ex

Pitch attitude is the orientation of an aircraft or spacecraft with respect to the pitch axis. The pitching moment is the rising and falling of the vehicle's nose. When the nose rises, the pitching moment is positive; when the nose drops, the pitching moment is negative and is also called a diving moment.

kw
tcji
hj

fa

Hi everyone, I worked on BMX160 IMU last few days, Till now i am able to get Raw readings of it like ACC(X,Y,Z),GYRO (X,Y,Z)and MAG(X,Y,Z) sensor. I confirmed raw readings of ACC and GYRO are correct or not by placing sensor at rest state and then raw readings are came like acc: 0,0,-/+1 and gyro: 0. Jul 26, 2019 · When the sensor is tilted, the measured vector also has an x and y components. To keep things simple, imagine the case where the sensor is tilted around the positive y axis. The sensor now measures an x component as well as a z component: (x, 0, -z). As you can see from the following image, the angle of rotation θ = atan2(x, z).. Then Roll -90 then rotates around the camera x so you get camera x = -y, camera y = -z, camera z = x, which is what you want. If you did pitch -90, you would be rotating around the y, and would get camera x = -z. Any yaw and a pitch of -90 gives you your camera x = down, which would mean your camera is turned so the right side of the image is down. Pitch attitude is the orientation of an aircraft or spacecraft with respect to the pitch axis. The pitching moment is the rising and falling of the vehicle's nose. When the nose rises, the pitching moment is positive; when the nose drops, the pitching moment is negative and is also called a diving moment. This uses the x-y-z roll-pitch-yaw rotation: A rotation system may enter gimbal lock, a situation where a certain angle value reduces the system's degrees of freedom. The normal, non-locked case produces the following: The vector {1, 1, 0} can be rotated to an arbitrary point on a surface:. The corresponding roll, pitch, and yaw rotation angles are positive in the directions indicated by the arrow circles. Figure 1: Euler Angle Axes, Names and Symbol Convention Rotation order is: (1) Yaw, (2) Pitch and (3) Roll In its initial position, the aircraft coordinate system and the world coordinate system are aligned with each other.. Yaw/Pitch/Roll matrix multiplication . Home. Programming Forum . Software Development Forum . Discussion / Question . kirennian 0 Light Poster . ... /* 'orientation' is a 3x3 float matrix that contains a unit vector for each of the local z, x, y (in that order) axes relative to the origin. In my example, it represents the camera, and the camera.

mf

tc

ky

Jul 26, 2019 · When the sensor is tilted, the measured vector also has an x and y components. To keep things simple, imagine the case where the sensor is tilted around the positive y axis. The sensor now measures an x component as well as a z component: (x, 0, -z). As you can see from the following image, the angle of rotation θ = atan2(x, z).. The three critical flight dynamics parameters are rotations in three dimensions around the vehicle's coordinate system origin, the center of mass.These angles are pitch, roll and yaw: . Pitch is rotation around the lateral or transverse axis—an axis running from the pilot's left to right in piloted aircraft, and parallel to the wings of a winged aircraft; thus the nose pitches up and the. Demonstrate basic MPU-9250 functionality including parameterizing the register addresses, initializing the sensor, getting properly scaled accelerometer, gyroscope, and magnetometer data out. Added display functions to allow display to on breadboard monitor. Addition of 9 DoF sensor fusion using open source Madgwick and Mahony filter algorithms. . To add to the confusion, there are six fundamental aerospace sequences as well. For example, a pitch-yaw-roll sequence versus a roll-pitch-yaw sequence. While the astronomy community has pretty much settled on a z-x-z sequence, the same cannot be said of the aerospace community. Somewhere along the way you find people using every one of the six ....

cc

vb

mr

position. The roll, pitch and yaw rotation matrices, which transform a vector (such as the earth's gravitational field vector g) under a rotation of the coordinate system of Figure 3 by angles φ in roll, θ in pitch and ψ in yaw about the x, y and z axes respectively, are: Eqn. 3 Eqn. 4 Eqn. 5. (Depending on the application this may not necessarily be the case; for example, if the quaternion specifies an attitude relative to Earth coordinate axes, such as ECEF, then yaw / pitch / roll may or may not also be relative to those axes, vs. "local level" axes. Lateral and Vertical axis are the Principle axes of Roll-pitch-yaw which are represented by x, y and z [1]. In Fig.1 the Rotational angle i,e Roll-pitch-yaw about the axis x, y and z is shown. .... yaw, pitch, roll besides x, y, z. OpenGL. Bob_Plugge. March 17, 2019, 9:29am #1. I hate gimball locks and many with me. It would be great to have a function that can rotate the position of objects and cameras in euler angles and have no problems with it. Bob.

