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kclhand_forward_kinematics.py
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#!/usr/bin/env python
__author__ = 'jiesun'
#Date: 11 Oct. 2015
#Email: [email protected]
#2015 10 12 finish the palm geometry calculation
#2015 10 13 finish the hand forward kinematics
import numpy as np
import math as m
class Rotation:
# Rotation about axis
def rotation_y(self,y_Angle):
#y_Angle = m.radians(y_Angle)
return np.array([[m.cos(y_Angle), 0, m.sin(y_Angle)],[0, 1, 0],[-m.sin(y_Angle), 0, m.cos(y_Angle)]],dtype = float)
def rotation_x(self,x_Angle):
#x_Angle = m.radians(x_Angle)
return np.array([[1, 0, 0],[0, m.cos(x_Angle), -m.sin(x_Angle)],[0, m.sin(x_Angle), m.cos(x_Angle) ]], dtype=float)
def rotation_z(self,z_Angle):
#z_Angle = m.radians(z_Angle)
return np.array([[m.cos(z_Angle), -m.sin(z_Angle), 0],[m.sin(z_Angle), m.cos(z_Angle), 0],[0, 0, 1]],dtype = float)
class Palm(Rotation):
# Define the palm geometry
angleAE = m.radians(120.0)
angleAB = m.radians(42.0)
angleBC = m.radians(80.0)
angleCD = m.radians(80.0)
angleDE = m.radians(42.0)
palmRadius = 1.0
posiE = np.array([0, 0, palmRadius])
def __init__(self, palmJointA, palmJointE):
self.palmJointA = m.radians(palmJointA)
self.palmJointE = m.radians(palmJointE)
def getPositionA(self):
return np.dot(self.rotation_y(self.angleAE),self.posiE)
def getPositionB(self):
self.posiBMiddle = np.dot(np.dot(self.rotation_y(self.angleAE), self.rotation_z(self.palmJointA)),self.rotation_y(self.angleAB))
return np.dot(self.posiBMiddle,self.posiE)
def getPositionD(self):
return np.dot(np.dot(self.rotation_z(-self.palmJointE), self.rotation_y(-self.angleDE)),self.posiE)
def palmJointC(self):
self.vectorBD = self.getPositionB() - self.getPositionD()
self.distanceSquareBD = np.dot(self.vectorBD,self.vectorBD)
self.cos_alpha_BD = 1.0-self.distanceSquareBD/2.0
self.alpha_BD = m.acos(self.cos_alpha_BD)
self.angleBCD_value =(self.cos_alpha_BD - m.cos(self.angleBC) * m.cos(self.angleCD)) / (m.sin(self.angleBC)*m.sin(self.angleCD))
if (self.angleBCD_value < -1.0):
self.angleBCD_value = -1.0
self.angleBCD = m.acos(self.angleBCD_value)
if ((self.palmJointA <= 0) & (self.palmJointE <= 0)):
self.palmJointCValue = self.angleBCD - m.pi
elif((self.palmJointA > 0) & (self.palmJointE > 0)):
self.palmJointCValue = m.pi - self.angleBCD
else:
self.palmJointCValue = 0
#print self.distanceSquareBD
#print self.cosAngleBD
#print self.angleBCD
#print m.degrees(self.palmJointCValue)
return self.palmJointCValue
def palmJointD(self):
self.vectorBE = self.getPositionB()-self.posiE
self.distanceSquareBE = np.dot(self.vectorBE,self.vectorBE)
self.cos_alpha_BE = 1.0 - self.distanceSquareBE / 2.0
self.alpha_BE = m.acos(self.cos_alpha_BE)
self.angleEDB = m.acos((self.cos_alpha_BE-m.cos(self.angleDE)*self.cos_alpha_BD) / (m.sin(self.angleDE)*m.sin(self.alpha_BD)))
self.angleBDC_value = (m.cos(self.angleBC) - m.cos(self.angleCD)*self.cos_alpha_BD) / (m.sin(self.angleCD)*m.sin(self.alpha_BD))
if(self.angleBDC_value > 1.0):
self.angleBDC_value = 1.0
self.angleBDC = m.acos(self.angleBDC_value)
if ((self.palmJointA <= 0) & (self.palmJointE <= 0)):
self.palmJointDValue = self.angleEDB + self.angleBDC - m.pi
elif ((self.palmJointA > 0) & (self.palmJointE <= 0)):
self.palmJointDValue = self.angleEDB + self.angleBDC - m.pi
elif ((self.palmJointA <= 0) & (self.palmJointE > 0)):
self.palmJointDValue = self.angleEDB + self.angleBDC - m.pi
