{ "id": 247834, "title": "About IMU: OrientationDeg to Rotation Vector", "url": "/competitions/google-smartphone-decimeter-challenge/discussion/247834", "author_name": "Alvin.ai", "post_date": "2021-06-21T10:11:43.869000", "votes": 13, "comment_count": 0, "views": 0, "content": "

I believe some people want to use IMU data as top winners did in Indoor competition, but Google's data doesn't provide the Rotation Vector. I searched on many open websites and found that Orientation Degree (pitch, yaw, roll) In GnssLog is quite similar to Euler Angles, so I wondering if it is possible to convert Orientation Degree to Rotation Vector.

\n

Thanks for @DiegoJohnson Kaggler, he shared \"Representing Rotation with Rotation Vector\" is helpful. Also, @GreatGameDota's comment is informative too.

\n

1. Euler Angles to Rotation Vector

\n
import math\nimport numpy as np\nfrom cv2 import Rodrigues\nfrom math import sin, cos, atan2, sqrt\n
\n
def an2v(y_delta, z_delta, x_delta):\n    '''\n    Euler Angles ->Rotation Matrix -> Rotation Vector\n\n    Input：\n        1. y_delta          (float): the angle with rotateing around y-axis.\n        2. z_delta         (float): the angle with rotateing around z-axis. \n        3. x_delta         (float): the angle with rotateing around x-axis. \n   Output：\n        rx/ry/rz             (float): the rotation vector with rotateing around x/y/z-axis.\n\n    Code Ref.: https://www.zacobria.com/universal-robots-knowledge-base-tech-support-forum-hints-tips/python-code-example-of-converting-rpyeuler-angles-to-rotation-vectorangle-axis-for-universal-robots/\n    (Note：In Code Ref: pitch=y,yaw=z,roll=x. But Google is pitch=x,yaw=z,roll=y)\n    '''\n    # yaw: z\n    Rz_Matrix = np.matrix([\n    [math.cos(z_delta), -math.sin(z_delta), 0],\n    [math.sin(z_delta), math.cos(z_delta), 0],\n    [0, 0, 1]\n    ])\n\n    # pitch: y\n    Ry_Matrix = np.matrix([\n    [math.cos(y_delta), 0, math.sin(y_delta)],\n    [0, 1, 0],\n    [-math.sin(y_delta), 0, math.cos(y_delta)]\n    ])\n\n    # roll: x\n    Rx_Matrix = np.matrix([\n    [1, 0, 0],\n    [0, math.cos(x_delta), -math.sin(x_delta)],\n    [0, math.sin(x_delta), math.cos(x_delta)]\n    ])\n\n    R = Rz_Matrix * Ry_Matrix * Rx_Matrix\n\n    theta = math.acos(((R[0, 0] + R[1, 1] + R[2, 2]) - 1) / 2)\n    multi = 1 / (2 * math.sin(theta))\n\n    rx = multi * (R[2, 1] - R[1, 2]) * theta\n    ry = multi * (R[0, 2] - R[2, 0]) * theta\n    rz = multi * (R[1, 0] - R[0, 1]) * theta\n\n    return rx, ry, rz\n
\n

2. Rotation Vector to Euler Angles

\n
def v2a(rotation_v):\n    \"\"\"\n    Rotation Vector -> Rotation Matrix -> Euler Angles\n\n    Input：\n        rx/ry/rz             (float): the rotation vector with rotateing around x/y/z-axis.\n   Output：\n        1. y_delta          (float): the angle with rotateing around y-axis.\n        2. z_delta         (float): the angle with rotateing around z-axis. \n        3. x_delta         (float): the angle with rotateing around x-axis.   \n    “”“\n    # Rotation Vector -> Rotation Matrix\n    R = Rodrigues(rotation_v)[0]\n\n    sq = sqrt(R[2,1] ** 2 +  R[2,2] ** 2)\n\n    if  not (sq < 1e-6) :\n        x_delta = atan2(R[2,1] , R[2,2])\n        y_delta = atan2(-R[2,0], sq)\n        z_delta = atan2(R[1,0], R[0,0])\n    else :\n        x_delta = atan2(-R[1,2], R[1,1])\n        y_delta = atan2(-R[2,0], sq)\n        z_delta = 0\n\n    return y_delta, z_delta, x_delta\n
\n

3. Test

\n
pitch, yaw, roll = 0.254839, -2.57534, -3.10256\nrotation_v = an2v(pitch, yaw, roll)\nrotation_v\n
\n
\n
\n

(-0.7992088080637765, 2.772797963612602, 0.04919481302670785)

\n
\n
\n
v2a(rotation_v)\n
\n
\n
\n

(0.2548389999999962, -2.5753400000000006, -3.102560000000001)

\n
\n
\n

But I wonder if it is right to obtain the Rotation Vector from the Orientation Degree or not? it's my first time playing Kaggle, please feel free to discuss and comment. 🤝

", "messages": [ { "id": 1359475, "postDate": "2021-06-21T10:11:43.870Z", "content": "

I believe some people want to use IMU data as top winners did in Indoor competition, but Google's data doesn't provide the Rotation Vector. I searched on many open websites and found that Orientation Degree (pitch, yaw, roll) In GnssLog is quite similar to Euler Angles, so I wondering if it is possible to convert Orientation Degree to Rotation Vector.

