Questions tagged [rotation]

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1answer
28 views

Does every rotation vector has an one-to-one corresponding rotation matrix?

Given a rotation vector, can we always get the same corresponding rotation matrix computed by the Rodrigue's rotation formula?
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1answer
34 views

what are shoulder ball and socket joints called? (i am trying to design and build a hydraulic assistance mech suit)

I'm having problems finding the right sort of joint for my shoulder connection. It is a flat surface on the side of the mech body and I need to create a joint with maximum movement rotating: up, down ...
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0answers
29 views

Angular movement of a controlled arm relative to an object via Two IMUs

I've been tasked to use two YEI 3-space sensors (IMUs) to detect the azimuth and elevation (altitude in the image below) angle of a moving arm with respect to a fixed object, with a sensor on the end ...
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2answers
45 views

Compute path in absolute frame from sequence of measurements

I have a sequence of measurements $\{(x_i, y_i, \theta_i)\}_{i = 1 \:...\: N}$. Each of these represents the new pose of the robot seen from the previous pose, i.e. a measurement $(x', y', \theta')$ ...
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1answer
49 views

Reset coordinate system of robot while maintaining relationship to the previous

I am currently estimating a robot's pose (3d position and rotation matrix) with an IMU and I want to reset the localizer in the middle of the run while keeping the relationship to the pose it had when ...
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0answers
18 views

Motion model and homogeneous transformation issue on a drone

I am trying to develop a EKF-SLAM algorithm for a drone, and I want to estimate its position in the inertial/world reference frame. I have as control variables the linear and angular velocities in the ...
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1answer
101 views

Conveyor Belt Calibration for a Robot - Rotation Matrix

Short Question: As demonstrated in the image below, how can I calculate the rotation matrix that relates the base coordinate and the rectangle coordinate, given 3 known points P1, P2, P3 on the ...
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1answer
92 views

What is my last rotation matrix for the last three angles when i have found the first three when doing inverse kinematics to a 6dof robot?

I am doing inverse kinematics for a 6dof robot. I have used the geometrical method to describe the angles from one to three. I have trouble doing the next part. I know I that I have found the ...
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1answer
213 views

What are wheel ticks and wheel impulses?

I'm tracking the position of a vehicle along a certain trajectory using the Kalman filter and we have odometry data provided to us which gives the x-position of the vehicle, y-position of the vehicle ...
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2answers
43 views

Understanding Twists as 3D Velocities

I am just learning about twists to represent 3D velocities (e.g. of a robot's end-effector), and I have two questions: 1) Wikipedia defines a twist as "an angular velocity around an axis and a linear ...
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1answer
58 views

How to calculate rotation angle from 3D points

I have 4 3d points(x, y, z). Using these points how can I calculate rotation angle? Consequently, I want to have a 4x4 transformation matrix including rotation and translation information. 4 points ...
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Convert point coordinates from inclined to inertial coordinate system using inclinometer angles

I have a point (red dot) coordinates given as [vector magnitude, azimuth angle (blue), elevation angle (yellow)] in the inclined local system X'Y'Z', which must be converted into coordinates [x, y, z] ...
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23 views

2-axis inclinometer angles to quaterion angles

How to derive quaterion angles (3 angles of the rotation vector with respect to the inertial coordinate frame and the rotation angle around that vector) knowing X and Y angles from a 2-axis ...
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0answers
31 views

Rotate coordinate frame using 2-axis inclinometer angles

How to rotate coordinate frame (transform point or vector coordinates) using angles from 2-axis inclination sensor if both X and Y angles are non-zero?
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1answer
27 views

Doubt about axis\angle representation

I am trying to understand the axis/angle representation. So far, I have understood that the main idea is that every rotation can be represented as a rotation around an arbitrary axis of an angle $\...
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2answers
546 views

Finding correct RPY for approaching a known point on a plane

I have a robot with 6 DOF that I want to use to grab a hanging sheet at a specific point near its edge. The grip needs to be perpendicular to the edge and co-planar with the point of course. I have ...
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1answer
268 views

Rotation composition When using Kalman Filter

I am implementing a Kalman Filter for the following situation. I have a camera set in a room that can detect the position and orientation of a marker (ARUCO) in the room. Therefore I have the ...
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1answer
559 views

Rotating NED to ENU

I have an IMU in NED of which I need to rotate to ENU to conform with ROS. I know its a roll of pi and a yaw of pi/2 but what ...
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1answer
30 views

