Models

bicycle

SimpleBicycleModel

Simple Bicycle Model.

State-space equation is:

\[ \begin{aligned} \dot{x} &= v\cos(\phi), \\ \dot{y} &= v\sin(\phi), \\ \dot{\phi} &= \frac{v}{L} \tan(\delta), \\ \dot{v} &= a. \end{aligned} \]

where \(x, y, \phi, v\) are \(x\) position, \(y\) position, yaw, and velocity; \(\delta, a\) are the steering angle and acceleration inputs; and \(L\) is the wheel base length. This object also includes a method for dynamics updates based on the set sampling time and the embedded bicycle model. Units are [m, rad, s, m/s].

Parameters:

Name	Type	Description	Default
state	Optional[VehicleState]	Initial state of model, defaults to origin.	None

update(steering, velocity, dt)

Updates state.

Updates state using set sampling time, dt, and embedded bicycle dynamics. Designed to take same inputs as SVEA vehicle’s low-level interface.

Parameters:

Name	Type	Description	Default
steering	float	Input steering angle for the car	required
velocity	float	Input velocity for the car	required

cooperative

Module for cooperative models with params set for SVEA cars. This model can be used for maintaining platoon structures with various setups of intra-platoon communication.

TODO

• Finish documentation of the state-space equation
• Create nice printout for Laplacian
• Add support for arbitrary communication structures, currently the model creation only supports k-nearest neighbor communication.

C_OVRV

Bases: object

Cooperative model for the SVEA car.

The cooperative version of the optimal-velocity-relative-velocity (OVRV) model, aka the C-OVRV model. The model dictates the longitudinal speed of a given vehicle in a platoon based on the communicated state of the k-nearest platoon members. Specifically, the expected communicated values are the forward space-gap, velocity and length of each of the communicating vehicles. This C-OVRV model has the following state-space equation:

\[ \begin{aligned} \dot{s} &= R\dot{x} + ce_1, \\ \ddot{x} &= (K_1+K_4D)s + M\dot{x} - K_1\nu - K_4D(\nu + l) + w. \end{aligned} \]

where \(s, \dot{x}\) are the space-gap between a vehicle and the vehicle in front of it and the longitudinal speed of the vehicle. Units are [m, s, m/s].

This model is meant to be used at steady-state. In other words, the platoon should already be formed and travelling at the intended speed.

Parameters:

Name	Type	Description	Default
platoon_size	int	Number of vehicles in platoon.	required
num_neighbors	int	Number of forward neighbors communicating with initially.	required
k_gains	Sequence	Gains \(k_1, k_2, k_3, k_4\). Exception will be thrown if given number of values is not 4.	required
min_spacing	float	Jam or minimum spacing, corresponds to \(\eta\) in [m].	required
time_headway	float	Desired time headway, corresponds to \(\tau\) in [s].	required
init_leader_vel	float	Initial velocity of leader vehicle in [m/s].	required
length	float	Bumper-to-bumper length in [m], defaults to length of SVEA.	0.586
dt	float	Sampling time for dynamics update in [s].	0.01

:type platoon_size: int :type num_neighbors: int :type k_gains: list :type min_spacing: float :type time_headway: float :type init_leader_vel: float :type length: float :type dt: float

compute_accel(spaces, velocities, leader_v)

Given current spacing and velocity in the platoon, compute the acceleration based on the C-OVRV model.

Parameters:

Name	Type	Description	Default
spaces	Sequence	Spaces in front of each vehicle in the platoon, must be same length as the size of the platoon.	required
velocities	Sequence	Velocity of each vehicle in the platoon, must be same length as the size of the platoon.	required
leader_v	float	Current velocity of the vehicle in front of the platoon.	required

Returns:

Type	Description
list	Accelerations for each vehicle to properly maintain the platoon.
list	These can be considered control inputs.

update_k_neighbors(new_k)

Update number of communicating neighbors (in the forward direction) for updating dynamics and equilibrium point of C-OVRV model.

Parameters:

Name	Type	Description	Default
new_k	int	New number of communicating neighbors.	required

update_leader_vel(new_vel)

Update leader velocity [m/s] for updating equilibrium of C-OVRV model.

Parameters:

Name	Type	Description	Default
new_vel	float	New velocity of the vehicle in front of the platoon (leader).	required

update_platoon_size(new_size)

Update platoon size for updating dynamics and equilibrium point of C-OVRV model.

Parameters:

Name	Type	Description	Default
new_size	int	New platoon size.	required