The hardware for the test rig has arrived, and the first leg has been set up!

The metal brackets are from Trossen Robotics and largely match the dimensions of their equivalent plastic parts from Robotis. Some parts do not have metal counterparts, so I used spare plastic parts from my Bioloid kit. I also ordered an ArbotiX-M controller (Arduino-based), which communicates with the PC via a spare SparkFun FT232RL I had. The test rig frame is made out of MakerBeam XL aluminium profiles.

Unfortunately, I thought I had more 3-pin cables than I actually did, so I can’t control all the motors just yet. However, I’ve got an Xbox One controller controlling the IK’s foot target position and a simple serial program on the ArbotiX-M which receives the resulting position commands for each motor.

The code for both the Python applet and the Arduino can be found on GitHub here.

Some of the more useful snippets of code are shown below:

The following code handles gamepad inputs and converts them to a natural-feeling movement, based on equations of motion. The gamepad input gets converted into a virtual force, which is opposed by a drag proportional to the current velocity. The angles resulting from the IK are sent to the controller via serial port:

class GamepadHandler(threading.Thread):
def __init__(self, master):
self.master = master
# Threading vars
threading.Thread.__init__(self)
self.daemon = True # OK for main to exit even if instance is still running
self.paused = False
self.triggerPolling = True
self.cond = threading.Condition()
# Input vars
devices = DeviceManager()
self.target = targetHome[:]
self.speed = [0, 0, 0]
self.inputLJSX = 0
self.inputLJSY = 0
self.inputRJSX = 0
self.inputRJSY = 0
self.inputLJSXNormed = 0
self.inputLJSYNormed = 0
self.inputRJSXNormed = 0
self.inputRJSYNormed = 0
self.dt = 0.005
def run(self):
while 1:
with self.cond:
if self.paused:
self.cond.wait() # Block until notified
self.triggerPolling = True
else:
if self.triggerPolling:
self.pollInputs()
self.pollIK()
self.pollSerial()
self.triggerPolling = False
# Get joystick input
try:
events = get_gamepad()
for event in events:
self.processEvent(event)
except:
pass
def pause(self):
with self.cond:
self.paused = True
def resume(self):
with self.cond:
self.paused = False
self.cond.notify() # Unblock self if waiting
def processEvent(self, event):
#print(event.ev_type, event.code, event.state)
if event.code == 'ABS_X':
self.inputLJSX = event.state
elif event.code == 'ABS_Y':
self.inputLJSY = event.state
elif event.code == 'ABS_RX':
self.inputRJSX = event.state
elif event.code == 'ABS_RY':
self.inputRJSY = event.state
def pollInputs(self):
# World X
self.inputLJSYNormed = self.filterInput(-self.inputLJSY)
self.target[0], self.speed[0] = self.updateMotion(self.inputLJSYNormed, self.target[0], self.speed[0])
# World Y
self.inputLJSXNormed = self.filterInput(-self.inputLJSX)
self.target[1], self.speed[1] = self.updateMotion(self.inputLJSXNormed, self.target[1], self.speed[1])
# World Z
self.inputRJSYNormed = self.filterInput(-self.inputRJSY)
self.target[2], self.speed[2] = self.updateMotion(self.inputRJSYNormed, self.target[2], self.speed[2])
with self.cond:
if not self.paused:
self.master.after(int(self.dt*1000), self.pollInputs)
def pollIK(self):
global target
target = self.target[:]
runIK(target)
with self.cond:
if not self.paused:
self.master.after(int(self.dt*1000), self.pollIK)
def pollSerial(self):
if 'ser' in globals():
global ser
global angles
writeStr = ""
for i in range(len(angles)):
x = int( rescale(angles[i], -180.0, 180.0, 0, 1023) )
writeStr += str(i+1) + "," + str(x)
if i < (len(angles) - 1): writeStr += "," else: writeStr += "\n" ser.write(writeStr) with self.cond: if not self.paused: self.master.after(int(5*self.dt*1000), self.pollSerial) # 10x slower than pollIK def filterInput(self, i): if (i > 3277) or (i < -3277): # ~10% if i > 3277:
oldMax = 32767
elif i < -3277:
oldMax = 32768
inputNormed = math.copysign(1.0, abs(i)) * rescale(i, 0, oldMax, 0, 1.0)
else:
inputNormed = 0
return inputNormed
def updateMotion(self, i, target, speed):
c1 = 10000.0
c2 = 10.0
mu = 1.0
m = 1.0
u0 = speed
F = c1*i - c2*u0 # Force minus linear drag
a = F/m
t = self.dt
x0 = target
# Equations of motion
u = u0 + a*t
x = x0 + u0*t + 0.5*a*pow(t, 2)
# Update self
target = x
speed = u
return target, speed
def rescale(old, oldMin, oldMax, newMin, newMax):
oldRange = (oldMax - oldMin)
newRange = (newMax - newMin)
return (old - oldMin) * newRange / oldRange + newMin

