7 votes

Forward kinematic computing the transformation matrix

Start with coordinate systems. I've drawn one example. In my analysis, if all $q_i = 0$ then the manipulator would point straight up. You can choose other coordinate frames to get the same result....
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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 \\ ...
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5 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 ...
  • 1,335
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 ...
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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
4 votes

Forward kinematic computing the transformation matrix

In your forward kinematics transformation matrix (4x4, incl. also translation, of just 3x3) the orientation of the end-effector is expressed relative to the base (or world) coordinate system. SteveO ...
  • 6,507
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 ...
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 ...
3 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 ...
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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 ...
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3 votes

Is there a way to measure 3 axis orientation without a magnetometer?

Calibration procedures for magnetometers exist, to compensate for soft iron (nearby ferromagnetic objects) and hard iron (nearby magnetic fields) offsets, which skew the measurements. However, these ...
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3 votes
Accepted

Manipulator end-effector orientation with quaternions

As Brian indicated in a comment, you simply need to convert your rotation matrix (or Euler angles) into a quaternion. Maths - Conversion Matrix to Quaternion is my favorite site for geometric ...
  • 5,740
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
2 votes

Manipulator end-effector orientation with quaternions

I'm not familiar with your device, but here are a few tips that might help... Since the device is using a quaternion to describe an orientation, they must also specify some base coordinate frame ...
  • 121
2 votes

Orienting rectangular plastic bricks

Its a bit difficult to give you an exact answer because its quite an open question. You are sorting the bricks based on an optical characteristics so I can't see any way of doing it other than by ...
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). ...
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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 ...
  • 15.4k
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 ...
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 ...
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, ...
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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 ...
  • 1,621
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 ...
  • 15.4k
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 ...
  • 15.4k
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....
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 - ...
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 ...
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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
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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, ...
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1 vote

State of a Robot

The state of the Robot refers to the properties of the robot that you want to estimate. If you take a 2D robot as an example, then you might be interested in its 2d position which refers to $$ X(t)...
1 vote

What is an axial and polar vector?

It may be helpful to not get caught up in the author’s description of frames with respect to these vectors. The author is stating that an axial vector, like a force vector, acts along a line. But a ...
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