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This wiki page is about the simulation of Chalmers Autonomous Bicycle Project. If you have any question please don’t hesitate to ask to the owner of the repository (Umur E., umure@student.chalmers.se).
THEORETICAL BACKGROUND
Please see the following articles for the details of control scheme used in this bike simulations:
Modelling and control of an Autonomous Bicycle
In this simulation, a bicycle is controlled by 2 controllers in a loop is simulated. An LQR controller is used to balance the bicycle. It calculates the input for the bike to keep it balanced. Another controller (which includes several PID controllers in a loop) is used to calculate the reference stering angle for path tracking. Calculated reference steering angle is sent to LQR controller as a reference.
FILES IN THE REPOSITORY
Simulink model is available here. There are 2 files to run:
| FILE NAME | EXPLANATION |
|---|---|
| bike_init.m | Matlab m file to initialize the simulation variables and take the graphical results. |
| bike_model.slx | Simulink file for the simulation. (Matlab 2018a is required.) |
Please put all files to the same directory and be sure that your Matlab version is at least Matlab 2018a.
A SHORT INTRODUCTION TO INITIALIZATION CODE
In bike_init.m file there are 4 sections of the code:
| SECTION | EXPLANATION |
|---|---|
| 1 | Initializes the simulation variables and settings. It should be run before the simulation. It also plots the path to be followed and eigenvalues of the system for stability analysis. Plots can be turned off and on depending on the choice. |
| 2 | Runs the Simulink simulation (by calling bike_model.slx file). |
| 3 | It should be run after the simulation. It gives “reference path vs followed path” and “bike path errors” graphs. Plots can be turned off and on depending on the choice. |
| 4 | It is for generating plots where real test and simulation results are presented together. Do not use it if you don’t want to compare real test and simulation results. It requires the real test files in csv format. In default, this section is turned off, so the code file skip that part. |
One can run bike_init.m file all together at once; in this case, simulation variables and settings will be created, simulation will run automatically, and then resulting plots will be automatically created. Another option is to run the first section of the bike_init.m, and then to run bike_model.m file manually. By this, one can locate scopes to certain signals to have particular results. Then third section of the bike_init.m can be run after simulation for further plots for the results.
A SHORT INTRODUCTION TO SIMULATION
Simulation file bike_model.slx has several important blocks that represent:
| BLOCK | TYPE | EXPLANATION |
|---|---|---|
| physical bicycle | bike | without sensor or actuators |
| forward velocity motor | actuator | actuates the bike to front direction |
| steering motor | actuator | steers the steering bar |
| hall effect sensor | sensor | measures the forward speed |
| inertial measurement unit | sensor | measures the roll angle and roll rate |
| steering encoder | sensor | measures steering angle |
| balance controller | controller | an LQR controller that controls the bike so that it balances itself, calculates the steering input (steering rate) |
| path controller | controller | series of PID controllers that control the bike so that it follows a predetermined trajectory, calculates the reference steering angle to follow the path |
| global coordinate calculator | calculation | calculates the global coordinates of the bicycle |
A MORE DETAILED EXPLANATION OF THE SIMULATION
This simulation is intended to simulate the dynamics of the real bike. So, one needs to include every kind of detail that exist in the real life, like sensor noise, signal delay, dead-band, hysterisis, maximum acceleration limitations, etc.
In the following table, real life limitations and details taken into consideration for each sub-system of the bicycle is presented:
| BLOCK | DETAILS |
|---|---|
| physical bicycle | several different plant models are possible to simulate (linear, nonlinear, etc) |
| forward velocity motor | dynamics of the forward velocity motor (designed as a transfer function) |
| steering motor | max/min speed, max/min acceleration, dead-band, hysteresis, delay, max/min steering angle permitted |
| hall effect sensor | noise on the measurements, minimum possible measurement |
| inertial measurement unit | noise on the accelerometer and gyroscope measurements, several different filters to estimate the roll angle, different sampling time then the rest of the components, dimensions of the point where IMU is placed can be specified |
| steering encoder | noise of the measurements |
| balance controller | different plant models are available to calculate the LQR control law |
| path controller | an experimental look-forward path planning alghoritm is available (NOT FINALIZED!) |
There are several different types of the paths created for the simulations. Simplest paths are straight and circular paths. Raidus of the circular path can be scpecified. Another option is to make a simulation with no path tracking, only with self-balancing control.