Finding quaternion Q, where Y = q * X * q.inv()

Problem Quaternions $X$, $Y$, which represents 3-dimensional points are given. Quaternion $q$ is what is to be solved. I want to know unknown rotation between $X$ and $Y$. In other words, I want to ...
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1answer
39 views

Solving for rotation matrix: Aligning vector a with vector b and then rotating around vector b

Currently working on a quadcopter simulation. I have a desired thrust vector, t =sin(30)cos(45)a1+sin(30)sin(45)a2+cos(30)a3 and desired yaw angle, ...
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0answers
51 views

What's the result of multiplying a rotation matrix having only ψ components by another which has (−φ,θ,−ψ) components?

Given the following rotation matrix: $ R(φ, θ, ψ) = \left( \begin{smallmatrix} cos(θ)*cos(ψ) & -sin(φ)*sin(θ)*cos(ψ)-cos(φ)*sin(ψ) & -cos(φ)*sin(θ)*cos(ψ)+sin(φ)*sin(ψ) \\ ...
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2answers
66 views

How to compute the orientation error between two 3D coordinate frames?

For my master thesis in robotics I have to compute the orientation error between two coordinate frames, called E and H. Their orientation is expressed through rotation matrices (3x3) with respect to a ...
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1answer
55 views

Rotating a lever with a small servo

I'm trying to rotate a lever link to gently "offload" a load using a servo. Here's a drawing: Here, the red is a lever, yellow pivot and black is the load. To offload, the lever needs to be turned 90 ...
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4answers
1k views

Most accurate rotation representation for small angles

Assume that I have a rigid body for which I know that it can rotate with respect to a global reference frame (which is considered fixed and already given) for only a few degrees of angle, so I can ...
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0answers
23 views

MPU6050 Gyro rotaion always around Y axis

I am using an MPU6050 IMU. I did a small experiment having Z-axis pointing upwards. 1. Rotate 90deg around Z-axis (yaw) and back to the original position 2. Rotate 90deg around X-axis (roll) and back ...
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0answers
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Moment of Inertia of a planar rotation link with a 6-DOF base

I'm interested in analytic calculation of a moment of inertia of a robot's arm in the following situation. Let us assume the following: Stationary reference frame $ \{b\} = \{X_B, Y_B, Z_B\}$ and ...
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2answers
77 views

How to calculate heading more accurately using dead wheels?

I am trying to figure out a more accurate way to calculate the change in the heading of a robot. I have two small omni wheels on either side of the robot facing forward and one on the right side ...
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3answers
6k views

Rotation matrix sign convention confusion.

In rotation matrix, Why do we rotate the first and third rotation in the opposite direction of the 2nd rotation, this is confusing. Image is attached with this. In this image we can note that for x ...
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1answer
47 views

Does Vehicle Yaw angle measures same at every point on it? If not, how to translate yaw rotation to COG of the vehicle from different point?

I am using an IMU to measure the yaw rotation angle of a car. I need to translate the rotation measured to COG of the vehicle. I can ignore roll and pitch as I am driving it on a flat surface. So, ...
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4answers
2k views

Why Euler Angle is set to be in ZYZ order?

We have 3 DOF for rotation in 3D space. So to describe an arbitrary rotation, we need to describe its 3 DOF. Euler angle does this by dividing a rotation in 3 steps, first rotate along the Z axis of ...
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1answer
50 views

Rotation at SerialLink.teach Robotic Toolbox

Im using robotic toolbox to simulate my robot, but i always confused when i see the value of rpy. It always different if i compare with tr2rpy and tr2eul. What kind of rotation used in SerialLink....
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0answers
73 views

How to get RPY(Roll, Pitch, Yaw) from directional cosines from a single vector?

I'm trying to find the pose of an 3D vector in terms of RPY. Let's say the two end points of the vector is P0(x0, y0, z0) and P1(x1, y1, z1). So the centered vector I get is V(Vx, Vy, Vz) = P1 - P0 = (...
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1answer
25 views

Observed position update after motion of the robot

The equation (14) in this paper, $$ P_{Cj}=RP_{Pj}+T+e_j $$ where $P_{Cj}$ and $P_{Pj}$ are the observed positions of feature $j$ prior to and after the current robot motion, $R$(otation) and $T$(...
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0answers
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Undo pitching effect of camera when pose (y-axis) is near 90 degrees?

