# Questions tagged [matrix]

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### Inverse Kinematics, indicate if multiple soltuions exist using a matrix

I'm trying to practice inverse kinematics and I'm having a really tough time understanding how you can indicate if multiple solutions exist just using a matrix. I also don't know how I would indicate ...
1k views

### From euler angles to rotation matrix and vice versa

I want to check if I am using the correct functions to transform from euler angles to rotation matrix and viceversa. I am using XY’Z” convention of euler intrinsic angles. As example, I have the ...
1 vote
178 views

### Rotate sensor frame to body frame

I'm working with a lsm303agr from ST. Here is the frame attached to the chip Here is the body frame So I have some doubts about the rotations, before to fuse data ...
1 vote
84 views

### Siciliano et al. Rotation Matrix Notation

I'm reading Siciliano et al.'s Robotics: Modeling, Planning and Control, and I'm confused about the notation used in definiting rotation matrices. On page 46, they state If $\textbf{R}_i^j$ denotes ...
74 views

### geometric meaning of rotation matrices related to different frames

Consider the following rotation matrices: $^{a}R_{b}$, $^{a}R_{c}$ and $^{a}R_{d}$ in which $^{x}R_{y} \in SO(3)$ describes the orientation of a generic frame $y$ wrt the coordinates system of ...
1 vote
305 views

### Caculate/Specify the covariance matrix for a omniwheel robot

I have an omnidirectional robot (x, y and rotation around z), which I would like to use the SLAM-algorithm from ROS. But the odometry from the robot has a drift, which makes some error. To improve the ...
169 views

### Aligning accelerometer readings with vehicle's frame of reference

I have a device with an accelerometer installed in a vehicle. Its orientation in relation to the vehicle is unknown. So I am looking for a reliable way to align the coordinate system of the ...
51 views

### Why do we parametrize matrices?

I'm learning about rotation matrices in class and one of the topics mentioned to parametrize a matrix. What do we need to do this? For further reference: https://www.youtube.com/watch?v=Y8gB7nvtmrU
311 views

### Finding 6 angles for UR5 a 6Dof Robot

I am looking for a method to find 6 rotation angles for the 6DOF, 6joint, 5 link UR5 robot. these angles would be used to control UR5 through ROS but unfortunately I cant find any way to find these ...
1 vote
480 views

### Multiple Rotations via Matrix Multiplication

so I am having an issue understanding why you right multiply for current frame rotation vs left multiply for fixed frame. Let us say you want to: Rotate about x, then Rotate about current y, then ...
516 views

### Matrix Algebra vs Trigonometry for Inverse Kinematics

What method is “better” for solving inverse kinematics for a robot arm: matrix algebra or trigonometry? To define “better”: efficiency/performance vs memory usage generality (how well can it be ...
439 views

### Derive the system's dynamics function and the Jacobian Matrix G of Extended Kalman Filter of a differential drive robot on a 2D plane

I have found the following answer on the system's dynamics function and what the Jacobian matrix G of the Extended Kalman Filter look like for a 2D robot with a differential drive. Taken from slides ...
257 views

### Multiplication of rotation matrix help

I'm Watching Angela Sodemann video on 6DOF robots and am following her example, but I'm getting a different answer for my R3_6 matrix and I'm not sure where I'm going wrong. She uses this as her ...
1 vote
587 views

### calculation sequences when using RPY-transformation vs Euler-transformation

I have trouble understanding calculation sequences for RPY-transformation and Euler-transformation. Let's assume that there are 3 (rotation/translation) instructions. I will notate transformation ...
105 views

### IK Jacobian is always a singular matrix

I am trying to solve an inverse kinematics equation for 6DOF system, 3 rotation and 3 prismatic joints. I am trying to solve using perturbation method, by adjusting each joint and calculating the ...
1 vote
183 views

### Equations of motion in matrix form and energy consumption

I am working on Lagrangian derived high-dimensional motion equations for a robot in matrix form. The structure of such an equation is known: $M(q)\ddot{q}+C(q,\dot{q})\dot{q}+G(q)=0$ In here, $M(q)$, \$...
257 views

### The modulus of each columns of the rotation matrix is

The modulus of each columns of the rotation matrix is 1, 0.5, 0.866 or 1.366 which one is correct?
1 vote