else:
self.palmJointDValue = m.pi - self.angleEDB - self.angleBDC
return self.palmJointDValue
def palmJointB(self):
self.vectorAD = self.getPositionA()-self.getPositionD()
self.distanceSquareAD = np.dot(self.vectorAD,self.vectorAD)
self.cos_alpha_AD = 1.0 - self.distanceSquareAD / 2.0
self.alpha_AD = m.acos(self.cos_alpha_AD)
self.angleABD = m.acos((self.cos_alpha_AD-m.cos(self.angleAB)*self.cos_alpha_BD) / (m.sin(self.angleAB)*m.sin(self.alpha_BD)))
self.angleDBC_value = (m.cos(self.angleCD) - m.cos(self.angleBC)*self.cos_alpha_BD) / (m.sin(self.angleBC)*m.sin(self.alpha_BD))
if (self.angleDBC_value > 1.0):
self.angleDBC_value = 1.0
self.angleDBC = m.acos(self.angleDBC_value)
if ((self.palmJointA <= 0) & (self.palmJointE <= 0)):
self.palmJointBValue = self.angleABD + self.angleDBC - m.pi
elif((self.palmJointA > 0) & (self.palmJointE <= 0)):
self.palmJointBValue = self.angleABD + self.angleDBC - m.pi
else:
self.palmJointBValue = m.pi - self.angleABD - self.angleDBC
return self.palmJointBValue
class HandFK (Palm):
#parameters for the hand, unit: m
fingerLowerLength = 0.05
fingerUpperLength = 0.04586
palmRadiusMiddle = 0.041
palmRadiusSide = 0.0475
middleFingerBaseLength = 0.020
sideFingerBaseLength = 0.021
deltaMiddle = m.radians(60) # for middle finger
deltaSide = m.radians(20) # for side finger
upperFingerPreBending = m.pi/4.
fingerRadio = 3.0/7.0
# for the 5 active joints of the hand, define the initial state
def __init__(self, palmJointA = -30, palmJointE = -60 , leftFingerLower = 0, middleFingerLower = 0, rightFingerLower = 0):
self.palmJointA = m.radians(palmJointA)
self.palmJointE = m.radians(palmJointE)
self.leftFingerLower = m.radians(leftFingerLower)
self.middleFingerLower = m.radians(middleFingerLower)
self.rightFingerLower = m.radians(rightFingerLower)
#self.middleFingerUpper = self.middleFingerLower * self.fingerRadio - m.pi/12
#self.leftFingerUpper = self.leftFingerLower * self.fingerRadio - m.pi/6
#self.rightFingerUpper = self.rightFingerLower * self.fingerRadio + m.pi/6
self.middleFingerUpper = self.middleFingerLower * self.fingerRadio + m.radians(90. * 3/7) - m.pi/16
self.leftFingerUpper = self.leftFingerLower * self.fingerRadio + m.radians(90. * 3/7) - m.pi/4
self.rightFingerUpper = self.rightFingerLower * self.fingerRadio + m.radians(90. * 3/7) - m.pi/4
def middleFinger(self):
self.middleR1 = self.rotation_y(self.deltaMiddle)
self.middleR2 = np.array([[0 , 0, -1],[1, 0, 0],[0, -1 ,0]])
self.middleR3 = self.rotation_z(self.middleFingerLower)
self.middleR4 = self.rotation_z(self.middleFingerLower * self.fingerRadio + self.upperFingerPreBending)
self.middleP1 = np.array([0, self.middleFingerBaseLength, self.palmRadiusMiddle])
self.middleP2 = np.array([self.fingerLowerLength, 0, 0])
self.middleP3 = np.array([self.fingerUpperLength, 0, 0])
self.middleOrientationR123 = np.dot(np.dot(self.middleR1, self.middleR2), self.middleR3)
self.middleOrientation = np.dot(self.middleOrientationR123, self.middleR4)
self.middlePosition = np.dot(self.middleOrientation, self.middleP3) + np.dot(self.middleOrientationR123, self.middleP2) + np.dot(self.middleR1, self.middleP1)
return self.middlePosition
def leftFinger(self):
# change orientation for the left finger
self.joinC = self.palmJointC()
self.leftPalm1 = self.rotation_z(-self.palmJointE)
self.leftPalm2 = self.rotation_y(-self.angleDE)
self.leftPalm3 = self.rotation_z(-self.palmJointD())
