10
votes
Accepted
Why do current manipulators tend to use 7 DoF instead of 6 DoF?
Adding a 7th joint, and still targeting a 6D pose, would result in a
null space of at least one dimension anywhere in the workspace.
That is basically one the reasons people may wish to use a 7-DOF ...
- 328
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
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, ...
- 6,652
6
votes
Accepted
D(q) Inertia Matrix and the Jacobian Matrix
I think this is a matter of notations.
In the given formula for $D(q)$, the matrices $J_{vi}$ and $J_{\omega i}$ are not simply the direct extraction of columns of the Jacobian of the system.
$J_i$ ...
- 1,829
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
Accepted
Why in trajectory planning in joint space the manipulator never crosses a singularity?
The term "singularity" characterizes those configurations in the joint space where the Jacobian matrix loses rank and thus it is not directly invertible.
The Jacobian, in turn, is used to remap a ...
- 3,995
5
votes
Can workspace of a manipulator change after considering its dynamics?
The workspace of a manipulator is strictly determined by its kinematics. Since kinematics only consider the geometry of motion, without regard to forces and torques needed to accomplish tasks, you ...
- 4,386
5
votes
Accepted
Cartesian Impedance control Damping Design (Double Diagonalization)
A hint towards what the answer is given in the paper. Namely, one can use the generalized eigenvalue decomposition, which in this case can be formulated as finding eigenvalues $\lambda \in \mathbb{R}$ ...
- 941
5
votes
Accepted
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 ...
- 3,995
4
votes
Accepted
Robotic manipulator Jacobian by product of exponentials
The Jacobian in that equation is from the joint velocity to the "spatial velocity" of the end effector.
The spatial velocity of an object is a somewhat unintuitive concept: it is the velocity of a ...
- 619
4
votes
Human arm inverse kinematics
You are tackling two non trivial problem at the same time
1. Inverse kinematics of an overactuated manipulator
2. Obstacle avoidance using the null space
By definition of the null-space projection ...
- 1,402
4
votes
Dynamic torque simulation for a 6 DOF robotic arm
The dynamics of robotic arms are fairly complex, especially when there are more than three joints to consider. The problem is that the movement of each joint moves all the links beyond it, which can ...
- 218
4
votes
Proportional controller error doesn't approach zero
Controllers type
A more mathematical approach to the error.
Suppose you have a close loop system like above. The equation is:
$\hspace{2.5em}$ $Y(s) = \frac{G(s)C(s)}{1+G(s)C(s)} R(s)$
The error ...
- 143
4
votes
Accepted
Integrating Forward Kinematics Map
(EDITED TO CLARIFY PARENTHETICAL ABOUT CARTESIAN MANIPULATORS)
Your equation is true in general only for those manipulators in which $J_a$ is independent of $\theta$ (such as with Cartesian ...
- 4,386
4
votes
Accepted
What is the difference between the pose of a robot and the configuration of a robot?
Do "configuration" and "pose" means the same thing?
No.
One of the most clear definitions of 'pose' that I've heard is in Peter Corke's Robotics, Vision and Control (RVC). It states that:
"The ...
- 1,054
4
votes
Accepted
Definition of robotics manipulator?
The original manipulators referred to in that article were through-the-wall pantographs which moved radioactive materials without the human operator having direct contact with those materials. The ...
- 4,386
4
votes
Accepted
Visual-Positioning Method
So it sounds like you have an external camera system to track the end effector position and orientation?
In that case I would use QR codes or april tags. Stick a couple of these on your end effector, ...
- 1,831
4
votes
Accepted
How do I assign the origin of the frames in the Denavit Hartenberg convention?
There is not one correct DH Frame assignment, but there are many. Even if you do not get the same results, you might still have a correct frame assignment.
The first, base frame at the root of the ...
- 6,652
4
votes
Controlling the pose of a manipulator using inverse kinematics
As you already have the Jacobian vector, I assume you also solved the inverse kinematics problem. I will refer to the IK problem as $f^{-1}$
In order to get the joint space equivalent of the ...
- 6,652
3
votes
Accepted
Different methods to determine DOF: Chebychev-Kutzbach-Grubler method vs. Screw method
I will try not to skip too many steps. Assuming a Global coordinate frame at the base and the arm is fully extended along the Y-axis of the base frame.
Since SCARA has four joints, we will create ...
- 103
3
votes
Accepted
Robot Graphical Representation in Real Time
If you are already using Qt, then Q3 3D would be an obviuos choice for 3D representations. Gaming engines like Unity (C#/JavaScript) or the Unreal Engine (C++) are also a suitable choice for ...
- 6,652
3
votes
Dynamic torque simulation for a 6 DOF robotic arm
I think you may be going about this problem wrong. If you find a simulator that reports joint torques, then what? Are you going to iterate through every possible start and end location?
You should ...
- 16k
3
votes
Accepted
Dealing with fixed transformations while solving inverse kinematics
Hopefully you still have only 4 rows in your DH matrix, not 8 as you said. I think you mean that your Jacobian matrix has 8 $\require{enclose} \enclose{horizontalstrike}{\text{rows}}$ columns.
...
- 4,386
3
votes
Accepted
Difference between Degrees of Freedom (DOF) and Degrees of Motion (DOM)
The way you are describing it, DOM is the number of independent dimensions in $\vec q$. DOF is the number of independent dimensions in $\vec x$. In practice, a robotics engineer will use DOF to ...
- 4,386
3
votes
Understanding MoveIt! and OMPL more deeply
Actually I wish to implement my own algorithm (like some variation of
RRT) without MoveIt!/OMPL hence it is important for me to know all the
details.
I am really confused about this. Any ...
- 301
3
votes
Why do I need impedance control?
Imagine that you hold a position very stiff in your arm. You are holding your muscles tight to keep that position and hold it very tightly. Then you walk to move your arm without moving your arm with ...
- 497
3
votes
Accepted
Calculating Error of Arm Manipulator
The interpretation of error for a robot manipulator pose is subjective in terms of what is the error being used for. A robot manipulator pose is combination of both position (x, y, z) and the ...
- 671
3
votes
Accepted
Understanding Impedance Control
Yes, it is the same, $F$ should be the same as $F_{ext}$. And $F$ comes from a sensor or an estimation, in general from a force sensor.
The diagram seems correct and you may have $F$ and $F_{ext}$ ...
- 497
3
votes
Accepted
Why applied joint torque will affect another joint?
When you apply torque to the first joint, it makes the first link rotate. This means that the far end of the first link translates.
Because the second joint pins the near end of the second link to the ...
- 619
3
votes
Accepted
How do I find the minimum time for computing a trajecotry for a robotic arm?
Your problem statement is:
using a bang-coast-bang acceleration profile with symmetric acceleration and deceleration phases, each of duration $T_s=\frac{T}{4}$.
So, right off, you know the time ...
- 16k
Only top scored, non community-wiki answers of a minimum length are eligible