# Questions tagged [rotation]

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### Generate transformation matrices for rotating around a object?

How do i compute all transformation matrices which places a robot endeffector at the shell of this sphere, with the end effector pointing toward the object in the center. I know at all time how far ...
224 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 ...
113 views

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 ...
7k 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 ...
78 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 ...
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 ...
3k 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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### 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'...
313 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 ...
237 views

### Dealing with fixed transformations while solving inverse kinematics

I am trying to solve inverse kinematics (using the Jacobian pseudoinverse method) for a 7 DoF arm, but because of the way the robot is mounted, the base frame does not coincide with the frame of the ...
3k views

### What is the torque/force required to rotate the base of a robot arm?

Take a look at the following simple example robot arm: I want to know the torque required on that bottom motor to rotate the arm. Since it's not exactly rotating directly against gravity like the ...
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 ...
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 ...
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 ...
742 views

### Mechanical odometer with digital output

I would like to mechanically measure the distance a kids electric ATV traveled. The ATV will not be used with kids but as a mobile robot instead. It has a common rear axle for both rear wheels which I ...
54 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 $(x', y', \theta')$ ...
103 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 ...
76 views

### integrating perfect rate gyro data (noiseless)

Having a perfect gyro (with no noise/drift or bias), the gyro produces angular velocities in the form (wx, wy, wz) in rad/sec. I would like to convert the rate gyro readings (which are expressed in ...
17 views

### 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). ...
678 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 ...
109 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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### 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 ...
211 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 ...
33 views

### What type of rigid body rotation can best be learned by neural networks?

I am training a reinforcement learning network in simulation for a robot which at the current stage learns Euler Angles to rotate the end-effector based on the actual state. The performance is overall ...
108 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 ...
213 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 (...
497 views

### Orocos KDL issue with Rotation (matrix) - Inverse Kinematics

I have a problem with the Orocos IK solver, especially with the KDL::Rotation matrix input. I try to call my KDL IK solver with a normal vector and a rotation. If I use the example values for the ...
44 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 ...
57 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 ...
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 $T$(...
2k views

### Get Yaw from quaternion

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

### Ignoring yaw for pick and place

I get an object pose from the camera in quaternion. Since these are tetrahedron shaped objects, the robot needs to align the vacuum gripper to one of the sides of the object. But the yaw (rotation ...
483 views

### How to construct rotary turn table (S/J1 axis) from ball bearing? [closed]

For my robotics arm project I have recently come across the following ball bearing at low discount price which I think could make a great rotary table for my arm. However it does not seem to have any ...
19 views

### Rotate while strafing with mecanum wheels

I have a robot with a drivetrain that is comprised of 4 mecanum wheels. These wheels are able to move vertically and horizontally, as well as rotate. The robot is square (18in x 18in) with the front 2 ...
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### What could cause quaternion error to go up drastically when a gyroscope is rotated on more than one axis at a time?

Alright, I'm working on a small Arduino script that determines orientation using a a gyroscope and a quaternion. My hardware: LSM9DS1 IMU (Gyroscope, Accelerometer, Magnetometer) Teensy 4.0 My basic ...
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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?
57 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 ...
67 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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### 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 ...
85 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 = (...
276 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 ...
34 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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### 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 ...
294 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 ...