Pedestrian Models

Pedestrian Models#

JuPedSim allows creating pedestrian simulations with different microscopic models. Below is a list of all the models that are currently available. Please refer to the links in the respective section for a detailed discussion of the respective model.

Collision Free Speed Model#

The collision-free speed model is a mathematical approach designed for pedestrian dynamics, emphasizing the prevention of collisions among agents. The direction in which an agent moves is determined through an isotropic combination of exponential repulsion from nearby agents. The strength of this repulsion is influenced by the proximity to others within their surroundings, treating all directions equally in terms of influence. Agents adjust their speed according to the nearest neighbor in their headway, allowing them to navigate through congested areas without overlapping or obstructing each other. The collision-free speed model takes into account the length of the agent, which determines the required space for movement, and the maximum achievable speed of the agent. This simplified and computationally efficient model aims to mirror real-world pedestrian behaviors while maintaining smooth movement dynamics.

The collision-free speed model is available in two variants in JuPedSim. Both variants implement the same algorithm but differ when it comes to defining model parameters globally vs. per-agent.

In CollisionFreeSpeedModel neighbor and geometry repulsion parameters are global parameters, i.e. all agents use the same values and the values are constant over the simulation.

In CollisionFreeSpeedModelV2 neighbor and geometry repulsion parameters are per-agent parameters that can be set individually via CollisionFreeSpeedModelV2AgentParameters and can be changed at any time.

A detailed description is available on PedestrianDynamics.

The original publication can be found at https://arxiv.org/abs/1512.05597

Anticipation Velocity Model#

The anticipation velocity model (AVM) is a mathematical approach for pedestrian dynamics that prevents collisions through anticipatory behavior. The model divides anticipation into three components: situation perception, future prediction, and strategy selection. Building upon the collision-free speed model (CSM), AVM determines agent movement through exponential repulsion from nearby agents. Unlike CSM, the influence direction is orthogonal to the agent’s desired direction. Repulsion strength is affected by agents within the perception field - specifically, those in the union of two half-planes where the agent moves or intends to move. Agents adjust their speed based on anticipated distance to the nearest neighbor in their headway, enabling navigation through congested areas without overlap. The model incorporates a reaction time factor to adjust the turning process rate from the current to the new direction.

Wall Influence

Walls are treated as gliding surfaces, meaning that agents adjust their movement to avoid collisions while maintaining smooth trajectories along wall boundaries. The influence of walls on an agent’s movement is determined based on their distance to the wall and the direction of their movement. The following rules govern the behavior:

  1. Critical Wall Distance:

    • A critical wall distance is defined as the sum of the agent’s radius and a configurable buffer distance (wallBufferDistance).

    • If an agent comes within this critical distance to a wall, their direction is adjusted to ensure a minimum distance is maintained.

  2. Influence Start Distance:

    • An influence start distance is set at twice the critical wall distance to allow for smoother adjustments as the agent approaches the wall.

  3. Direction Adjustment:
    • When an agent is within the critical wall distance and moving toward the wall:

      • The direction is projected parallel to the wall to ensure no penetration occurs.

      • A small outward component is added to maintain the minimum distance from the wall.

    • When an agent is between the critical wall distance and the influence start distance:

      • If moving toward the wall, their direction is adjusted with a smooth transition factor to gradually reduce components moving perpendicular to the wall.

  4. Wall Direction Handling:

    • The agent’s movement direction is decomposed into parallel and perpendicular components relative to the wall surface.

    • Adjustments are applied only to the perpendicular component, ensuring the parallel component remains intact for smooth movement along the wall.

In summary, walls do not affect the speed of agents, only their direction. Agents glide along walls by adjusting their direction while maintaining the desired movement as much as possible. When necessary, the influence transitions smoothly as the agent moves closer to or farther from the wall.

The anticipation velocity model takes into account the length of the agent, which determines the required space for movement, and the maximum achievable speed of the agent. This simplified and computationally efficient model aims to mirror real-world pedestrian behaviors while maintaining smooth movement dynamics.

The parameters of the anticipation velocity model can be defined per-agent.

In AnticipationVelocityModel neighbor and wall parameters are per-agent parameters that can be set individually via AnticipationVelocityModelAgentParameters and can be changed at any time.

For an in-depth explanation of the model, refer to the detailed description available on the PedestrianDynamics website.

The original research is published in Transportation Research Part C.

Generalized Centrifugal Force Model#

The Generalized Centrifugal Force Model is a force-based model that defines the movement of pedestrians through the combination of small-range forces. This model represents the spatial requirement of pedestrians, including their body asymmetry, in an elliptical shape with two axes dependent on speed. The semi-axis representing the dynamic space requirement in the direction of motion increases proportionally as speed increases. Conversely, the semi-axis along the shoulder direction decreases with higher velocities.

A detailed description is available on PedestrianDynamics.

Note

The implementation does not allow to modify all parameters described. Espcially the following parameters are defined constant as:

  • \(r'_c = r_c - r_{eps}\)

  • \(s_0 = \tilde{l} - r_{eps}\)

  • \(\tilde{l} = 0.5\)

The original publication can be found at https://arxiv.org/abs/1008.4297

Social Force Model#

The Social Force Model [1] is a force-based model that defines the movement of pedestrians by the combination of different social forces affecting an individual. The model defines forces that affect an individual:

  • A driving force

  • A repulsive force

  • An obstacle force

The driving force represents a person’s desire to move in a certain direction, independent of other people and obstacles. The repulsive force is caused by the interaction between the individuals and causes them to avoid each other in order to avoid collisions. The obstacle force acts in a similar way to the person force to avoid collisions with obstacles in the environment.

A detailed description is available on PedestrianDynamics.

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