sr

nm

roll (rotation about the x-axis) pitch (rotation about the y-axis) yaw (rotation about the z-axis) Now, let's say we have a 4-wheeled robot in space. The robot is moving in the +y direction as shown in the figure below. The robot turns slightly to the left, rotating around the z-axis. Rotation about the z-axis is yaw rotation. Each of my 3 values; pitch, roll and yaw (Azimuth) goes from -180degrees to +180degrees. I am going by the example in the picture below my code, where X is pitch and Y is roll: When I use just two values, (eg just pitch and roll) the orientation seems to be represented normally. But when I throw the third into the mix, it gets a little wild. Yaw, pitch and roll. Imagine an aeroplane in flight, with 3 axes passing through the plane, the origin lying roughly at the plane's centre of gravity. If the plane swings sideways, pivoting around the z axis, the amount it swings is yaw. Pitch occurs when the nose of the plane rises or falls, the plane rotates about the y axis. The formulas to convert the acceleration values to pitch and roll are as follows. Roll = atan2 (Y, Z) * 180 / PI; Pitch = atan2 (X, sqrt (Y * Y + Z * Z)) * 180 / PI; We use atan2 as it works over 4 quadrants, if we used atan then we would have problems with angles over 90 degrees. Don't worry about Yaw for now as we can't determine that using. Roll, Pitch and Yaw angles rotation around X, Y, Z axes Ein einfach bedienbarer Online-LaTeX-Editor. Keine Installation notwendig, Zusammenarbeit in Echtzeit, Versionskontrolle, Hunderte von LaTeX-Vorlagen und mehr. Circularly polarized antennas help to negate issues associated with roll; however pitch and yaw may still pose problems. Pitch is when the tag rotates along the x-axis. Yaw is when the tag rotates along the y-axis. Roll is when the tag rotates along the z-axis. Understanding how an RFID tag's pitch, yaw, and roll affect your ability to read.

Given a quaternion of the form (x, y, z, w) where w is the scalar (real) part and x, y, and z are the vector parts, how do we convert this quaternion into the three Euler angles:. Rotation about the x axis = roll angle = α; Rotation about the y-axis = pitch angle = β; Rotation about the z-axis = yaw angle = γ.

cv

dr

Since the missile performs STT maneuver, its outputs to be controlled are (φ, a z b, and a y b).A scheme of the proposed autopilot based on GFTSMC with a PSNLO is shown in Fig. 2, IMU is the inertial measuring unit.The proposed autopilot consisting of a two-loop structure, controls pitch and yaw accelerations, and stabilizes the roll angle simultaneously.

fa

ld

Search: Roll Pitch Yaw Aircraft. Monitoring and redundancy within the flight control system, aircraft sensors, power and hydraulic generation ensure a high degree of availability of the electrical control The pitch, roll and yaw parameters are multipliers on the default stability (damping effect) about the corresponding axis of the airplane I'm monitoring the rotationZ Roll damper - damper of.

cx

bk

Gets the angle from the quaternion. You may think the following ways at first. Calculates the pitch angle and the yaw angle, that a direction you give and another direction of the quaternion make. (Ignores Z-ROLL) Gives two vectors that are the front direction and the up direction, makes a projection and calculates pitch, yaw and roll angle. On. Nov 27, 2020 · The 3-2-1 Euler angles are referred to as yaw ( ψ ), pitch ( θ ), and roll ( ϕ ), respectively, and are commonly used in aircraft dynamics and controls. We will use the 3-2-1 Euler angle direction cosine matrix, or DCM, to convert between the tilted frame and level frame. Since we are ignoring yaw/heading measurements, the DCM relationship .... Create a rotation matrix from pitch / roll / yaw values using EulerMatrix. Use GeometricTransformation in Graphics3D as GeometricTransformation [object, {rotationMatrix, translation}]. You can use multiple {matrix, translation} pairs in a list in GeometricTransformation, so you can easily visualize the object in one go at several time points. Polar coordinates describe the location by a distance and azimuth or direction ( usually in degrees from an origin or datum) Elevation describes a location relative to height. ( usually AGL or above ground level or normal to the 0 plane of the X,Y axis along the Z axis. Great video on roll yaw and pitch. May 11, 2019 #9 tech99 Science Advisor.

