yaik/python_run_import.py at main · qysong2008/yaik · GitHub

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
import numpy as np
import math
from typing import Tuple, Optional, List


# General utility
def safe_sqrt(a):
    return math.sqrt(a) if a >= 0 else 0


def safe_asin(a):
    if a > 1:
        return 0.5 * math.pi
    elif a < -1:
        return -0.5 * math.pi
    else:
        return math.asin(a)


def safe_acos(a):
    if a > 1:
        return 0.0
    elif a < -1:
        return math.pi
    else:
        return math.acos(a)


# For general 6-dof
def compute_solution_from_tanhalf_LME(
        A_x2: np.ndarray,
        B_x: np.ndarray,
        C: np.ndarray,
        return_coupled_3_solution: bool = False):
    """
    The solver in Equation 15 of Efficient Inverse Kinematics for General 6R Manipulators.
    """
    # To 12x12 matrix
    A_12x12 = np.zeros(shape=(12, 12))
    A_12x12[0:6, 0:9] = A_x2
    A_12x12[6:12, 3:12] = A_x2
    A_inv = None
    try:
        A_inv = np.linalg.inv(A_12x12)
    except:
        # print('Cannot inverse the matrix A', print(np.linalg.det(A_12x12)))
        return None
    assert A_inv is not None
    B_12x12 = np.zeros(shape=(12, 12))
    B_12x12[0:6, 0:9] = B_x
    B_12x12[6:12, 3:12] = B_x
    C_12x12 = np.zeros(shape=(12, 12))
    C_12x12[0:6, 0:9] = C
    C_12x12[6:12, 3:12] = C

    M = np.zeros(shape=(24, 24))
    M[0:12, 12:24] = np.eye(12)
    M[12:24, 0:12] = - A_inv.dot(C_12x12)
    M[12:24, 12:24] = - A_inv.dot(B_12x12)

    # The case only need one solution
    if not return_coupled_3_solution:
        eigen_values = np.linalg.eigvals(M)
        imag_part = np.imag(eigen_values)
        real_part = np.real(eigen_values)
        solution: List[float] = list()
        for i in range(eigen_values.size):
            if abs(imag_part[i]) < 1e-6:
                atan_value = np.arctan(real_part[i])
                solution.append(2 * atan_value)
        return solution

    # We need all three coupled solution
    solution: List[Tuple[float]] = list()
    eigen_values, eigen_vectors = np.linalg.eig(M)
    for i in range(eigen_values.size):
        if abs(np.imag(eigen_values[i])) > 1e-6:
            continue
        tanhalf_x3 = np.real(eigen_values[i])
        theta3_value = 2.0 * np.arctan(tanhalf_x3)

        # The remaining part
        full_ev_i = eigen_vectors[:, i]
        ev_i = full_ev_i[0:12]
        tanhalf_x4 = ev_i[3] / ev_i[0]
        tanhalf_x5 = ev_i[1] / ev_i[0]
        if np.imag(tanhalf_x4) > 1e-6 or np.imag(tanhalf_x5) > 1e-6:
            continue
        theta4_value = 2.0 * np.arctan(np.real(tanhalf_x4))
        theta5_value = 2.0 * np.arctan(np.real(tanhalf_x5))
        solution.append((float(theta3_value), float(theta4_value), float(theta5_value)))
    return solution


# For linear solver type2
def try_solve_linear_type2(A: np.ndarray) -> Optional[Tuple[float, float]]:
    """
    Solve y from three linear equations in the form
    A sin(x) + B cos(x) + C sin(y) + D cos(y) == 0
    Each row of matrix corresponds to A, B, C, D
    """
    assert A.shape[0] == 3
    assert A.shape[1] == 4
    a, b = A[0, 0], A[0, 1]
    c, d = A[1, 0], A[1, 1]
    ad_minus_bc = a * d - b * c
    zero_tolerance = 1e-10
    if abs(ad_minus_bc) < zero_tolerance:
        return None
    A_inv = np.zeros(shape=(2, 2))
    A_inv[0, 0] = d
    A_inv[0, 1] = -b
    A_inv[1, 0] = -c
    A_inv[1, 1] = a
    A_inv /= ad_minus_bc
    # [sin(x), cos(x)].T = B * [sin(y), cos(y)].T
    B = - A_inv.dot(A[0:2, 2:4])

    # e sin(y) + f * cos(y) == 0
    e = A[2, 2] + A[2, 0] * B[0, 0] + A[2, 1] * B[1, 0]
    f = A[2, 3] + A[2, 0] * B[0, 1] + A[2, 1] * B[1, 1]
    if abs(e) < zero_tolerance and abs(f) < zero_tolerance:
        return None
    solution_0 = math.atan2(- f, e)
    solution_1 = solution_0 + np.pi
    if solution_1 > np.pi:
        solution_1 -= 2 * np.pi
    return solution_0, solution_1


def try_solve_linear_type2_specific_rows(
        A_combined: np.ndarray, row_0: int, row_1: int, row_2: int) -> Optional[Tuple[float, float]]:
    """
    For a m x 4 matrix A, each row of whom corresponds to a linear equation in the form of
    A sin(x) + B cos(x) + C sin(y) + D cos(y) == 0
    Select three equations from row_0/1/2 and solve it
    """
    A_tmp = np.zeros(shape=(3, 4))
    A_tmp[0, :] = A_combined[row_0, :]
    A_tmp[1, :] = A_combined[row_1, :]
    A_tmp[2, :] = A_combined[row_2, :]
    A_tmp_sol = try_solve_linear_type2(A_tmp)
    if A_tmp_sol is not None:
        return A_tmp_sol
    return None