\n

Thanks for @DiegoJohnson Kaggler, he shared \"Representing Rotation with Rotation Vector\" is helpful. Also, @GreatGameDota's comment is informative too.

\n

1. Euler Angles to Rotation Vector

\n
import math\nimport numpy as np\nfrom cv2 import Rodrigues\nfrom math import sin, cos, atan2, sqrt\n
\n
def an2v(y_delta, z_delta, x_delta):\n    '''\n    Euler Angles ->Rotation Matrix -> Rotation Vector\n\n    Input：\n        1. y_delta          (float): the angle with rotateing around y-axis.\n        2. z_delta         (float): the angle with rotateing around z-axis. \n        3. x_delta         (float): the angle with rotateing around x-axis. \n   Output：\n        rx/ry/rz             (float): the rotation vector with rotateing around x/y/z-axis.\n\n    Code Ref.: https://www.zacobria.com/universal-robots-knowledge-base-tech-support-forum-hints-tips/python-code-example-of-converting-rpyeuler-angles-to-rotation-vectorangle-axis-for-universal-robots/\n    (Note：In Code Ref: pitch=y,yaw=z,roll=x. But Google is pitch=x,yaw=z,roll=y)\n    '''\n    # yaw: z\n    Rz_Matrix = np.matrix([\n    [math.cos(z_delta), -math.sin(z_delta), 0],\n    [math.sin(z_delta), math.cos(z_delta), 0],\n    [0, 0, 1]\n    ])\n\n    # pitch: y\n    Ry_Matrix = np.matrix([\n    [math.cos(y_delta), 0, math.sin(y_delta)],\n    [0, 1, 0],\n    [-math.sin(y_delta), 0, math.cos(y_delta)]\n    ])\n\n    # roll: x\n    Rx_Matrix = np.matrix([\n    [1, 0, 0],\n    [0, math.cos(x_delta), -math.sin(x_delta)],\n    [0, math.sin(x_delta), math.cos(x_delta)]\n    ])\n\n    R = Rz_Matrix * Ry_Matrix * Rx_Matrix\n\n    theta = math.acos(((R[0, 0] + R[1, 1] + R[2, 2]) - 1) / 2)\n    multi = 1 / (2 * math.sin(theta))\n\n    rx = multi * (R[2, 1] - R[1, 2]) * theta\n    ry = multi * (R[0, 2] - R[2, 0]) * theta\n    rz = multi * (R[1, 0] - R[0, 1]) * theta\n\n    return rx, ry, rz\n
\n

2. Rotation Vector to Euler Angles

\n
def v2a(rotation_v):\n    \"\"\"\n    Rotation Vector -> Rotation Matrix -> Euler Angles\n\n    Input：\n        rx/ry/rz             (float): the rotation vector with rotateing around x/y/z-axis.\n   Output：\n        1. y_delta          (float): the angle with rotateing around y-axis.\n        2. z_delta         (float): the angle with rotateing around z-axis. \n        3. x_delta         (float): the angle with rotateing around x-axis.   \n    “”“\n    # Rotation Vector -> Rotation Matrix\n    R = Rodrigues(rotation_v)[0]\n\n    sq = sqrt(R[2,1] ** 2 +  R[2,2] ** 2)\n\n    if  not (sq < 1e-6) :\n        x_delta = atan2(R[2,1] , R[2,2])\n        y_delta = atan2(-R[2,0], sq)\n        z_delta = atan2(R[1,0], R[0,0])\n    else :\n        x_delta = atan2(-R[1,2], R[1,1])\n        y_delta = atan2(-R[2,0], sq)\n        z_delta = 0\n\n    return y_delta, z_delta, x_delta\n
\n

3. Test

\n
pitch, yaw, roll = 0.254839, -2.57534, -3.10256\nrotation_v = an2v(pitch, yaw, roll)\nrotation_v\n
\n
\n
\n

(-0.7992088080637765, 2.772797963612602, 0.04919481302670785)

\n
\n
\n
v2a(rotation_v)\n
\n
\n
\n

(0.2548389999999962, -2.5753400000000006, -3.102560000000001)

