Vehicle dynamics using Matlab: Stat-space models

This project has the following structure:

• +mt
  • +ss
  • +tools
• sym-modeling
• documentation
• examples

+mt

This is the main folder library. In order to use this the user should include this line in his matlab script:

import mt.*

+statespace

All state-space models will be added here:

• carNonlinear : Nonlinear state-space equation of car dynamics
• carNonlinearVxConstant : Nonlinear state-space equation with constant longitudinal velocity of car dynamics
• carLinear : Linear state-space equation of car dynamics. Linearize around (0,0)
• carLinearVxConstant : Linear state-space equation of car with constant longitudinal velocity.
• semitrailerNonlinear : Nonlinear state-space equation of semi-trailer dynamics.
• semitrailerNonlinearVxConstant : Nonlinear state-space equation of semi-trailer with constant longitudinal velocity. Linearize around (X0,U0) = (0,0)
• semitrailerLinear : Linear state-space equation of semi-trailer dynamics. Linearize around (X0,U0) = (0,0)
• semitrailerLinearVxConstant : Linear state-space equation of semi-trailer with constant longitudinal velocity. Linearize around (0,0)

+tools

Scripts use for modeling. The idea is to use this function for modeling using Euler-Lagrange Approach.

transM : Calculation of transformation matrix of a define Frame {V} with respect to a reference Frame {E}.

Rz : Calculation of rotation matrix around axis Z.

linearizeStateSpace : Linearize nonlinear state-space model around an stationary-point.

dtGen : Generation of symbolic derivative of vector.

dfdt : Estimation of df/dt while 'f' depends on generalized coordinates 'q'. Chain rule is applied

calQ : Calculation of generalized force of a system as a function of the generalized coordinates.

solveddq : Estimate the expression of the second derivative of the generalized coordinates (q) based on q, first derivative of q, Kinetic and Potential energy and generalized force of a system.

rk4 : Next discrete step calculation using Runge-Kutta 4 for state-stace equations.

wagon : Calculation of wheels and borders position with respect of Reference or Earth Frame. Inputs: vehicle position, inclination and dimensions of vehicle.

plotCar : Plotting minimalistic car shape.

sym-modeling

car-modelling.m : Car model using single axle bicycle model using Euler-Lagrange equation. Documentation: documentation/car-modelling/car-modelling.pdf

semitrailer-modelling.m : Semitrailer model using single axle bicycle model using Euler-Lagrange equation. Documentation: documentation/semitrailer-modelling/semitrailer-modelling.pdf

Examples

plot_car_trajectory : Example of plottting car using carNonlinearVxConstant state-space,rk4, wagon and plotCar. Steering input is constant. plot_car_trajectory_2 : Example of plottting car using carNonlinearVxConstant state-space, rk4, wagon and plotCar. Steering input is sinusoidal and then constant. plot_car_trajectory : Example of plottting car using semitrailerNonlinearVxConstant state-space, rk4, wagon and plotCar. Steering is maneuver for lane change.