# Tag Info

### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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

### 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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### 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 ...
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### 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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### 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 ...
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### 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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### 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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### Redundancy and Null space projection

If you multiply both members of the equation (3.9) by $J$, you'll get: $$J\dot{q} = JJ^+v + \left( J -JJ^+J \right)\dot{q_0}.$$ Then, we can exploit that $JJ^+=I$, obtaining: $$J\dot{q}=v,$$ which ...
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### cartesian velocity control loop implementation

The orientation error is not simply subtraction of your current pose and the desired pose. Given $\mathbf{R}_{a}, \ \mathbf{R}_{d} \in \text{SO}(3)$, where $\mathbf{R}_{d}$ is your desired ...
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