\n
\n
\n

But I wonder if it is right to obtain the Rotation Vector from the Orientation Degree or not? it's my first time playing Kaggle, please feel free to discuss and comment. 🤝

", "rawMarkdown": "I believe some people want to use IMU data as top winners did in Indoor competition, but Google's data doesn't provide the Rotation Vector. I searched on many open websites and found that **Orientation Degree (pitch, yaw, roll)** In GnssLog is quite similar to Euler Angles, so I wondering if it is possible to convert Orientation Degree to Rotation Vector. \n\nThanks for @DiegoJohnson Kaggler, he shared \"[Representing Rotation with Rotation Vector](https://www.kaggle.com/diegojohnson/representing-rotation-with-rotation-vector)\" is helpful. Also, @GreatGameDota's comment is informative too.\n\n**1. Euler Angles to Rotation Vector**\n\n```\nimport math\nimport numpy as np\nfrom cv2 import Rodrigues\nfrom math import sin, cos, atan2, sqrt\n```\n\n```\ndef an2v(y_delta, z_delta, x_delta):\n '''\n Euler Angles ->Rotation Matrix -> Rotation Vector\n \n Input：\n 1. y_delta (float): the angle with rotateing around y-axis.\n 2. z_delta (float): the angle with rotateing around z-axis. \n 3. x_delta (float): the angle with rotateing around x-axis. \n Output：\n rx/ry/rz (float): the rotation vector with rotateing around x/y/z-axis.\n \n Code Ref.: https://www.zacobria.com/universal-robots-knowledge-base-tech-support-forum-hints-tips/python-code-example-of-converting-rpyeuler-angles-to-rotation-vectorangle-axis-for-universal-robots/\n (Note：In Code Ref: pitch=y,yaw=z,roll=x. But Google is pitch=x,yaw=z,roll=y)\n '''\n # yaw: z\n Rz_Matrix = np.matrix([\n [math.cos(z_delta), -math.sin(z_delta), 0],\n [math.sin(z_delta), math.cos(z_delta), 0],\n [0, 0, 1]\n ])\n \n # pitch: y\n Ry_Matrix = np.matrix([\n [math.cos(y_delta), 0, math.sin(y_delta)],\n [0, 1, 0],\n [-math.sin(y_delta), 0, math.cos(y_delta)]\n ])\n \n # roll: x\n Rx_Matrix = np.matrix([\n [1, 0, 0],\n [0, math.cos(x_delta), -math.sin(x_delta)],\n [0, math.sin(x_delta), math.cos(x_delta)]\n ])\n\n R = Rz_Matrix * Ry_Matrix * Rx_Matrix\n\n theta = math.acos(((R[0, 0] + R[1, 1] + R[2, 2]) - 1) / 2)\n multi = 1 / (2 * math.sin(theta))\n\n rx = multi * (R[2, 1] - R[1, 2]) * theta\n ry = multi * (R[0, 2] - R[2, 0]) * theta\n rz = multi * (R[1, 0] - R[0, 1]) * theta\n\n return rx, ry, rz\n```\n\n**2. Rotation Vector to Euler Angles**\n\n```\ndef v2a(rotation_v):\n \"\"\"\n Rotation Vector -> Rotation Matrix -> Euler Angles\n \n Input：\n rx/ry/rz (float): the rotation vector with rotateing around x/y/z-axis.\n Output：\n 1. y_delta (float): the angle with rotateing around y-axis.\n 2. z_delta (float): the angle with rotateing around z-axis. \n 3. x_delta (float): the angle with rotateing around x-axis. \n “”“\n # Rotation Vector -> Rotation Matrix\n R = Rodrigues(rotation_v)[0]\n\n sq = sqrt(R[2,1] ** 2 + R[2,2] ** 2)\n\n if not (sq < 1e-6) :\n x_delta = atan2(R[2,1] , R[2,2])\n y_delta = atan2(-R[2,0], sq)\n z_delta = atan2(R[1,0], R[0,0])\n else :\n x_delta = atan2(-R[1,2], R[1,1])\n y_delta = atan2(-R[2,0], sq)\n z_delta = 0\n\n return y_delta, z_delta, x_delta\n```\n\n**3. Test**\n\n```\npitch, yaw, roll = 0.254839, -2.57534, -3.10256\nrotation_v = an2v(pitch, yaw, roll)\nrotation_v\n```\n>> (-0.7992088080637765, 2.772797963612602, 0.04919481302670785)\n\n```\nv2a(rotation_v)\n```\n>> (0.2548389999999962, -2.5753400000000006, -3.102560000000001)\n\nBut I wonder if it is right to obtain the Rotation Vector from the Orientation Degree or not? it's my first time playing Kaggle, please feel free to discuss and comment. 