16 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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  • 4,123
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 ...
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10 votes
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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=\...
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  • 214
9 votes
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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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7 votes
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Can a Jacobian be used to determine required joint angles for end effector velocity/position?

Yes, the Jacobian relates the joint velocities to end-effector velocity through this equation: $$ \mathbf{v}_e = \mathbf{J}(\mathbf{q}) \dot{\mathbf{q}} $$ Where $\mathbf{q}$ is the joint angles, $\...
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7 votes
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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

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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  • 4,336
7 votes
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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 ...
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  • 4,336
7 votes
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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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  • 1,522
7 votes
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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 ...
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  • 931
6 votes
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What are the advantages of using the Denavit-Hartenberg representation?

Aside from getting the final result as a composition of matrix multiplication, which helps a lot indeed, one crucial aspect of DH convention is the possibility of describing a rototranslation in terms ...
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6 votes
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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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  • 6,447
6 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, ...
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  • 6,447
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
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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 ...
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6 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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  • 1,522
6 votes
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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{...
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6 votes
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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 ...
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  • 619
5 votes

Is configuration space same as joint space?

In robotics the configuration space is exactly the joint space of the manipulator. Differently, to indicate the space where the forward kinematic law maps the joints configuration into, we use the ...
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5 votes
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Inverse Kinematics of Parallel Manipulator (Delta Robot)

For these sorts of problems, I always like to attempt to solve them myself. And they're surprisingly simple when you think about them geometrically. Parallel mechanisms are especially easy because ...
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  • 6,337
5 votes

jacobian of Abb irb140 robot

Here is the traditional way. I think this is the kinematics of your arm, but am not 100% sure. Here are the DH parameters and transformation matrix: DH Parameters for the anthropomorphic ...
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  • 5,245
5 votes
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How do you calculate the moment of inertia of a Quadcopter?

You can calculate the moment of inertia of a pendulum by measuring the period of oscillation for small amplitudes. Suspend the quad by one arm and give it a little push and time the period. It does ...
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  • 1,823
5 votes
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Jacobian-based trajectory following

The math required to deal with the orientation error (in terms of error with respect to both desired position and desired velocity) is well described in the book of Sciavicco-Siciliano. See section 3....
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5 votes
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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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  • 6,447
5 votes
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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 ...
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5 votes
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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 ...
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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 ...
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  • 4,336
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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  • 1,522
5 votes
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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
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