Parameters Set in the bike_init.m File
There are several parameters that need to be change for each bike or simulation in the bike_init.m file. In the first section, which needs to be run before the simulation, the following parameters exist:
| PARAMETER | EXPLANATION |
|---|---|
| sim_time | simulation time [s] |
| initial_states | initial states of the bike at t=0 [roll angle in rad, steering angle in rad, roll rate in rad/s] |
| input_velocity | reference speed of the bicycle [m/s] |
| min_max_velocity | if variable velocity is used in the simulation, min and max values of the reference velocity profile should be specified here for calculating corresponding dynamics [m/s] |
| noise | 1=enable noise on the sensors, 0=disable noise |
| look_ahead | 1=enable look-ahead path control, 0=disable (EXPERIMENTAL, NOT FINALIZED!) |
| fork_dynamics_lqr | 1=take fork dynamics into consideration for LQR calculation 0=don’t consider fork dynamics for LQR |
| forward_motor_dynamics | 1=enable forward motor dynamics, 0=disable |
| steering_motor_limitations | 1=enable limitations (deadband, delay), 0=disable |
| path_tracking=1; | 1=path tracking, 0=only self balancing, no path tracking |
| plant_model | 1=nonlinear plant, 2=linear plant, 3=linear plant with neglected fork angle (the simplest plant) |
| roll_acceleration_calculation | 1=derivate roll rate, 0=use the model to estimate |
| Ts | sample time of the controller [sec] |
| Ts_IMU | sample time of the IMU [sec] |
| Dead_Band | deadband characteristics for steering motor [Dead Band Limit(+,-), Relay], [rad/sec] |
| max_steering_motor_acc | maximum steering motor acceleration [rad/s^2] |
| min_steering_motor_acc | minimum steering motor acceleration [rad/s^2] |
| max_steering_motor_speed | maximum steering motor velocity [rad/s] |
| min_steering_motor_speed | minimum steering motor velocity [rad/s] |
| delay | delay of steering motor [sec] |
| complementary | complementary filter coefficient (0.5<c<1) %0.995 |
| roll_rate_coef | coefficient of the low pass filter at the gyro output %0.8 |
| noise_hall | variance of hall sensor noise |
| noise_encoder | variance of steering motor encoder noise |
| noise_gyro | variance of gyroscope noise |
| noise_acc | variance of noise of roll angle estimation based on accelerometer |
| max_roll | maximum roll angle permitted [rad] // otherwise simulation stops |
| max_handlebar | maximum handlebar angle [rad] before the saturation |
| min_roll | minimum roll angle permitted [rad] // otherwise simulation stops |
| min_handlebar | minumum handlebar angle [rad] before the saturation |
| h | height of the center of mass (see the paper for more details) |
| b | length between the wheel centers (see the paper for more details) |
| a | horizontal distance from rear wheel to the center of the mass (see the paper for more details) |
| c | length between front wheel contact point and the extention of the fork axis [m] |
| lambda | angle of the fork axis [rad] |
| IMU_height | IMU height [m] |
| Q | cost of the states for the LQR controller |
| R | cost of the inputs for the LQR controller |
| plots | Set to 1 to see the plots [eigenvalue plot, path plot] |
| radius | radius of the path if the path is circle [m] |
| x_ini_diff | initial off-set in x direction for the reference path |
| y_ini_diff | initial off-set in y direction for the reference path |
| path | path to be followed, out of 9 pre-determined paths |
In the second section of the bike_init.m, simulation file (bike_model.slx) is called automatically. At the thirds section, 2 plots are created, by setting the following parameters to 1:
| PARAMETER | EXPLANATION |
|---|---|
| Bike_Path_vs_Reference_Path | Set to 1 to see bike path vs reference path, set 0 to turn it off |
| Bike_Path_Error_Inscpection | Set to 1 to see bike path errors, set 0 to turn it off |
Hence, third section of the code should be run after the simulation.