compute logWeightedAccelerationTimes2 only once per run
Length.Rel right =
followerSpeed.multiplyBy(this.tSafe).plus(
dV.multiplyBy(followerSpeed.divideBy(logWeightedAccelerationTimes2)));
/*-
Calc.speedTimesTime(followerSpeed, this.tSafe).plus(
Calc.speedTimesTime(dV, Calc.speedDividedByAcceleration(followerSpeed, logWeightedAccelerationTimes2)));
*/
if (right.getSI() < 0)
{
// System.out.println("Fixing negative right");
right = new Length.Rel(0, LengthUnit.SI);
}
Length.Rel sStar = this.s0.plus(right);
if (sStar.getSI() < 0) // Negative value should be treated as 0
{
System.out.println("sStar is negative");
sStar = new Length.Rel(0, LengthUnit.SI);
}
// System.out.println("s* is " + sStar);
Acceleration aInteraction =
new Acceleration(-Math.pow(this.a.getSI() * sStar.getSI() / headway.getSI(), 2), AccelerationUnit.SI);
Acceleration newAcceleration = aFree.plus(aInteraction);
if (newAcceleration.getSI() * this.stepSize.getSI() + followerSpeed.getSI() < 0)
{
// System.out.println("Limiting deceleration to prevent moving backwards");
newAcceleration = new Acceleration(-followerSpeed.getSI() / this.stepSize.getSI(), AccelerationUnit.SI);
}
// System.out.println("newAcceleration is " + newAcceleration);
return newAcceleration;
}
/** {@inheritDoc} */
@Override
public final Time.Rel getStepSize()
{
return new Time.Rel(this.stepSize);
}
/** {@inheritDoc} */
@Override
public final Acceleration maximumSafeDeceleration()
{
return this.b;
}
/** {@inheritDoc} */
@Override
public final String getName()
{
return "IDM";
}
/** {@inheritDoc} */
@Override
public final String getLongName()
{
return String.format("%s (a=%.1fm/s\u00b2, b=%.1fm/s\u00b2, s0=%.1fm, tSafe=%.1fs, delta=%.2f)", getName(),
this.a.getSI(), this.b.getSI(), this.s0.getSI(), this.tSafe.getSI(), this.delta);
}
}