17
votes
Position Control vs Velocity Control vs Torque Control
I'm going to take a slightly different tack to Chuck.
What is Torque Control?
For me, Torque Control is about performing a move with an explicitly defined torque, rather considering torque just the ...
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15
votes
Position Control vs Velocity Control vs Torque Control
Torque is analogous to force for rotating systems, in that:
$$
F = m a \\
\tau = I \alpha \\
$$
Where $\alpha$ is angular acceleration and $I$ is moment of inertia. $m$ and $a$ are mass and linear ...
- 15.9k
10
votes
Accepted
Holonomics Movement vs Holonomics Constraint
You can look at degrees of freedom as if they were the number of variables that you need to use to describe your system. So, for a robot moving in a 2D plane, its state would be represented by:
$$
s=\...
- 224
9
votes
Accepted
Understanding the Robot Jacobian
Let's start from the forward kinematics equation
$$x = f(q),$$
where $x \in \mathbf{R}^6$ is the end-effector position, $q$ is the joint angles, and $f$ is a (usually highly nonlinear) forward ...
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8
votes
Accepted
Wrong forward-kinematic after calculating from DH-parameters
Your professor has made an error, but he or she is only human.
The upper-left 3x3 matrix must be an orthonormal rotation matrix. Every column of that must have a unit norm. The second column $[0, 1,...
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8
votes
Accepted
Cartesian Velocity Control between Two 3D Poses
You essentially want to find the time derivative of a linear interpolation between two rotations. The easiest way to obtain this would probably to convert the rotation matrix between the two ...
- 941
7
votes
Accepted
Difference between an underactuated system, and a nonholonomic system
They are different things. An underactuated system does mean that the number of independent control inputs is fewer than the number of degrees of freedom you are trying to command. This can happen ...
- 4,386
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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7
votes
Accepted
Why do we generally prefer DH parameters over other kinematic representations of robot arms?
I have been doing a lot of reading up on kinematic calibration and here is what I found:
From [1]:
A kinematic model should meet three basic requirements for
kinematic-parameter identification:
...
7
votes
Computing the Jacobian Matrix -- chain rule?
Writing the equations by hand and deriving them is certainly the best way to understand what is happening "in the background". Generating the equations and deriving them using a syombolics engine, ...
- 6,632
7
votes
What is the best SE3 library for python?
Writing your own package is always the best way to learn. If you want to try something premade here are a few packages to choose from:
Spatial Math Toolbox for Python Python3+numpy+scipy, also ...
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6
votes
Accepted
inverse kinematics for 6 jointed robots
I would recommend changing the naming convention since it is a bit misleading. In robotics the world Coordinate system (CS) is usually your fixed, absolute coordinate system. Lets call the ...
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6
votes
Is there any robot stability control equation that describes the relation between velocity of the robot and its orientation?
That's not obvious. If I'm in a tank, going 0.5 km/h, I don't need to slow down at all. If I'm in a bobsled going 100km/h and the track banks, I don't need to slow down at all.
When you steer, you ...
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6
votes
Accepted
Extended Kalman Filter in robotics - Worth it?
The Kalman filter is an optimal linear filter in the presence of Gaussian noise. It is optimal in the sense that it minimizes the mean-squared error. This means that the covariance of the estimated ...
- 340
6
votes
Accepted
question about spatial velocity in the book <modern robotics>
A coordinate transformation of a point P from Frame 1 to Frame 0 is given by:
$$
\mathbf{p}^0=\mathbf{o}^0_1+\mathbf{R}^0_1\mathbf{p}^1.
$$
Differentiating with respect to time gives:
$$
\dot{\mathbf{...
- 3,995
6
votes
Accepted
Why with the pseudo-inverse it is possible to invert the Jacobian matrix even in a singular configuration?
The pseudoinverse gives a “least squared error, minimum-norm” solution: Out of all $\dot{q}$ vectors at your current $q$, the vector
$$\dot{q}_{s} = J^{+}(q)\dot{p}_{\text{in}}$$
satisfies two ...
- 618
5
votes
Accepted
Does Inverse Kinematics need the current joint angles?
It depends on the method that you use for computing an IK solution. If you have an analytic formula for IK solutions then you do not need the current joint values of the robot. You just plug in the ...
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5
votes
How do CAD programs solve for Inverse/Forward Kinematics problem in Assembly?
EDIT: Improved based on the comments below.
If you have a CAD assembled, that means that you have one valid configuration given. You move the TCP (Tool Center Point) only a small amount, since your ...
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5
votes
Accepted
Confusion in fixing DH frames
The updated image solves the problem. You did not consider the end-effector coordinate frame earlier.
Also, the crosses (going into) in the diagrams should be replaced by dots(coming out), because the ...
- 263
5
votes
Accepted
How can serial manipulator have unique condition number for given end effector position?
Condition number and manipulability are measured at a specific joint configuration, not end-effector location. You already understand it correctly that the values change according to the robot ...
- 1,829
5
votes
Inverse Kinematics problem formulation (optimization)
The formulation is typical for redundant robots, in which there are an infinite number of joint velocity vectors that could satisfy the $\dot{r}_{t}$ goal. In the version you cite, the $Q$ matrix ...
- 4,386
5
votes
Screw based Jacobian
The geometric Jacobian provides all the information you need for singularity or manipulability analysis. Linearly dependent columns correspond to joints with parallel axes. More information about ...
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5
votes
Accepted
What is the best SE3 library for python?
ROS's tf.transformations.py has self-contained code for doing these functions and can be used without installing ros. In fact, the python code only depends on numpy!
transformations.py
- 301
5
votes
Accepted
Using pre multiply or post multipy for rotational matrix to get a new homogenous transformation matrix?
When working with rigid-body transformations, it is crucial to understand which coordinate frame the transformation is defined in. Further, there are different notations for this, so it is important ...
- 340
5
votes
Struggling to understand Jacobian Inverse Kinematics
You will find it helpful to keep the physical robot and the math separate.
The kinematics equations map joint parameters (which are often grouped as a vector $q$) to Cartesian coordinates ($x$,$y$,$z$...
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5
votes
Accepted
How do I find the inverse kinematics of a 5-DOF manipulator having the following DH parameters?
A general IK solution is not possible for an arm with less than 6 joints. You can move the gripper to any point (within reach) but you can't completely control the orientation. If you fix the ...
- 1,682
5
votes
State Space model for bouncing ball
Matrix notation in general is nice because of how compactly you're able to write and especially read everything, similar to using descriptive variable names in programming or performing algebra with ...
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5
votes
Accepted
How can Denavit-Hartenberg representation with only 4 variables describe rototranslations with 6 DOF?
In general you need 6 parameters to describe the position and orientation of any joint with respect to a link coordinate frame. The DH parameterisation includes 2 constraints so only 4 parameters ...
- 1,682
5
votes
Accepted
How do I compute the derivative of the Jacobian with Matlab?
To answer your solution, specifically, all you need to do is:
...
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5
votes
Accepted
Chebychev–Grübler–Kutzbach Formula of Degree of Freedom
You can check here how to apply the formula to a parallel robot.
For a 6DOF Stewart platform
$$d = 6\,n - \sum_{i= 1}^{m}\left( 6 - f_i\right)$$
$n = 13$ links, $m = 18$ joints, six of which with ...
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