Justinus Hartoyo

Last seen: 5 months ago | Active since 2021

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Determine roll pitch yaw angles from a 3D rotation matrix
Consider an aerospace application where the world reference coordinate frame {W} and a body-fixed coordinate frame {B}. The ori...

9 months ago

Solved

Invert a 3D rigid-body transformation
Given an SE(3) matrix representing a rigid-body motion, compute its inverse without using |inv()| or |pinv()| .

9 months ago

Solved

Invert a 3D rotation matrix
Given a 3D rotation matrix, belonging to the matrix group SO(3), compute its inverse without using the functions inv() or pinv()...

9 months ago

Solved

Relative points in 2D: problem 1
The 2D pose of a robot, with respect to a world coordinate frame {O}, is described by a 3x3 homogenous transform matrix T. A lan...

9 months ago

Solved

Relative pose in 2D: problem 2
We consider a world reference frame denoted by {0} which has its x-axis pointing east and its y-axis pointing north. There is a ...

9 months ago

Solved

Relative pose in 2D: problem 1
We consider a world reference frame denoted by {0} which has its x-axis pointing east and its y-axis pointing north. There is a...

9 months ago

Solved

Pose interpolation in 2D
Consider two poses represented by homogeneous transformation matrices: |T1| and |T2|. Write an algorithm to interpolate between...

10 months ago

Solved

Orientation of a 3D coordinate frame
The orientation of a body-fixed frame {B} with respect to the world frame {W} is described by an SO(3) rotation matrix. Compute...

10 months ago

Solved

Create a 3D rotation matrix
Consider an arbitrary coordinate frame {A}. Consider another coordinate frame {B} which has the same origin as {A} but is rotat...

10 months ago

Solved

Homogeneous lines and points in 2D: problem 1
In high school we learn the line equation y = mx + c where m is the gradient and c is the intercept. However this form is proble...

10 months ago

Solved

Create a 3D rotation matrix from roll-pitch-yaw angles
Consider a robotics application where the world reference coordinate frame {W} and a robot manipulator arm with an attached tool...

10 months ago

Solved

Composing relative poses in 2D: problem 2
We consider a world reference frame denoted by {0} which has its x-axis pointing east and its y-axis pointing north. There i...

10 months ago

Solved

Composing relative poses in 2D: problem 1
We consider a world reference frame denoted by {0} which has its x-axis pointing east and its y-axis pointing north. There i...

10 months ago

Solved

Relative points in 2D: problem 3
The 2D pose of a robot, with respect to a world coordinate frame {O}, is described by a 3x3 homogenous transform matrix T. A la...

10 months ago