Intelligent Driver Model - Model Characteristics

Model Characteristics

The acceleration of vehicle can be separated into a free road term and an interaction term:

$\dot{v}^\text{free}_\alpha = a\,\left( 1 - \left(\frac{v_\alpha}{v_0}\right)^\delta \right) \qquad\dot{v}^\text{int}_\alpha = -a\,\left(\frac{s^*(v_\alpha,\Delta v_\alpha)}{s_\alpha}\right)^2 = -a\,\left(\frac{s_0 + v_\alpha\,T}{s_\alpha} + \frac{v_\alpha\,\Delta v_\alpha}{2\,\sqrt{a\,b}\,s_\alpha}\right)^2$

Free road behavior: On a free road, the distance to the leading vehicle is large and the vehicle's acceleration is dominated by the free road term, which is approximately equal to for low velocities and vanishes as approaches . Therefore, a single vehicle on a free road will asymptotically approach its desired velocity .

Behavior at high approaching rates: For large velocity differences, the interaction term is governed by .

This leads to a driving behavior that compensates velocity differences while trying not to brake much harder than the comfortable braking deceleration .

Behavior at small net distances: For negligible velocity differences and small net distances, the interaction term is approximately equal to, which resembles a simple repulsive force such that small net distances are quickly enlarged towards an equilibrium net distance.

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