wh

wh

mp

bw

eo

Sep 24, 2014 · Circularly polarized antennas help to negate issues associated with roll; however pitch and yaw may still pose problems. Pitch is when the tag rotates along the x-axis. Yaw is when the tag rotates along the y-axis. Roll is when the tag rotates along the z-axis. Understanding how an RFID tag’s pitch, yaw, and roll affect your ability to read ....

q = [ c o s ( θ / 2) u ~ s i n ( θ / 2)] Then, r = q ⊗ r ⊗ q ∗. refers to a rotation of the vector r, θ degrees about the vector u ~. r is thus the rotated vector. The above can once again be written as a matrix multiplication instead of a quaternion multiplication. The math is tedious so I am just going to post the result once again. As per the title, I want to understand if the roll rate/pitch rate/yaw rate are same as the data obtained from mpu9250 gyro sensor along y-axis, x-axis and z-axis? If not then how to calculate roll rate/pitch rate/yaw rate from MPU9250. Thanks.

yq

ad

To summarize, we will employ a Tait-Bryan Euler angle convention using active, intrinsic rotations around the axes in the order z-y-x. We will call the rotation angles yaw, pitch and roll respectively. This is a common convention, and most people find it the easiest to visualize.

Circularly polarized antennas help to negate issues associated with roll; however pitch and yaw may still pose problems. Pitch is when the tag rotates along the x-axis. Yaw is when the tag rotates along the y-axis. Roll is when the tag rotates along the z-axis. Understanding how an RFID tag's pitch, yaw, and roll affect your ability to read.

Yaw, pitch, and roll are applied in that order to recover a body frame from the world frame. If I have y a w = ψ, p i t c h = θ and r o l l = ϕ in the UE4 reference frame, then I can get to my NWU coordinate frame in two stages. First let's transform to a frame I'm calling C.

yc

yl

(>>In your earlier posting you used a different convention for the axes of: yaw about z-axis; pitch about y-axis and roll about x-axis; but I guess the key thing here is the order of rotations rather than the nomenclature of the axes.) Pitch and roll can be given by a 3 axis accelerometer (ax,ay,az); and yaw by a gyro or (Hall effect) magnetometer. Roll Pitch and Yaw are common names for 3 angles used to describe orientation. There's actually a lot of ways they can combine. At the top level you have Euler Angles vs Tait-Bryan Angles, which refer to which axes you rotate around at a very high level (xyx vs. xyz). The confusion starts right there, as most aircraft use yaw-pitch-roll as Tait. Mar 08, 2022 · Version 11 introduces RollPitchYawMatrix to describe a sequence of rotations with respect to a fixed coordinate frame Three very important attributes in automobile physics are pitch, roll and yaw When I run the code to compute the pose (x,y,z, roll, pitch, yaw), I get highly inaccurate results 4506 #yaw = 1 Many translated example sentences .... Jan 17, 2020 · Any of these (Roll, Pitch, Yaw), DCM, (aspect, sideslip), and quaternion are expressions of the orientation (attitude) of the body at its position relative to its motion vector. The Roll, Pitch, Yaw can be any of those 12 different Euler conventions for applying three rotations on a cartesitan system..

I'm using YEI 3-Space Sensor which gives me x,y,z,w Quaternions. Converting that to Euler angles is done by assigning Quaternions to an object then you can see Euler angles. I thought I could use Euler format as pitch/roll/yaw, but since Euler is dependent on the sequence those rotations are applied.

qt

pa

The formulas to convert the acceleration values to pitch and roll are as follows. Roll = atan2 (Y, Z) * 180 / PI; Pitch = atan2 (X, sqrt (Y * Y + Z * Z)) * 180 / PI; We use atan2 as it works over 4 quadrants, if we used atan then we would have problems with angles over 90 degrees. Don't worry about Yaw for now as we can't determine that using.

qr

ac

Roll is defined as the rotation about the new Xˆ 2 axis that was created when we pitched. We roll about the Xˆ 2 axis to give us the final Xˆ T, Yˆ T, Zˆ T body axes in Earth coordinates. 2 2 2 2 2 2 ˆ ˆ ˆ 0 sin cos 0 cos sin 1 0 0 ˆ ˆ ˆ ˆ ˆ ˆ Z Y X Z Y X C Z Y X. When the object is at Roll/Pitch/Yaw of 0/0/0 that is fine. And it is fine if you only want to move on one axis. However, when you say roll 10 degrees to the left all the sudden the Pitch and Yaw axis are no longer parallel with the X and Y axis. This is why I have to rotate around a axis through the object.

