How to find the best combination of angles for minimum turn radius

Question

Gabe Mergenthaler 2024-2-15

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2082593-how-to-find-the-best-combination-of-angles-for-minimum-turn-radius

评论： Gabe Mergenthaler 2024-2-15

I am looking to find the best combination of a set of angles from 0 degrees to 68 degrees resulting in the minimum turning radius for a vehicle only turing with the front wheels. The goal is provide optimum ackermann steering and currently the wheel can roate a maximum of 68 degrees each way. I currently have this code however it doesn't seem correct and it isnt showing the best 2 angles for minimum radius. Any help would be appreciated. Wheelbase = 72 in. Track width = 54" want a radius of roughly 6-7ft I believe the equation for min radius at low speed is R = (track width/2) + (wheelbase/(Sin(average of outer + inner angle)) Thank you

radius = 72;
inner_angle = (0:68)
outer_angle = (0:68)
inner_angle_rad = inner_angle * pi /180
outer_angle_rad = outer_angle * pi /180
w = sin(outer_angle_rad+inner_angle_rad/2)
v = [72]
R= repelem (v,91)/w
if R < min_radius
    min_radius = R
end

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Image Analyst 2024-2-15

I don't understand why a car making a turn has to make two turns of different angles. Can you provide a diagram of the situation?

Gabe Mergenthaler 2024-2-15

For sure. Based upon ackermann steering criteria one wheel must turn sharper than the other for effective turning. hence why two angles. Here is a diagram where l is wheelbase, w is track width, and sigma o and sigma i are the steering angles:

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Answer 1

Walter Roberson 2024-2-15

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2082593-how-to-find-the-best-combination-of-angles-for-minimum-turn-radius#answer_1409668

在 MATLAB Online 中打开

radius = 72;
inner_angle = (0:68).';
outer_angle = (0:68);
inner_angle_rad = inner_angle * pi /180;
outer_angle_rad = outer_angle * pi /180;
w = sin(outer_angle_rad + inner_angle_rad/2);
v = [72]
v = 72
R = v./w;
[min_radius1, location1] = min(R, [], 'all', 'linear');
[r1, c1] = ind2sub(size(R), location1);
inner_angle1 = inner_angle(r1);
outer_angle1 = outer_angle(c1);
R(location1) = nan;
[min_radius2, location2] = min(R, [], 'all', 'linear');
[r2, c2] = ind2sub(size(R), location2);
inner_angle2 = inner_angle(r2);
outer_angle2 = outer_angle(c2);
result = table([min_radius1; min_radius2], [inner_angle1; inner_angle2], [outer_angle1; outer_angle2], 'VariableNames', {'Radius', 'Inner Angle', 'Outer Angle'});
result
result = 2x3 table
    Radius    Inner Angle    Outer Angle
    ______    ___________    ___________

      72          68             56     
      72          66             57     

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Gabe Mergenthaler 2024-2-15

Fantastic. So if I am reading this correctly to achieve a radius of 72 inches the inner vs outer steering angle must be 68 and 56 or 66 and 57 respectively. If i wanted a tighter or larger turning radius I would be ale to change the radius value to continue? Thanks

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