Click on Images above to see the build photos and Design notes

                            Click on Links below for the Circuit Python code



Video Demo code - Inverse kinematic movements followed by IK walk

Video Demo code - Wobble board

Video Demo code - Inverse kinematics walk

Interpolated movements: height > height and slew > height, slew and elevation > height, slew, elevation and roll

From my PDF page 3 - Height

knee = acos(1 - ((height * height) / 5000))
hip = knee / 2



From my PDF page 5 - ADD Slew

height_slew = sqrt((height * height) + (slew * slew))
knee = acos(1 - ((height_slew * height_slew) / 5000))
hip = (knee / 2) + atan(slew / height)



From my PDF page 7 - ADD Elevation

if elev != 0:
        F_height = height - elev
        B_height = height + elev
        hip_offset = asin(elev / 49)
else:
        F_height = height
        B_height = height
        hip_offset = 0

F_height_slew = sqrt((F_height * F_height) + (slew * slew))
B_height_slew = sqrt((B_height * B_height) + (slew * slew))

F_knee = acos(1 - ((F_height_slew * F_height_slew) / 5000))
B_knee = acos(1 - ((B_height_slew * B_height_slew) / 5000))

F_hip = (F_knee / 2) + atan(slew / F_height) + hip_offset
B_hip = (B_knee / 2) + atan(slew / B_height) + hip_offset



ADD Roll

if elev != 0:
        F_height = height - elev
        B_height = height + elev
        hip_offset = asin(elev / 49)
else:
        F_height = height
        B_height = height
        hip_offset = 0

F_height_slew = sqrt((F_height * F_height) + (slew * slew))
B_height_slew = sqrt((B_height * B_height) + (slew * slew))

if roll != 0:
        F_L_height = F_height_slew - roll
        F_R_height = F_height_slew + roll
        B_L_height = B_height_slew - roll
        B_R_height = B_height_slew + roll
else:
        F_L_height = F_height_slew
        F_R_height = F_height_slew
        B_L_height = B_height_slew
        B_R_height = B_height_slew

F_L_knee = acos(1 - ((F_L_height * F_L_height) / 5000))
F_R_knee = acos(1 - ((F_R_height * F_R_height) / 5000))
B_L_knee = acos(1 - ((B_L_height * B_L_height) / 5000))
B_R_knee = acos(1 - ((B_R_height * B_R_height) / 5000))

F_L_hip = (F_L_knee / 2) + atan(slew / F_L_height) + hip_offset
F_R_hip = (F_R_knee / 2) + atan(slew / F_R_height) + hip_offset
B_L_hip = (B_L_knee / 2) + atan(slew / B_L_height) + hip_offset
B_R_hip = (B_R_knee / 2) + atan(slew / B_R_height) + hip_offset

Inverse Kinematics: Python 3.9.2 code to understand and generate trajectories

From my PDF page 8 - INVERSE KINEMATICS

from numpy import *

drop = 60 # y
slew = -20 # x

hypotenuse = sqrt(drop**2+slew**2)
phi_1 = arccos((hypotenuse**2)/(100*hypotenuse))
phi_2 = arctan(slew/drop)
hip = 90+(rad2deg(phi_2-phi_1))
knee = rad2deg(arccos(1-((hypotenuse**2)/5000)))

print('hip: ', hip, ' knee: ', knee)





From my PDF page 12 - CIRCLE FOR FOOT TRAJECTORY

import matplotlib.pyplot as plt
import numpy as np

r = 60
drop = 105
def xy(r,phi):
        return r*np.cos(phi), r*np.sin(phi) - drop

fig = plt.figure()
ax = fig.add_subplot(111,aspect='equal')

phis=np.arange(0,6.28,0.01)

for x in range(-40, 41, 1):
        y = np.sqrt((r**2) - (x**2)) - drop
        print(x,round(-y, 1))

ax.plot( *xy(r,phis), c='r',ls='-' )
plt.show()