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arxiv: 1907.04120 · v1 · pith:GONFYMLYnew · submitted 2019-07-09 · 🧮 math.OC

Funnel cruise control

Thomas Berger , Anna-Lena Rauert This is my paper

Pith reviewed 2026-05-25 00:31 UTC · model grok-4.3

classification 🧮 math.OC
keywords funnel controladaptive cruise controlvehicle followingsafety distancemodel-free controlvelocity regulationdistance regulation
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The pith

A model-free funnel cruise controller maintains safety distance while approaching a target velocity by switching between speed and distance regulation.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents a funnel cruise controller for the vehicle following problem. It guarantees a minimum safety distance to the leader at all times and reaches a favorite velocity as much as possible. The design is model-free and combines a velocity funnel controller for distant leaders with a distance funnel controller for close ones. A switching logic determines which controller is active. The authors prove that the overall design is feasible and demonstrate it through simulations of everyday traffic situations.

Core claim

The funnel cruise controller achieves guaranteed safety distance and maximal approach to favorite velocity. It consists of a velocity funnel controller that acts when the leader is far and a distance funnel controller that acts when the leader is close, together with a logic that switches between them. The feasibility of this combined controller is established by rigorous proof.

What carries the argument

The funnel cruise controller, which switches between a velocity funnel controller and a distance funnel controller according to the leader distance.

If this is right

  • The safety distance is guaranteed at all times regardless of the leader's behavior.
  • The favorite velocity is reached whenever the leader vehicle is sufficiently far ahead.
  • The controller requires no model of the vehicle dynamics or the leader.
  • The same design works across multiple common traffic scenarios.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The approach may extend to platoons of several vehicles by applying the same switching idea between consecutive pairs.
  • Sensor noise or actuator limits could be incorporated by adjusting the funnel boundaries without changing the core structure.
  • The model-free property suggests the method could be combined with learning-based velocity selection.

Load-bearing premise

The switching logic between the two funnel controllers must be arranged so that the safety distance is never violated during any transition.

What would settle it

A concrete simulation or vehicle test in which the distance to the leader drops below the safety threshold at any time while the controller is running.

Figures

Figures reproduced from arXiv: 1907.04120 by Anna-Lena Rauert, Thomas Berger.

Figure 1
Figure 1. Figure 1: Vehicle following framework. to be taken into account. Therefore, we use the following sim￾ple models which are taken from [3, Sec. 3.1]: Fg : R≥0 → R, t 7→ mgsinθ(t), Fa : R≥0 ×R → R, (t, v) 7→ 1 2 ρ(t)CdAv2 , Fr : R → R, v 7→ mgCr sgn(v), where m (in kg) denotes the mass of the (following) vehicle, g = 9.81m/s 2 is the acceleration of gravity, θ(t) ∈ [− π 2 rad, π 2 rad] and ρ(t) (in kg/m3 ) denote the s… view at source ↗
Figure 2
Figure 2. Figure 2: The case ϕ(0) = 0 is explicitly allowed, meaning that no restriction is put on the initial value since ϕ(0)|e(0)| < 1; the funnel boundary 1/ϕ has a pole at t = 0 in this case. λ b (0, e(0)) 1/φ(t) t 1 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Illustration of the distance funnel controller. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Illustration of the final control design. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Simulation of the funnel cruise controller (13) for the system (2) with [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Simulation of the funnel cruise controller (13) for the system (2) with [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
read the original abstract

We consider the problem of vehicle following, where a safety distance to the leader vehicle is guaranteed at all times and a favourite velocity is reached as far as possible. We introduce the funnel cruise controller as a novel universal adaptive cruise control mechanism which is model-free and achieves the aforementioned control objectives. The controller consists of a velocity funnel controller, which directly regulates the velocity when the leader vehicle is far away, and a distance funnel controller, which regulates the distance to the leader vehicle when it is close so that the safety distance is never violated. We provide a rigorous proof for the feasibility of the overall controller design. The funnel cruise controller is illustrated by a simulation of three different scenarios which may occur in daily traffic.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper introduces the funnel cruise controller, a model-free adaptive cruise control mechanism for vehicle following. It combines a velocity funnel controller (active when the leader is far) with a distance funnel controller (active when close) to guarantee a safety distance at all times while approaching a favorite velocity when possible. The design is supported by a rigorous feasibility proof for the overall switched system and illustrated via simulations of three daily traffic scenarios.

Significance. If the feasibility proof holds, the result offers a novel model-free approach to adaptive cruise control with explicit safety invariants, which could be significant for control theory applications in autonomous vehicles. The combination of funnel-based regulation for both velocity and distance, with a switching mechanism, provides a universal controller without requiring vehicle models.

major comments (1)
  1. [overall controller design and switching logic] The feasibility proof for the composite controller (the section describing the overall controller design and switching logic): the argument that the switching condition preserves the safety distance for arbitrary leader trajectories must explicitly show that the distance error remains inside the funnel boundary at the instant of activation, accounting for worst-case closing speeds before the switch. The provided description of the 'close' threshold does not bound this, which is load-bearing for the central safety claim.
minor comments (2)
  1. [simulations] The simulation section would benefit from explicit parameter values for the funnels and switching threshold to allow reproducibility.
  2. [controller definitions] Notation for the funnel boundaries and error signals should be defined consistently across the velocity and distance controllers.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and the constructive comment regarding the switching logic in the feasibility proof. We address the point below.

read point-by-point responses

  1. Referee: The feasibility proof for the composite controller (the section describing the overall controller design and switching logic): the argument that the switching condition preserves the safety distance for arbitrary leader trajectories must explicitly show that the distance error remains inside the funnel boundary at the instant of activation, accounting for worst-case closing speeds before the switch. The provided description of the 'close' threshold does not bound this, which is load-bearing for the central safety claim.

    Authors: We agree that an explicit verification of the funnel invariant at the switching instant is essential for arbitrary leader trajectories. The existing feasibility argument establishes that the velocity funnel maintains sufficient separation prior to the switch and that the distance funnel is only activated when the error lies inside its boundary by construction of the threshold; however, to strengthen clarity we will revise the overall controller design section to include a dedicated lemma that explicitly bounds the distance error at activation, incorporating a worst-case relative-velocity estimate derived from the velocity funnel performance. This addition will make the preservation of the safety distance fully rigorous without altering the controller or the core proof strategy. revision: yes

Circularity Check

0 steps flagged

No circularity; feasibility proof stands independently of inputs

full rationale

The paper presents a novel model-free funnel cruise controller composed of velocity and distance funnel components plus switching logic, with an explicit claim of a rigorous feasibility proof. No equations or claims reduce a prediction to a fitted parameter by construction, no self-citation is invoked as the sole justification for a uniqueness or invariance result, and the switching safety argument is asserted to rest on an independent proof rather than on redefinition of the funnels themselves. This matches the default case of a self-contained derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based solely on the abstract, no specific free parameters, axioms, or invented entities are identifiable. The controller is described as model-free, suggesting avoidance of typical system parameters, but details are absent.

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

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contradicts
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unclear
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Reference graph

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