WaveDriving® and Jam-Absorption Driving

Introduction to WaveDriving®

WaveDriving® is a innovative and certified technique developed in Spain Melchor that redefines the understanding of vehicular traffic dynamics through the analysis of movement waves.

Fundamental equation of WaveDriving®: "The movement wave of a vehicle in a platoon is the wave of the first vehicle plus the sum of the individual waves of the following drivers (excluding the leader)".

Mathematical Formalization

If \(\phi_0(t)\) describes the leader's trajectory (position as a function of time), the dynamics of the \(i\)-th vehicle (\(i \geq 1\)) is modeled as:

\[ \phi_i(t) = \phi_0(t) + \sum_{k=1}^{i-1} \Delta \phi_k(t), \]

where:

\(\Delta \phi_k(t)\) captures the disturbances (accelerations/braking) of driver \(k\)
\(i\) is the vehicle index in the platoon
\(t\) represents time

Physical Interpretation:

The position of each vehicle is the superposition of:

The leader's base wave (\(\phi_0(t)\))
The cumulative sum of disturbances (\(\sum \Delta \phi_k(t)\)) from all preceding vehicles

This approach radically differs from classical models like Newell's car-following theory, as it considers the complete system of interactions rather than isolated vehicle pairs.

Jam-Absorption Driving (JAD)

Jam-Absorption Driving (JAD) is a driving strategy inspired by the principles of Newell's vehicle-following theory, but which reaches its full potential when integrated with WaveDriving®.

Principles of JAD

Proactive absorption of disturbances
Minimization of traffic jam propagation
Optimization of distance and speed

Relationship with WaveDriving®

JAD can be interpreted as a technique to minimize individual disturbances (Δφₖ(t)) in the context of the wave superposition described by WaveDriving®.

The Three Gaps in WaveDriving®

One of the most innovative conclusions of WaveDriving® is that between a vehicle and its predecessor there isn't a single gap, but three distinct spaces with specific functions:

1Wave Absorption Zone

Space dedicated to dampening the energy disturbance generated by the preceding vehicle. Acts as a "cushion" to absorb waves without transmitting them to the rest of the platoon.

2Road Safety Distance

The minimum space for emergency braking (classic "2-second rule"), but dynamically adjusted based on the phase of the preceding vehicle's wave.

3Space Balancing

Indicator of asphalt use efficiency. Positive means space wastage, negative indicates safety distance invasion.

Balance = Real distance - (Gap 1 + Gap 2)

The Six Electro-Car-Diagrams

By projecting a driver's wave onto six distinct planes, we obtain the six electro-car-diagrams that enable multidimensional analysis of vehicular performance:

Diagram	What it measures	Relationship with WaveDriving®
1. Speed Efficiency	Speed management to maintain stable wave	Minimizes Δφₖ(t) (disturbances)
2. Consumption Efficiency	Relationship between motion wave and energy consumption	Abrupt disturbances generate higher consumption
3. Space Efficiency	Use of surrounding space for harmonic flow	Optimal position minimizes interference
4. Distance and Safety Relationship	Management of front, side and rear distances	Extends Newell's distance concept to 3D
5. Frontal Road Safety	Risk of frontal or rear-end collision	Analyzes φᵢ(t) - φᵢ₋₁(t)
6. Rear Road Safety	Impact on following vehicles	Evaluates downstream disturbance propagation

Visual diagram of the 6 Electro-Car-Diagrams

Figure 1: Visual representation of the 6 Electro-Car-Diagrams
Actual driver: before and after completing WaveDriving® training

Comparison with Classical Models

Aspect	Newell's Theory	WaveDriving®
Unit of analysis	Leader-follower pair	Entire platoon (wave system)
Mathematical basis	Time-shifted trajectories	Wave superposition (φᵢ(t))
Origin of disturbances	Binary interaction	Sum of individual waves
Distance concept	Single gap	Three dynamic gaps

Practical Applications

For Autonomous Vehicles

Algorithms can use the three gaps to anticipate disturbances and adjust distances in real time. Space balancing would serve as an optimization metric.

In ADAS Systems

Driving assistants could integrate the electro-car-diagrams to provide real-time feedback to human drivers.

Driver Training

Teaching drivers to actively manage their three gaps and understand how their actions affect global traffic flow.

Traffic Dynamics Training Technique

To facilitate understanding and application of WaveDriving® principles, we've developed a web simulator that uses a training technique called 'Mental Analogies'. These consist of three fundamental concepts:

1 Vehicle as Traffic Light

A vehicle is a traffic light on wheels: green when moving, amber when braking, and red when stopped.

2 Imaginary Spring

Between every two vehicles there's an imaginary spring that compresses or expands according to accelerations and braking, representing energy transfer between vehicles.

3 Safety Bar and Spring

When following another vehicle, imagine: a rigid bar marking the minimum safety distance, followed by a spring representing additional space to maintain momentum.

Simulator objective: These mental analogies help drivers visualize and intuitively understand wave dynamics in traffic, facilitating practical application of WaveDriving® and Jam-Absorption Driving principles.