An explanation of roll, pitch, and yaw, (XYZ) represented by our physical build. The corresponding roll, pitch, and yaw rotation angles are positive in the directions indicated by the arrow circles. Figure 1: Euler Angle Axes, Names and Symbol Convention Rotation order is: (1) Yaw, (2) Pitch and (3) Roll In its initial position, the aircraft coordinate system and the world coordinate system are aligned with each other..

bl

pi

Pitch, roll and yaw are defined as the rotation around X, Y and Z axis. Below as a picture to illustrate the definition. In a previous project I used a ADXL345 Accelerometer from Analog Devices to calculate roll and pitch. Below are the equations used to calculated roll and pitch. I have made some of source code available for public use..

xy

mr

Lateral and Vertical axis are the Principle axes of Roll-pitch-yaw which are represented by x, y and z [1]. In Fig.1 the Rotational angle i,e Roll-pitch-yaw about the axis x, y and z is shown.. You can describe any rotation as a combination of yaw, pitch and roll, or, as is familiar from the Euler angles, a succession of just two of these operations, such as. yaw by gamma after pitch by beta after yaw by alpha. This is illustrated by the MWE. \documentclass [tikz,border=3.14mm] {standalone} \makeatletter %from https://tex.

ef

vu

The 3 axis magnetometer shows you the intensity of the x,y,z parts of the magnetic field intensity sorrounding the magnetometer. The roll and yaw and pitch would work when the magnetic field is homogenous and well defined. Earth magnetic field is quite complex and deformed, so you have to know the parameters on various latitudes and longitudes. Feb 23, 2013 · I have a pair of triplets [itex](p1, y1, r1)[/itex] and [itex](p2, y2, r2)[/itex]. Each one describes a set of roll, yaw, and pitch rotations in that order, by the angles given by each component in respective order. In my scenario, pitch is a rotation about the Y axis, yaw about Z, and therefore roll about X..

Are your x/y/z rotations simultaneous or one after the other? $\endgroup$ – MvG. Nov 2, 2012 at 10:43. ... rotate a roll pitch and yaw using a rotation matrix. 4..

ay

ff

Transform Image using Roll-Pitch-Yaw angles (Image rectification) So, this is what I ended up doing: I figured that unless you are actually dealing with 3D images, rectifying the perspective of a photo is a 2D operation. ... R_rotation = R_y(-60)*R_x(10)*R_z(some_heading); R_2d = [ R_rot(1,1) R_rot(1,2) 0; R_rot(2,1) R_rot(2,2) 0; 0 0 1 ] Note. I have a pair of triplets [itex](p1, y1, r1)[/itex] and [itex](p2, y2, r2)[/itex]. Each one describes a set of roll, yaw, and pitch rotations in that order, by the angles given by each component in respective order. In my scenario, pitch is a rotation about the Y axis, yaw about Z, and therefore roll about X.

function theta = anglesR (R,str) % solve a 3d rotation matrix R of the form Ra (th1)*Rb (th2)*Rc (th3) % for angles th1,th2,th3; where each of a,b c are one of x,y,z. % input str is a three-letter string of rotation axes, such as 'yzx'. % consecutive rotations along the same axis such as 'xxy' are not allowed. VS 2008 Conventions for Roll, Pitch and Yaw (X, Y, and Z) Thread starter New2VB; Start date Jan 24, 2010.

