# Questions tagged [rotation]

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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
20 views

### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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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### 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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### 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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### Get Yaw from quaternion

I found a formula online to extract yaw from a quaternion like so: ...
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### 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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### 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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### 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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### 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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