# puma / PumaIK.py

 ```Trammell Hudson 2d73c51 2013-07-07 ``` ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148``` ```#!/usr/bin/python # Direct inverse kinesmatics for the PUMA. # # Based on "A geometric approach in solving the inverse kinematics of # PUMA robots" by Lee and Ziegler, 1983. # # http://deepblue.lib.umich.edu/bitstream/handle/2027.42/6192/bac6709.0001.001.pdf?sequence=5 import sys from math import pi, sin, cos, sqrt, atan2, fabs from Joint import Joint class PumaIK: def __init__(self, right, above, joints): if len(joints) != 6: raise Exception("PUMA must have six joints") self.joints = joints self.theta = [0,0,0,0,0,0] self.counts = [0,0,0,0,0,0] if right: self.right = 1 else: self.right = -1 if above: self.above = 1 else: self.above = -1 def major(self, xyz): px = xyz[0] py = xyz[1] pz = xyz[2] a2 = self.joints[1].a a3 = self.joints[2].a d2 = self.joints[1].d d4 = self.joints[3].d if px*px + py*py < d2*d2: print "Out of reach" return False r = sqrt(px*px + py*py - d2*d2) R = sqrt(px*px + py*py + pz*pz - d2*d2) # theta[0] defined in equation 26 self.theta[0] = atan2( -self.right * py * r - px * d2, -self.right * px * r + py * d2 ) # theta[1] is equations 28 - 35. sin_alpha = -pz / R cos_alpha = -self.right * r / R cos_beta = (a2*a2 + R*R - (d4*d4 + a3*a3)) / (2*a2*R) if cos_beta > 1 or cos_beta < -1: print "Beta out of range" return False sin_beta = sqrt(1 - cos_beta*cos_beta) sin_t2 = sin_alpha * cos_beta + self.right * self.above * cos_alpha * sin_beta cos_t2 = cos_alpha * cos_beta - self.right * self.above * sin_alpha * sin_beta self.theta[1] = atan2(sin_t2, cos_t2) # theta[2] t2 = d4*d4 + a3*a3 t = sqrt(t2) cos_phi = (a2*a2 + t2 - R*R) / (2 * a2 * t) if cos_phi > 1 or cos_phi < -1: print "Phi out of range" return False sin_phi = self.right * self.above * sqrt(1 - cos_phi*cos_phi) sin_beta = d4 / t cos_beta = fabs(a3) / t sin_t3 = sin_phi*cos_beta - cos_phi*sin_beta cos_t3 = cos_phi*cos_beta + sin_phi*sin_beta self.theta[2] = atan2(sin_t3, cos_t3) return True # Compute the wrist commands given the desired wrist configuration. # The major positions must have already been computed to position # the major axes. def wrist(self, a, s, n): M = 1 ax = a[0] ay = a[1] az = a[2] sx = s[0] sy = s[1] sz = s[2] nx = n[0] ny = n[1] nz = n[2] C1 = cos(self.theta[0]) S1 = sin(self.theta[0]) C23 = cos(self.theta[1] + self.theta[2]) S23 = sin(self.theta[1] + self.theta[2]) S4 = M * (C1*ay - S1*ax) C4 = M * (C1*C23*ax + S1*C23*ay- S23*az) self.theta[3] = atan2(S4, C4) S5 = (C1*C23*C4 - S1*S4)*ax + (S1*C23*C4 + C1*S4)*ay - C4* S23*az C5 = C1*S23*ax + S1*S23*ay + C23*az self.theta[4] = atan2(S5,C5) S6 = (-S1*C4 - C1*C23*S4)*nx + (C1*C4-S1*C23*S4)*ny + S4*S23*nz C6 = (-S1*C4-C1*C23*S4)*sx + (C1*C4-S1*C23*S4)*sy + S4*S23*sz self.theta[5] = atan2(S6,C6) return True def get_counts(self): counts = [] for i in range(0, 6): j = self.joints[i] c = (self.theta[i] - j.theta) * j.scale / pi if j.coupling: c += counts[i-1] * j.coupling counts.append(int(c)) return counts if __name__ == "__main__": j1 = Joint(0, 0, 0, -11200 - +12000, 0) j2 = Joint(130, 205, -90, +18000 - -18000, 0) j3 = Joint(0, 0, +90, -10500 - +11200, 0) j4 = Joint(225, 0, -90, +8000 - -8000, 0) j5 = Joint(0, 0, 0, -8000 - +8000, 9000/-40000.0) j6 = Joint(50, 0, 0, -6500 - +6500, 1200/-10000.0) r = PumaIK(True, True, (j1,j2,j3,j4,j5,j6)) if len(sys.argv) != 3+1: sys.exit(0) pos = [int(x) for x in sys.argv[1:]] r.major(pos) print r.get_counts() ```