7
votes
Accepted
In SLAM loop closure, What does a sim3 matrix do?
Sim3 is just the lie group associated a similarity transform which is the exact same thing as your 3D Affine transform. If you work out the multiplication for your two matrices you would find that ...
- 1,901
6
votes
Accepted
State of a Robot
To extends the answer from the_parzival a bit:
There are different kind of robots so that 'robot state' can have different meanings. If you have a drone or Roomba-robot, the most important state is ...
- 1,375
6
votes
Paradox: I can't use accelerometer measurements to obtain information about my states in a quadcopter?
If the drone is not falling (holding height in the sky), and it's not accelerating in any particular direction, then the accelerometer should be reading:
$$
a = \left[ \begin{array}{}
g_x \\
g_y \\
...
- 15.9k
5
votes
Accepted
How to compute the orientation error between two 3D coordinate frames?
The rotation error between two frames can be viewed in two ways:
The orientation of one frame as seen from the other, calculated by multiplying the inverse of the observing frame by the observed ...
- 619
4
votes
Accepted
Inverse kinematic orientation problem
Up till now, I am using the Euler angle representation but I have not been successful. After referring to the book "Robotics Modelling, Planning and control" by Bruno Siciliano form Springer ...
- 186
4
votes
Accepted
Paradox: I can't use accelerometer measurements to obtain information about my states in a quadcopter?
I encountered the same puzzle. I had a clue at the beginning that the gravity information is contained within accelerometer measurements due to aerodynamic drag. Then I found a paper The True Role of ...
- 56
3
votes
How to compute the orientation error between two 3D coordinate frames?
A rotation matrix represents the rotation between two frames. Therefore, it does not make sense to talk about in which "one" frame the error rotation is expressed. Namely, the rotation matrix $R^B_A$ ...
- 941
3
votes
Accepted
Solving Inverse Kinematics with unknown orientation
There is no way that you can solve for an IK solution without you -- either explicitly or implicitly -- specifying a criterion for choosing one solution among many others. But that does not mean that ...
- 1,879
3
votes
Paradox: I can't use accelerometer measurements to obtain information about my states in a quadcopter?
Accelerometers measure kinematic acceleration with the addition of gravity. So for an accel to measure 0, the vehicle would need to be accelerating downward at $g$. To get inertial acceleration out of ...
- 1,863
3
votes
Accepted
Can Euler angles cause gimbal lock when you always rotate along body or fixed frame axes?
You refer to the forward kinematics problem: given three angles, one specific orientation results.
Gimbal lock however is related to the inverse kinematics problem: "Given an orientation, which ...
- 2,749
2
votes
Multicopter: What are Euler angles used for?
Your own equations make a lot of assumptions about the problem you are trying to solve. They are sufficient to solve your problem, but will not work for certain conditions (z = 0 for instance).
...
- 4,455
2
votes
Handling GYROSCOPE BIAS DRIFT
You say,
Then why can't we track [the angles] for first ten seconds and then keep subtracting the present angles from initially calculated angles for every ten seconds during movement?
You can't ...
- 15.9k
2
votes
Inverse kinematic orientation problem
Referring to the equation $\dot{x} = J(q)\dot{q}$, what the last three elements of $\dot{x}$ should be depends on what kind of Jacobian you are using.
Geometric Jacobian:
Suppose your Jacobian is ...
- 1,879
2
votes
Sensor complement in Drone
1) Yes, a megnetometer is an instrument that measures magnetism — either the magnetization of a magnetic material like a ferromagnet, or the direction, strength, or relative change of a magnetic field ...
- 41
2
votes
Accepted
Forward Kinematics for Two Axis Gimbal Mount
To expand on my comment, the last line of your DH table gives the transform between END_EFFECTOR-1 and END_EFFECTOR frames, ...
- 15.9k
2
votes
Accepted
GPS Course vs IMU Course
So this probably won't work as course over ground and heading are often 2 different things. Heading is the direction your vehicle is facing, while course over ground is the direction your vehicle is ...
- 1,901
2
votes
Obtaining Heading vector from IMU
Probably the easiest way to do this would be to convert from Quaternion to Roll-Pitch-Yaw rotations, and then your heading is the Yaw angle.
I'll note that the Yaw angle is not fixed/correct unless ...
- 15.9k
2
votes
Kalman filter problem with the output
You haven't made a mistake. There is a bias in your accelerometer readings (which is a true statement for all accelerometers) and then you're numerically integrating that bias, which results in ...
- 15.9k
2
votes
Accepted
geometric meaning of rotation matrices related to different frames
Using the notation you have given, the intuitive geometric meaning of rotation matrix multiplication is most clear when the subscript of the first matrix is equal to the superscript of the second (i.e....
- 904
2
votes
Accepted
IMU Orientation from madwick filter is stucked between -+ 90°
Found it ! the problem was coming from an intermediate node which was converting imu data from one frame to another. In this node, I convert imu data with a static tf like this :
...
1
vote
What type of rigid body rotation can best be learned by neural networks?
Every three-dimensional parameterization of rotations has singularity. So even if you would implement the kinematics directly you would still run into trouble for some rotations when using Euler ...
- 941
1
vote
Compute orientation velocities 6-DOF robot
I was able to figure out after digging further through several other posts and google searches.
This post pointed me in the right direction:
https://physics.stackexchange.com/questions/293037/how-to-...
- 21
1
vote
Signed difference between two directions
Assuming you know the heading of your own vehicle, you then need to find the absolute bearing of your target so you can find the relative bearing between your vehicle and the target.
The best way to ...
- 15.9k
1
vote
Extract Euler angles from angular velocity profile
Although this is quite late, I believe this question should get an answer. The solution for this problem is:
If one has no other information but the angular velocity and needs to get the Euler angles, ...
- 21
1
vote
Accepted
Finding quaternion Q, where Y = q * X * q.inv()
Your question is related to Wahba's problem, which initially is defined for rotation matrices but can also be defined for unit quaternions and can be solved with Davenport's q-method. However, in ...
- 941
1
vote
Problem defining rotation matrix
A rotation matrix is also called a director cosine matrix. The elements of the rotation matrix are the cosines of the unit vectors of two coordinate systems involved. You can find a more generic ...
- 6,682
1
vote
Accepted
Problem defining rotation matrix
It looks like both frames are attached to the end effector at point P, and are offset by a constant angle $\beta$. So you don't really have to consider the D-H parameters to answer this question - ...
- 231
1
vote
Accepted
Finding orientation angles of end-effector from the DH parameter table and transformation matrices
Your $A_{0.3}$ matrix is a 4x4 transformation matrix. In a general form these 4x4 matrices can be subdivided into a 3x3 rotation and a 3x1 translation part. (The remaining parts can be used for ...
- 6,682
1
vote
In SLAM loop closure, What does a sim3 matrix do?
I think you'll find section IV. Loop Closure useful here:
http://www.roboticsproceedings.org/rss06/p10.pdf
- 11
1
vote
State of a Robot
The answer by parzival is only a partial answer. Especially with robots with more than 3 axes, the matrix cannot be solved for a deterministic state, a famous example of this is Dirac's belt trick, ...
- 195
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