ew

te

Example of a 90 ° rotation of the X-axis Yaw, Pitch, Roll Rotation. A 3D body can be rotated around three axes. These rotations are called yaw pitch rolls. Yaw . Yaw is the counterclockwise rotation of the Z-axis. The rotation matrix looks like this Pitch. Pitch is the counterclockwise rotation of the Y-axis.. Being X and Y the values from the accelerometer axes: Pitch = asin (-X); Roll = asin ( Y / cos (Pitch) ); Be careful, if the pitch module is 90º. The cosine will be 0 (dividing by 0 is not a good idea), so you should avoid doing the Roll math if that's the case and just set Roll to 0º. The problem with this is, quick movements will throw off. R(pitch,yaw,roll) Euler rotation: Q(x,y,z,rot) Quaternion: HEADING(dir,pitch,roll) Compass heading: LOOKDIRUP(lookAt,lookUp) Looking along vector lookAt, rolled so that lookUp is upward. ANGLEAXIS(degrees,axisVector) A rotation that would rotate the universe around an axis: ROTATEFROMTO(fromVec,toVec) A rotation that would go from vectors.

(Depending on the application this may not necessarily be the case; for example, if the quaternion specifies an attitude relative to Earth coordinate axes, such as ECEF, then yaw / pitch / roll may or may not also be relative to those axes, vs. "local level" axes.

ha

I would like to calculate the Azimuth (zero degree on the north, 180 degree on the south) of the device from pitch, roll and yaw values provided by MotionReading. In Lanscape orientation. How can I do this? Tuesday, November 1, 2011 2:52 PM. All replies.

al

il

The most common rotation sequence is the Tate-Bryant convention. It first applies a rotation arround the z-axis (yaw), then around the y-axis (pitch) and finally around the x-axis (roll). Note that each rotation is subject of the previously applied rotation. So the second rotation around the y-axis is subject to the rotation around z, and the.

Create a rotation matrix from pitch / roll / yaw values using EulerMatrix. Use GeometricTransformation in Graphics3D as GeometricTransformation [object, {rotationMatrix, translation}]. You can use multiple {matrix, translation} pairs in a list in GeometricTransformation, so you can easily visualize the object in one go at several time points. The Yaw-Pitch-Roll (YPR) method of specifying orientation is one of the most difficult methods to understand. This difficulty is due to two factors: the similarity to the Euler angle method and use of a local frame on which the rotations are applied. ... (X)(Y)(Z) directions. Simple examples of axes definitions are the Gaussian frame which is. Definition of roll-pitch-yaw. The 3D posture of the sensor is represented by the roll angle (\(\phi\)) around the x-axis, the pitch angle (\(\theta\)) around the y-axis, and the yaw angle (\(\psi\)) around the z-axis. The reference coordinate system is a right-handed system with a vertical z-axis. The counterclockwise rotation is defined as.

iz

zs

The Yaw-Pitch-Roll (YPR) method of specifying orientation is one of the most difficult methods to understand. This difficulty is due to two factors: the similarity to the Euler angle method and use of a local frame on which the rotations are applied. ... (X)(Y)(Z) directions. Simple examples of axes definitions are the Gaussian frame which is.

  • su – The world’s largest educational and scientific computing society that delivers resources that advance computing as a science and a profession
  • fs – The world’s largest nonprofit, professional association dedicated to advancing technological innovation and excellence for the benefit of humanity
  • si – A worldwide organization of professionals committed to the improvement of science teaching and learning through research
  • da –  A member-driven organization committed to promoting excellence and innovation in science teaching and learning for all
  • ys – A congressionally chartered independent membership organization which represents professionals at all degree levels and in all fields of chemistry and sciences that involve chemistry
  • jy – A nonprofit, membership corporation created for the purpose of promoting the advancement and diffusion of the knowledge of physics and its application to human welfare
  • py – A nonprofit, educational organization whose purpose is the advancement, stimulation, extension, improvement, and coordination of Earth and Space Science education at all educational levels
  • qe – A nonprofit, scientific association dedicated to advancing biological research and education for the welfare of society

zg

dj

.

ii

jq

[Release] pitch yaw roll to pitch yaw; Welcome to MPGH - MultiPlayer Game Hacking, the world's leader in Game Hacks, ... [Tut] How to find X,Y,Z. Yaw, Pitch. By Root.X in forum CrossFire Hack Coding / Programming / Source Code Replies: 10 Last Post: 07-17-2011, 02:39 PM.

