Hello everyone, I hope you have a good day,
As we all know, the lateral dynamic system of vehicles has two output, lateral error and heading error, and we have one input, which is steering angle, I always have one big problem:
How to Design a Controller to have zero steady-state error, when I have XY reference path?
I designed a controller to track the heading, but when the vehicle gets departed from the path, as it does not have any sense of lateral error, it will not come back to the path, it will just follow the heading with some offset.
I read a lot of papers in this area, but none of them talked about XY reference paths.
I add a photo to clear up some points, please check the attached file.
Thanks in advanced,
Arash
Look at Github:
for example: https://github.com/TUMFTM/trajectory_planning_helpers
Hello Arash
Vehicles have nonholonomic constraints. As a general rule, a nonholonomic system cannot follow arbitrary reference trajectories.
I suggest using motion planning algorithms and find a trajectory that satisfies the constraints in your system. After that, you can use the LQR algorithm around the nominal trajectory.
You may find the following books useful:
-http://underactuated.csail.mit.edu/index.html
-Jerry Ginsberg, “Advanced Engineering Dynamics”, Cambridge University Press (1995)
I suggest you follow https://www.yanmar.com/au/about/technology/technical_review/2020/0326_5.html
https://www.tomtom.com/industries/fleet-management-logistics/?gclid=EAIaIQobChMIxL3jrZf66gIVygorCh3uNwirEAAYAiAAEgKgnfD_BwE
Hi Arash,
To design a controller to follow the given XY reference path is one of the common practices in fully autonomous or semi-autonomous (steering assistance) system design for on-road and off-road vehicles. You can have a look this paper (in which we have designed a path tracking controller using fuzzy logic rules for a tractor-cart system): https://www.mdpi.com/2076-3417/10/15/5223
Good luck.
As you wrote, you have only one input (steering angle), it is mandatory to eliminate both lateral error and heading error, for that I advise you to adopt an expression of an error which combines the both such as the projected error that is adopted in several papers
Hi Arash,
To follow desired reference you need to remove two errors: Lateral error (e1 = y - y_ref) and orientation error (e2 = yaw - yaw_ref). You can combine these two errors by looking ahead of the path by defining e = e1 + ds*e2 (Attached figure) and ds is the distance of looking ahead. For more information please check out these articles:
Article Vehicle lateral control in the presence of uncertainty for l...
Article Lateral control of an autonomous vehicle using integrated ba...
Article Stability Control of an Autonomous Vehicle in Overtaking Man...
If you try least square method for curve fitting the errors can be minimised. Still errors will be there.
This code provides some helper functions we frequently use in our trajectory planning software stack at FTM/TUM. Many of the functions are based on third order splines because we use them as a basis for our path planning:
https://github.com/TUMFTM/trajectory_planning_helpers
I suggest you follow :
https://www.yanmar.com/au/about/technology/technical_review/2020/0326_5.html
Conference Paper Combined Trajectory Tracking and Path Following Control for ...
Abdelghani Rouini , I read the combined paper, but I have a problem there, if you read that paper, in the control law (u), we have Y, and to calculate Y we have to calculate U with a minimization problem on zeta. I wrote down the problem but I can't solve that.
I actually asked this question on this page:
https://www.researchgate.net/post/Solve_a_complex_equation_in_MATLAB
Hi Arash,
I suggest you using fuzzy controller,
which has the inputs as e1, e1_dot, e2 and e2_dot, where e1 = y-yf and e2 = psi - psif, where f denotes reference parameter.
Your biggest challenge is finding the range of these four and also designing the rules.
I think fuzzy algorithm almost always has zero steady state error but it may have a large overshoot in the response.
Good luck!
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