🤝", "votes": 13 } ], "comments": [], "raw_markdown_by_id": { "1359475": "I believe some people want to use IMU data as top winners did in Indoor competition, but Google's data doesn't provide the Rotation Vector. I searched on many open websites and found that **Orientation Degree (pitch, yaw, roll)** In GnssLog is quite similar to Euler Angles, so I wondering if it is possible to convert Orientation Degree to Rotation Vector. \n\nThanks for @DiegoJohnson Kaggler, he shared \"[Representing Rotation with Rotation Vector](https://www.kaggle.com/diegojohnson/representing-rotation-with-rotation-vector)\" is helpful. Also, @GreatGameDota's comment is informative too.\n\n**1. Euler Angles to Rotation Vector**\n\n```\nimport math\nimport numpy as np\nfrom cv2 import Rodrigues\nfrom math import sin, cos, atan2, sqrt\n```\n\n```\ndef an2v(y_delta, z_delta, x_delta):\n '''\n Euler Angles ->Rotation Matrix -> Rotation Vector\n \n Input：\n 1. y_delta (float): the angle with rotateing around y-axis.\n 2. z_delta (float): the angle with rotateing around z-axis. \n 3. x_delta (float): the angle with rotateing around x-axis. \n Output：\n rx/ry/rz (float): the rotation vector with rotateing around x/y/z-axis.\n \n Code Ref.: https://www.zacobria.com/universal-robots-knowledge-base-tech-support-forum-hints-tips/python-code-example-of-converting-rpyeuler-angles-to-rotation-vectorangle-axis-for-universal-robots/\n (Note：In Code Ref: pitch=y,yaw=z,roll=x. But Google is pitch=x,yaw=z,roll=y)\n '''\n # yaw: z\n Rz_Matrix = np.matrix([\n [math.cos(z_delta), -math.sin(z_delta), 0],\n [math.sin(z_delta), math.cos(z_delta), 0],\n [0, 0, 1]\n ])\n \n # pitch: y\n Ry_Matrix = np.matrix([\n [math.cos(y_delta), 0, math.sin(y_delta)],\n [0, 1, 0],\n [-math.sin(y_delta), 0, math.cos(y_delta)]\n ])\n \n # roll: x\n Rx_Matrix = np.matrix([\n [1, 0, 0],\n [0, math.cos(x_delta), -math.sin(x_delta)],\n [0, math.sin(x_delta), math.cos(x_delta)]\n ])\n\n R = Rz_Matrix * Ry_Matrix * Rx_Matrix\n\n theta = math.acos(((R[0, 0] + R[1, 1] + R[2, 2]) - 1) / 2)\n multi = 1 / (2 * math.sin(theta))\n\n rx = multi * (R[2, 1] - R[1, 2]) * theta\n ry = multi * (R[0, 2] - R[2, 0]) * theta\n rz = multi * (R[1, 0] - R[0, 1]) * theta\n\n return rx, ry, rz\n```\n\n**2. Rotation Vector to Euler Angles**\n\n```\ndef v2a(rotation_v):\n \"\"\"\n Rotation Vector -> Rotation Matrix -> Euler Angles\n \n Input：\n rx/ry/rz (float): the rotation vector with rotateing around x/y/z-axis.\n Output：\n 1. y_delta (float): the angle with rotateing around y-axis.\n 2. z_delta (float): the angle with rotateing around z-axis. \n 3. x_delta (float): the angle with rotateing around x-axis. \n “”“\n # Rotation Vector -> Rotation Matrix\n R = Rodrigues(rotation_v)[0]\n\n sq = sqrt(R[2,1] ** 2 + R[2,2] ** 2)\n\n if not (sq < 1e-6) :\n x_delta = atan2(R[2,1] , R[2,2])\n y_delta = atan2(-R[2,0], sq)\n z_delta = atan2(R[1,0], R[0,0])\n else :\n x_delta = atan2(-R[1,2], R[1,1])\n y_delta = atan2(-R[2,0], sq)\n z_delta = 0\n\n return y_delta, z_delta, x_delta\n```\n\n**3. Test**\n\n```\npitch, yaw, roll = 0.254839, -2.57534, -3.10256\nrotation_v = an2v(pitch, yaw, roll)\nrotation_v\n```\n>> (-0.7992088080637765, 2.772797963612602, 0.04919481302670785)\n\n```\nv2a(rotation_v)\n```\n>> (0.2548389999999962, -2.5753400000000006, -3.102560000000001)\n\nBut I wonder if it is right to obtain the Rotation Vector from the Orientation Degree or not? it's my first time playing Kaggle, please feel free to discuss and comment. 🤝" } }