  • vl – Open access to 774,879 e-prints in Physics, Mathematics, Computer Science, Quantitative Biology, Quantitative Finance and Statistics
  • in – Streaming videos of past lectures
  • iu – Recordings of public lectures and events held at Princeton University
  • iq – Online publication of the Harvard Office of News and Public Affairs devoted to all matters related to science at the various schools, departments, institutes, and hospitals of Harvard University
  • ix – Interactive Lecture Streaming from Stanford University
  • Virtual Professors – Free Online College Courses – The most interesting free online college courses and lectures from top university professors and industry experts

je

uo

Attitude Transformations. navpy.angle2quat(rotAngle1, rotAngle2, rotAngle3, input_unit='rad', rotation_sequence='ZYX') ¶. Convert a sequence of rotation angles to an equivalent unit quaternion. This function can take inputs in either degree or radians, and can also batch process a series of rotations (e.g., time series of Euler angles). To define roll, pitch, and yaw in linear systems, we first need to establish the three primary axes: X, Y, and Z. The two axes of the horizontal plane are typically defined as X and Y, with the X axis being in the direction of motion. The Y axis is orthogonal (perpendicular) to the direction of motion and is also in the horizontal plane. pose: the abosolute pose (roll,pitch,yall,x,y,z) of each image related to a map (Notice this is converted from the 4x4 pose matrix from Apolloscape dataset) camera_params: the intrinsic parameter of the camera; split: the train val split used in the paper. The first thing we will do is to point the nose to the correct compass heading, that’s a rotation within the xy-plane and about the world z-axis. Next we are going to describe the pitch, the elevation of the front with respect to the horizontal plane, which is a rotation about the new y-axis. Finally, we describe the roll, the rotation about. . X, Y & Z - Yaw, Pitch & Roll First things you should know about are the 3 axises X, Y & Z and pitch, yaw & roll. I'll have to assume you already know what X, Y & Z are. If you don't, how do you even know how to use locations in Minecraft? Now for the pitch, yaw & roll. Those are the names of rotations around X, Y & Z. Pitch is the rotation. To add to the confusion, there are six fundamental aerospace sequences as well. For example, a pitch-yaw-roll sequence versus a roll-pitch-yaw sequence. While the astronomy community has pretty much settled on a z-x-z sequence, the same cannot be said of the aerospace community. Somewhere along the way you find people using every one of the six .... Gets the angle from the quaternion. You may think the following ways at first. Calculates the pitch angle and the yaw angle, that a direction you give and another direction of the quaternion make. (Ignores Z-ROLL) Gives two vectors that are the front direction and the up direction, makes a projection and calculates pitch, yaw and roll angle. On. In this video we will see how to get orientation quaternions from a IMU sensor-MPU6050. I've used Jetson's I2C bus to directly get the IMU data without using. What's the easiest way to plot a simple arrow of arbitrary dimensions given a starting position (x,y,z) and euler angles (roll,pitch,yaw)? 0 Comments. Show Hide -1 older comments. Sign in to comment. Sign in to answer this question. ... In other words, the X/Y/Z positions I have are in ECEF coord, and I'd need to first rotate the initial arrow.

Nov 27, 2020 · The 3-2-1 Euler angles are referred to as yaw ( ψ ), pitch ( θ ), and roll ( ϕ ), respectively, and are commonly used in aircraft dynamics and controls. We will use the 3-2-1 Euler angle direction cosine matrix, or DCM, to convert between the tilted frame and level frame. Since we are ignoring yaw/heading measurements, the DCM relationship .... Roll, Pitch and Yaw angles rotation around X, Y, Z axes Un éditeur LaTeX en ligne facile à utiliser. Pas d’installation, collaboration en temps réel, gestion des versions, des centaines de modèles de documents LaTeX, et plus encore.

fa

ny

kn
sc
Re: Roll, pitch and yaw angles. by coppelia » Mon Mar 28, 2016 1:20 pm. Hello, V-REP uses this set of Euler angles to describe an orientation in space (next to using Quaternions and/or matrices). Let's say you have following 3 Euler angles for an object in space: alpha, beta and gamma. Then, it is the same as placing that object in the same. The original field of view is what the viewer first sees when they view your 360-degree photo in a 360-degree photo viewer (before they start looking around). By adjusting yaw, pitch, and roll; if the camera was leaning to the right, you might adjust the roll to make the horizon level (you’ll often see a horizon leveling feature in stitching.
qk em ep mu bo