Component: State space model

Overview

Generating a state space representation using a ‘black box model’ with MATLAB includes the following steps

• Recording step-responses with rosbag
• Generating the model with MATLAB
  • prepare input and output data from rosbag files
  • estimate a model using MATLAB application Sytem Identification Toolbox

For the MATLAB code to work, the following applications are required:

• Robotics System Toolbox
• System Identification Toolbox

Documentation for rosbag can be found at: http://wiki.ros.org/rosbag

Files neccesary to generate the model

The matlab_ss folder contains all neccessary files and includes the following:

minireach_docs/
└── matlab_ss
    ├── handle_data.m
    ├── h2h.m
    ├── v2v.m
    ├── quaternion2angular_velocity.m
    └── nonlinear_truck.slx

File	Description
handle_data.m	Run simulation of nonlinear_truck and plot various results.
h2h.m	Load a linear-step rosbag file and generate state space matrices for the linear part.
v2v.m	Load a angular-step rosbag file and generate state space matrices for the angular part.
quaternion2angular_velocity.mat	Handles conversion between quaternions and angular velocity.
nonlinear_truck.slx	Simulink model of the discrete nonlinear truck. The ‘discrete_truck’ within the simulink model handles the final discrete state space matrix.

Black box model outline

This ‘black box’ approach uses System Identification Toolbox to estimate a state space model with just input and output data. The important data will be recorded in files using rosbag and MATLAB will in trun require Robotics System Toolbox to read these files.

Recording data with rosbag

Before recording any data for use in this code, it is recommended to prepare suitable step-responses in linear velocity as well as angular velocity in test cases to run on the truck.

ROS-topics to record:

• nav_vel - control signals / input to the truck
• robot_pose - position in x, y and z (quaternion)
• joint_states - includes velocity and angle of the steer wheel

Depending on which live truck will used, the name preceding the robot_pose topic will vary. Using the flareon truck will result in the following command:

rosbag record /nav_vel /flareon/robot_pose /joint_states

Suggestions for extensions

• Expand on the extra MATLAB-file: v2h.m containing work on the impact of angular velocity on linear velocity.
• Further look into approximations of the position model and possibly linearization of this model.