I am using KITTI odometry dataset whereby the camera's axis is pointing X (east), Y (down) and Z (north). It also contain the frame to frame poses of the camera (first pose is fixed as the map frame). ...
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1answer
18 views

How should I create a Pangolin (Armadillo) structure?

I am new to this forum. I want to create a mechanical structure as depicted in the image A pangolin bag. And further wouls like to automate the closing and opening of the bag. But I am facing issues ...
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1answer
183 views

Adjusting the PWM frequency and duty cycle to achieve the desired angular velocity in differential drive robots

I am practicing C++ and intro to robotics using a simple differential drive robot and a raspberry pi. Also following along the GA Tech course on control of mobile robotics. The implementation I am ...
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1answer
351 views

How can I attach an arm to a double-flat drive stepper motor?

This is my first robotics experience, outside of one class 10 years ago. I've been Googling this question for about an hour but I can't find an answer! I'm using a ROHS Step Motor 28BYJ-48 (with an ...
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1answer
1k views

Using pre multiply or post multipy for rotational matrix to get a new homogenous transformation matrix?

I am confused about how do I multiply the rotational matrix in this case. I know that both T1 and T2 needs to be multiplied by a rotational matrix but I don't know how to multiply the rotational ...
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3answers
187 views

Forward Kinematics with matrices

From the image, I would like to find out how joint 1, 2 and 3 can be computed by using forward kinematics? (Assuming a theta value was given) I understand that to get point 3 to origin (...
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1answer
1k views

Get Yaw from quaternion

I found a formula online to extract yaw from a quaternion like so: ...
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0answers
99 views

Equivalence of Alias and Alibi interpretation of Rotation Matrices [closed]

Let's consider two right handed frames $\mathcal R_A$, with coordinate axes $i_A$, $j_A$ and $k_A$ and $\mathcal R_B$, with coordinate axes $i_B$, $j_B$ and $k_B$. Defining the rotation matrix $R^A_B$ ...
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3answers
126 views

A closed-form solution of $\textbf{R}\textbf{R}_1=\textbf{R}_2\textbf{R}$ w.r.t $\textbf{R}$

Is there a closed-form solution of $\textbf{R}\textbf{R}_1=\textbf{R}_2\textbf{R}$ with respect to $\textbf{R}\in SO(3)$? $\textbf{R}_1$, $\textbf{R}_2 \in SO(3)$ are given. Added: I tried holmeski'...
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1answer
2k views

How to rotate a rotation quaternion in the body frame to a rotation quaternion in the world frame?

I have a sensor (3 axis gyroscope) which can rotate and measure angular velocity in 3 dimensions (aligned with the sensor). I know what its current orientation is with respect to the world frame. Call ...
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1answer
102 views

SE3 composition operator gives unexpected results

Given Data and Algorithm I have a stream of SE3 poses supplied by a basic wheel encoder odometry through ROS message passing system. Odometry publishes data in traditional to ROS ENU coordinate frame ...
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1answer
45 views

Angular velocity vector expression uncertain?

I have this problem of an excavator from a test I took a while ago. Frame $\underline{\vec{e}}^0$ is the origin. Frame $\underline{\vec{e}}^1$ rotates around $\underline{\vec{e}}_{3}^0$ with angle $\...
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2answers
76 views

Nested Rotation of a point around arbitrary vector in 3D

I have a point (x,y,z) in the 3D space. This point rotates by theta1 about the arbitrary axis ax1. This axis (ax1) rotates by theta2 about another axis ax2. What will be the new coordinates of the ...
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1answer
204 views

Solving Inverse Kinematics with unknown orientation

This may be a very basic question, but I haven't had much success finding an answer. I'm currently trying to solve the inverse kinematics of a 3-RRR Planar kinematic arm, whose purpose is to move ...
2
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2answers
259 views

Explanation for exponential coordinate of rotation

From figure above, suppose a three-dimensional vector $p(0)$ is rotated by an angle $\theta$ about the fixed rotation axis $\omega$ to $p(\theta)$. Here we assume all quantities are expressed fixed ...
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2answers
503 views

How to reduce the small free rotation/movement of a stepper motor shaft?

I was successful in running a 28BYj-48 stepper motor with 4096 steps per revolution. I am happy with the result. But there is a free movement of the motor shaft itself - you can move the motor shaft ...
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5answers
2k views

Shield IMU from magnetic interferences

I experienced some drifting when coming near to magnetic fields with my IMU, so I wondered if it is possible to completely shield the IMU from external influences. Would this be theoretically possible ...