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Questions tagged [matrix]

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69 views

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 ...
• 1
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
85 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 ...
1 vote
180 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 ...
• 173
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 ...
• 81
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
318 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 ...
443 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 ...
• 163
263 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 ...
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 ...
• 101
1 vote
494 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 ...
• 11
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, $M(q)$, \$...
• 183
525 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 ...
• 63
1 vote
600 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 ...
• 13
259 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
2k views

Questions about time derivative of jacobian matrix

I find that in some robotic toolboxs(e.g. FROST https://ayonga.github.io/frost-dev/index.html) they use to calculate time derivative of jacobian matrix. Here is my guess about the reason of using ...
• 11
1 vote