Platoon Following Simulator

Slow Free-flow vehicle color = its current speed

Near lead End of platoon chart-line color = position in the platoon

Speed

–

Relative speed Δv

–

Space gap Δx

–

Time gap

–

Acceleration

–

Time–space diagram

position vs. time, colored by instantaneous speed — watch a slowdown propagate backward as a shockwave

Lead vehicle

Target speed 20.0 m/s

Max acceleration 3.0 m/s²

Caps how fast the lead car can speed up or brake — it ramps toward the slider, it doesn't jump.

Car-following model

Following policy

Time gap: desired distance grows with speed. Space gap: a fixed desired distance (no τ). Time + ΔV: the time-gap law plus λ·ΔV, a term that reacts to relative speed. Cruise: every follower tracks a set speed and ignores the vehicle ahead, so it needs the CBF filter to stay safe. Changing it mid-run is a live perturbation; Reset starts every follower at the active model's equilibrium.

α — gap gain 0.50 s⁻²

τ — desired time gap 1.50 s

g_des — desired gap 20.0 m

A fixed following distance, independent of speed; g_min stays a separate, small safety floor.

λ — relative-speed gain 0.70 s⁻¹

Closing on the vehicle ahead (ΔV < 0) brakes you; pulling away lets you accelerate.

v_set — set speed 28.0 m/s

κ — speed-tracking gain 0.30 s⁻¹

Cruise control ignores the vehicle ahead: dv/dt = κ·(v_set − v). Alone it is unsafe behind a slower vehicle (the nominal controller in Gunter et al.'s RAV4 experiment); only the CBF filter below keeps each follower off the one ahead.

dΔx_i/dt = v_i-1 − v_i
dv_i/dt = α · [Δx_i − (g_min + τ·v_i)]
same parameters for every follower i = 1…N

String stability (linearized)

L∞

Small perturbations only: ignores acceleration caps, speed and gap floors, and large disturbances.

Follower acceleration cap

Applied to every follower. Prius: speed-dependent a_max(v) = 0.4 + 0.015(40−v), a_min(v) = −0.6 − 0.04(40−v) m/s², fit from instrumented test drives (Zhou et al. 2021, arXiv:2108.03232). RAV4: flat −3.5 / +1.5 m/s² (limits supplied by the lab, not from that fit).

uncapped

CBF safety filter

Control barrier function (Gunter et al.) on every follower: keeps h = Δx − t_min·v − d_min ≥ 0 by capping acceleration at u ≤ (k·h + ΔV)/t_min, i.e. u = min(u_model, u_CBF). Applied on top of the model and before the acceleration caps above. Reset starts inside the safe set; switching it on mid-run from an unsafe state shows the recovery.

t_min — minimum time gap2.0 s

d_min — standoff distance15.0 m

k — class-K gain (α(h) = k·h)0.10 s⁻¹

Equivalent α = k / t_min s⁻²

Safety property:

–

L2L∞

L — vehicle length 4.5 m

g_min — minimum gap 2.0 m

Platoon

N — number of followers 10

Changing this resets the platoon to a fresh, fully-settled state.