self.leftPalm4 = self.rotation_y(-self.deltaSide)
# calculate the forward kinematics
self.leftR1 = np.dot(np.dot(self.leftPalm1, self.leftPalm2), np.dot(self.leftPalm3, self.leftPalm4))
self.leftR2 = np.array([[0 , 0, -1],[1, 0, 0],[0, -1 ,0]])
self.leftR3 = self.rotation_z(self.leftFingerLower)
self.leftR4 = self.rotation_z(self.leftFingerLower * self.fingerRadio + self.upperFingerPreBending)
self.leftP1 = np.array([0, self.sideFingerBaseLength, self.palmRadiusSide])
self.leftP2 = np.array([self.fingerLowerLength, 0, 0])
self.leftP3 = np.array([self.fingerUpperLength, 0, 0])
self.leftOrientationR123 = np.dot(np.dot(self.leftR1, self.leftR2), self.leftR3)
self.leftOrientation = np.dot(self.leftOrientationR123, self.leftR4)
self.leftPosition = np.dot(self.leftOrientation, self.leftP3) + np.dot(self.leftOrientationR123, self.leftP2) + np.dot(self.leftR1, self.leftP1)
return self.leftPosition
def rightFinger(self):
# change orientation for the right finger
self.joinC = self.palmJointC()
self.rightPalm1 = self.rotation_y(self.angleAE)
self.rightPalm2 = self.rotation_z(self.palmJointA)
self.rightPalm3 = self.rotation_y(self.angleAB)
self.rightPalm4 = self.rotation_z(self.palmJointB())
self.rightPalm5 = self.rotation_y(self.deltaSide)
# calculate the forward kinematics
self.rightR1 = np.dot(np.dot(np.dot(self.rightPalm1, self.rightPalm2), np.dot(self.rightPalm3, self.rightPalm4)), self.rightPalm5)
self.rightR2 = np.array([[0 , 0, -1],[1, 0, 0],[0, -1 ,0]])
self.rightR3 = self.rotation_z(self.rightFingerLower)
self.rightR4 = self.rotation_z(self.rightFingerLower * self.fingerRadio + self.upperFingerPreBending)
self.rightP1 = np.array([0, self.sideFingerBaseLength, self.palmRadiusSide])
self.rightP2 = np.array([self.fingerLowerLength, 0, 0])
self.rightP3 = np.array([self.fingerUpperLength, 0, 0])
self.rightOrientationR123 = np.dot(np.dot(self.rightR1, self.rightR2), self.rightR3)
self.rightOrientation = np.dot(self.rightOrientationR123, self.rightR4)
self.rightPosition = np.dot(self.rightOrientation, self.rightP3) + np.dot(self.rightOrientationR123, self.rightP2) + np.dot(self.rightR1, self.rightP1)
return self.rightPosition
def get_joint_displacement(self):
self.joint_displacement = [self.palmJointE + np.pi/3, -self.palmJointA - np.pi/3, -0.491072+self.palmJointD(), -self.palmJointB()+0.491072,
-self.rightFingerLower, self.rightFingerUpper, self.middleFingerLower, -self.middleFingerUpper,
-self.leftFingerLower, -self.leftFingerUpper]
return self.joint_displacement
# def leftFinger(self):
a = HandFK(-30, -30, -30, -30, -30)
print a.palmJointC()
print a.palmJointB()
print a.palmJointD()
print a.get_joint_displacement()
"""
print "-10 ----------------------------------------------------------"
b = Palm(-10, -10)
print b.palmJointC()
print b.palmJointD()
print b.palmJointB()
print "-30 ----------------------------------------------------------"
c = Palm(-30, -30)
print c.palmJointC()
print c.palmJointD()
print c.palmJointB()
print "-60 ----------------------------------------------------------"
a = Palm(-60,-60)
print a.palmJointC()
print a.palmJointD()
print a.palmJointB()
print "-30, -45 ----------------------------------------------------------"
d = Palm(-30, -45)
print d.palmJointC()
print d.palmJointD()
print d.palmJointB()
print "-60, -45 ----------------------------------------------------------"
e = Palm(-60, -45)
print e.palmJointC()
print e.palmJointD()
print e.palmJointB()
"""