The following Python code is the leg’s Forward Kinematics (click to expand):

def runFK(angles):
global a
global footOffset
global T_1_in_W
global T_2_in_W
global T_3_in_W
global T_4_in_W
global T_5_in_W
global T_F_in_W
a = [0, 0, 29.05, 76.919, 72.96, 45.032] # Link lengths "a-1"
footOffset = 33.596
s = [0, 0, 0, 0, 0, 0]
c = [0, 0, 0, 0, 0, 0]
for i in range(1,6):
s[i] = math.sin( math.radians(angles[i-1]) )
c[i] = math.cos( math.radians(angles[i-1]) )
# +90 around Y
T_0_in_W = np.matrix( [ [ 0, 0, 1, 0],
[ 0, 1, 0, 0],
[ -1, 0, 0, 0],
[ 0, 0, 0, 1] ] )
T_1_in_0 = np.matrix( [ [ c[1], -s[1], 0, a[1]],
[ s[1], c[1], 0, 0],
[ 0, 0, 1, 0],
[ 0, 0, 0, 1] ] )
T_2_in_1 = np.matrix( [ [ c[2], -s[2], 0, a[2]],
[ 0, 0, -1, 0],
[ s[2], c[2], 0, 0],
[ 0, 0, 0, 1] ] )
T_3_in_2 = np.matrix( [ [ c[3], -s[3], 0, a[3]],
[ s[3], c[3], 0, 0],
[ 0, 0, 1, 0],
[ 0, 0, 0, 1] ] )
T_4_in_3 = np.matrix( [ [ c[4], -s[4], 0, a[4]],
[ s[4], c[4], 0, 0],
[ 0, 0, 1, 0],
[ 0, 0, 0, 1] ] )
T_5_in_4 = np.matrix( [ [ c[5], -s[5], 0, a[5]],
[ 0, 0, -1, 0],
[-s[5], -c[5], 1, 0],
[ 0, 0, 0, 1] ] )
T_F_in_5 = np.matrix( [ [ 1, 0, 0, footOffset],
[ 0, 1, 0, 0],
[ 0, 0, 1, 0],
[ 0, 0, 0, 1] ] )
T_1_in_W = T_0_in_W * T_1_in_0
T_2_in_W = T_1_in_W * T_2_in_1
T_3_in_W = T_2_in_W * T_3_in_2
T_4_in_W = T_3_in_W * T_4_in_3
T_5_in_W = T_4_in_W * T_5_in_4
T_F_in_W = T_5_in_W * T_F_in_5

The following Python code is the leg’s Inverse Kinematics (click to expand):

def runIK(target):
# Solve Joint 1
num = target[1]
den = abs(target[2]) - footOffset
a0Rads = math.atan2(num, den)
angles[0] = math.degrees(a0Rads)
# Lengths projected onto z-plane
c0 = math.cos(a0Rads)
a2p = a[2]*c0
a3p = a[3]*c0
a4p = a[4]*c0
a5p = a[5]*c0
j4Height = abs(target[2]) - a2p - a5p - footOffset
j2j4DistSquared = math.pow(j4Height, 2) + math.pow(target[0], 2)
j2j4Dist = math.sqrt(j2j4DistSquared)
# # Solve Joint 2
num = target[0]
den = j4Height
psi = math.degrees( math.atan2(num, den) )
num = pow(a3p, 2) + j2j4DistSquared - pow(a4p, 2)
den = 2.0*a3p*j2j4Dist
if abs(num) <= abs(den):
phi = math.degrees( math.acos(num/den) )
angles[1] = - (phi - psi)
# Solve Joint 3
num = pow(a3p, 2) + pow(a4p, 2) - j2j4DistSquared
den = 2.0*a3p*a4p
if abs(num) <= abs(den):
angles[2] = 180.0 - math.degrees( math.acos(num/den) )
# # Solve Joint 4
num = pow(a4p, 2) + j2j4DistSquared - pow(a3p, 2)
den = 2.0*a4p*j2j4Dist
if abs(num) <= abs(den):
omega = math.degrees( math.acos(num/den) )
angles[3] = - (psi + omega)
# Solve Joint 5
angles[4] = - angles[0]
runFK(angles)

The following Arduino code is the serial read code for the Arbotix-M (click to expand):

#include <ax12.h>
int numOfJoints = 5;
void setup()
{
Serial.begin(38400);
}
void loop()
{
}
void serialEvent() {
int id[numOfJoints];
int pos[numOfJoints];
while (Serial.available())
{
for (int i = 0; i < numOfJoints; ++i)
{
id[i] = Serial.parseInt();
pos[i] = Serial.parseInt();
}
if (Serial.read() == '\n')
{
for (int i = 0; i < numOfJoints; ++i) { if ( (id[i] > 0) && (0 <= pos[i]) && (pos[i] <= 1023 ) )
SetPosition(id[i], pos[i]);
}
}
}
}