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
|
import math
import pytest
import numpy as np
import dartpy as dart
def kinematics_tester(joint):
num_tests = 2
joint.setTransformFromChildBodyNode(dart.math.expMap(np.random.rand(6)))
joint.setTransformFromParentBodyNode(dart.math.expMap(np.random.rand(6)))
dof = joint.getNumDofs()
q = np.zeros(dof)
dq = np.zeros(dof)
for _ in range(num_tests):
q_delta = 1e-5
for i in range(dof):
q[i] = dart.math.Random.uniform(-math.pi, math.pi)
dq[i] = dart.math.Random.uniform(-math.pi, math.pi)
joint.setPositions(q)
joint.setVelocities(dq)
if dof == 0:
return
T = joint.getRelativeTransform()
J = joint.getRelativeJacobian(q)
dJ = joint.getRelativeJacobianTimeDeriv()
# Verify transform
assert dart.math.verifyTransform(T)
# Test analytic Jacobian and numerical Jacobian
numericJ = np.zeros((6, dof))
for i in range(dof):
q_a = q.copy()
joint.setPositions(q_a)
T_a = joint.getRelativeTransform()
q_b = q.copy()
q_b[i] += q_delta
joint.setPositions(q_b)
T_b = joint.getRelativeTransform()
Tinv_a = T_a.inverse()
dTdq = (T_b.matrix() - T_a.matrix()) / q_delta
Ji_4x4matrix = np.matmul(Tinv_a.matrix(), dTdq)
Ji = np.zeros(6)
Ji[0] = Ji_4x4matrix[2, 1]
Ji[1] = Ji_4x4matrix[0, 2]
Ji[2] = Ji_4x4matrix[1, 0]
Ji[3] = Ji_4x4matrix[0, 3]
Ji[4] = Ji_4x4matrix[1, 3]
Ji[5] = Ji_4x4matrix[2, 3]
numericJ[:, i] = Ji
assert np.allclose(J, numericJ, atol=1e-5)
def test_kinematics():
skel = dart.dynamics.Skeleton()
joint, _ = skel.createWeldJointAndBodyNodePair()
kinematics_tester(joint)
skel = dart.dynamics.Skeleton()
joint, _ = skel.createRevoluteJointAndBodyNodePair()
kinematics_tester(joint)
skel = dart.dynamics.Skeleton()
joint, _ = skel.createPrismaticJointAndBodyNodePair()
kinematics_tester(joint)
skel = dart.dynamics.Skeleton()
joint, _ = skel.createScrewJointAndBodyNodePair()
kinematics_tester(joint)
skel = dart.dynamics.Skeleton()
joint, _ = skel.createUniversalJointAndBodyNodePair()
kinematics_tester(joint)
skel = dart.dynamics.Skeleton()
joint, _ = skel.createTranslationalJoint2DAndBodyNodePair()
kinematics_tester(joint)
skel = dart.dynamics.Skeleton()
joint, _ = skel.createEulerJointAndBodyNodePair()
kinematics_tester(joint)
skel = dart.dynamics.Skeleton()
joint, _ = skel.createTranslationalJointAndBodyNodePair()
kinematics_tester(joint)
skel = dart.dynamics.Skeleton()
joint, _ = skel.createPlanarJointAndBodyNodePair()
kinematics_tester(joint)
def test_access_to_parent_child_transforms():
skel = dart.dynamics.Skeleton()
joint, _ = skel.createRevoluteJointAndBodyNodePair()
parentToJointTf = dart.math.Isometry3.Identity()
parentToJointTf.set_translation(np.random.rand(3, 1))
childToJointTf = dart.math.Isometry3.Identity()
childToJointTf.set_translation(np.random.rand(3, 1))
joint.setTransformFromParentBodyNode(parentToJointTf)
joint.setTransformFromChildBodyNode(childToJointTf)
storedParentTf = joint.getTransformFromParentBodyNode()
storedChildTf = joint.getTransformFromChildBodyNode()
assert np.allclose(parentToJointTf.matrix(), storedParentTf.matrix())
assert np.allclose(childToJointTf.matrix(), storedChildTf.matrix())
def test_BallJoint_positions_conversion():
assert np.allclose(
dart.dynamics.BallJoint.convertToPositions(np.eye(3)),
np.zeros((1, 3))
)
assert np.allclose(
dart.dynamics.BallJoint.convertToPositions(
np.array([[0, 1, 0], [-1, 0, 0], [0, 0, 1]])),
np.array([0, 0, -np.pi/2])
)
for i in range(30):
ballJointPos = np.random.uniform(-np.pi/2, np.pi/2, 3)
assert np.allclose(
dart.dynamics.BallJoint.convertToRotation(
dart.dynamics.BallJoint.convertToPositions(
dart.dynamics.BallJoint.convertToRotation(ballJointPos)
)),
dart.dynamics.BallJoint.convertToRotation(ballJointPos)
)
if __name__ == "__main__":
pytest.main()
|
