Kiwi Drive Concept

[GeeTwo]

I skipped the research when I realized that all of the square roots and trig functions canceled out, and the mapping was pretty straightforward. To map rotation about a point x_r, y_r at angular speed w_r (measured in radians/second, with rotation from the positive x axis towards the positive y axis being a positive angular speed) to translation speed v_x,v_y and rotation w₀:

w₀ = w_r
v_x = w y_r
v_y = -w x_r

you can use this same preliminary mapping to make a mecanum drive rotate around a desired point.

For conversion purposes, 1 radian per second is 30/pi ~ 9.55 rpm.

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Using the WPIlib convention for your coordinate system (+x to the right, +y forward, rotations clockwise as viewed from above), your angular speeds will be reversed from this, and you will need to use:

w₀ = w_r
v_x = -w y_r
v_y = w x_r

[Ginger Power]

Originally Posted by GeeTwo

I skipped the research when I realized that all of the square roots and trig functions canceled out, and the mapping was pretty straightforward. To map rotation about a point x_r, y_r at angular speed w_r (measured in radians/second, with rotation from the positive x axis towards the positive y axis being a positive angular speed) to translation speed v_x,v_y and rotation w₀:

w₀ = w_r
v_x = w y_r
v_y = -w x_r

you can use this same preliminary mapping to make a mecanum drive rotate around a desired point.

For conversion purposes, 1 radian per second is 30/pi ~ 9.55 rpm.

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If you use mathematical conventions for your coordinate system (+x to the right, +y forward), and measure your rotations with the navigation convention of clockwise as viewed from above, your angular speeds will be reversed from this, and you will need to use:

w₀ = w_r
v_x = -w y_r
v_y = w x_r

Thanks a ton for all the information about kiwi drives! It has definitely influenced my plans moving forward!

[Ether]

Originally Posted by GeeTwo

Using the WPIlib convention for your coordinate system (+x to the right, +y forward, rotations clockwise as viewed from above), your angular speeds will be reversed from this, and you will need to use:

w₀ = w_r
v_x = -w y_r
v_y = w x_r

Once you've got Vx (strafe right speed), Vy (forward speed), and ω,
the inverse kinematics for your 3 wheel tangential speeds are:

S₁ = r*ω + Vx

S₂ = r*ω - 0.5*Vx - 0.866*Vy

S₃ = r*ω - 0.5*Vx + 0.866*Vy

(see attached sketch)

[GeeTwo]

Combining the two transformations, to rotate an equilateral kiwi drive around a pivot point (x_p, y_p) with angular speed ω, the inverse kinematics using Ether's diagram above are:

S₁ = ω * (r - y_p)

S₂ = ω * (r + 0.5*y_p - 0.866*x_p)

S₃ = ω * (r + 0.5*y_p + 0.866*x_p)

Checking rotation points to verify that we didn't swap sign conventions along the way:

(0,0): all are ωr, check
(0,r): S₁ = 0, S₂ = S₃ = 1.5ωr, reasonable
(0,2r): S₁ = -ωr, S₂ = S₃ = 2ωr, reasonable
(0,-2r): S₁ = 3ωr, S₂ = S₃ = 0, check
(1.155r, 0): S₁ = ωr, S₂ = 0, S₃ = 2ωr, ok
(-1.155r, 0): S₁ = ωr, S₂ = 2ωr, S₃ = 0, ok

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If you want "forward" to be directly between wheels rather than through one (for example if you'll be picking up pieces or doing an internal stack), rotate the robot 180 degrees, leaving the axes and forward arrow in place. Then, the inverse kinematics for rotation about (x_p, y_p) become:

S₁ = ω * (r + y_p)

S₂ = ω * (r - 0.5*y_p + 0.866*x_p)

S₃ = ω * (r - 0.5*y_p - 0.866*x_p)