11
votes
Rotation matrix sign convention confusion.
I think that the main issue is that you're trying to read your rotation matrices from left to right. The sign changes seem random, but actually cycle in an ordinary way. Below follows a more elaborate ...
- 562
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
Forward kinematic and inverse kinematic... When to use what?
Let me give you a mathematician's perspective on the difference between the two kinds problems.
Forward kinematics asks the question: given a certain input (i.e. control command), what will be the ...
- 1,258
8
votes
Forward kinematic and inverse kinematic... When to use what?
Forward kinematics uses joint angles (with known link lengths) to compute the tool position and orientation. Inverse kinematics uses tool position and orientation, to compute joint angles. Note: if ...
- 4,366
8
votes
Accepted
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, $\...
Ben♦
- 5,780
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
Is the geometric inverse problem's solution "continuous" for a redundant robot?
I don't know if there is a formal proof to this, but in general, no the set of all possible joint configurations that correspond to a particular end-effector pose is not continuous. I think of the ...
Ben♦
- 5,780
7
votes
Accepted
Is there a way to determine which degrees of freedom are lost in a robot at a singularity position by looking at the jacobian?
Not by merely looking at Jacobian but by looking at the Singular Value Decomposition of the Jacobian, one can see the degrees of freedom that are lost, if lost. Of course it technically somehow turns ...
- 196
7
votes
Accepted
Finding Center of Mass for Humanoid Robot
Yes. As @hauptmech mentioned, you can use your forward kinematics to get the center of mass of each link in the base frame. Then you can simply compute the weighted average of the masses and ...
Ben♦
- 5,780
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, ...
- 6,612
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 ...
- 6,612
6
votes
Programming Inverse Kinematics in C++
I agree with SteveO that there is nothing wrong with reinventing the wheel if you want to learn about wheels. And for a single application, 4 DoF arm, the IK is probably not too hard.
But I feel ...
Ben♦
- 5,780
6
votes
Accepted
Why are joint velocities very high near a singularity?
First of all, singularities are not configurations that have the same end-effector position and orientation. Those configurations are inverse kinematic (IK) solutions to that end-effector pose (...
- 1,819
6
votes
Inverse kinematics for differential robot knowing linear and angular velocities
Your linear velocity should be the average of both wheel values. Assuming there's some wheel radius of WHEEL_RADIUS, as you've stated, then you should get each ...
- 15.7k
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 ...
- 619
5
votes
is it possible to get all possible solutions of inverse kinematics of a 6 DOF arm?
I suggest you look at Craig's book Introduction to Robotics Mechanics and Control. In the inverse kinematics chapter he addresses the multiple closed-form solutions obtained analytically. Many other ...
- 4,366
5
votes
Accepted
Programming Inverse Kinematics in C++
It is rather straightforward to implement inverse kinematics for a particular manipulator in C++. Of course, you need to begin with the inverse kinematic equations themselves. Putting those into ...
- 4,366
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 ...
- 1,819
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 ...
- 6,612
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 ...
- 4,366
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 ($x$,$y$,$z$...
- 4,335
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 ...
- 1,642
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 ...
- 4,366
5
votes
Accepted
Velocity-Control of a manipulator without a dynamic model
Your intuition is partially correct in the sense that you ought to go with position control implemented via velocity commands resorting to a kinematic (not dynamic) model of the manipulator.
This can ...
- 3,875
5
votes
Accepted
Solving inverse kinematics with non-linear optimization libraries
Is it a good idea to solve inverse kinematics with non-linear optimization libraries such as Ceres?
Yes, definitely!
The trend in literature during the last years is to walk away from the traditional ...
- 3,875
4
votes
Accepted
Kinematics of a 4 wheeled differential drive robots
This is an old question but I see it repeated without a real answer.
Sticking with a kinematic model only, here's what I would do:
The linear velocity of the robot is $\upsilon$ and the angular ...
- 4,335
4
votes
Finding inverse kinematics algorithm for a specific manipulator
To expand on Ugo's answer, some libraries that implement these general IK algorithms:
OpenRave
ROS MoveIt!
Matlab Robotics Toolkit
Orocos
For people just starting out with kinematics, I highly ...
Ben♦
- 5,780
4
votes
Accepted
Robot arm reachability of a pose in Cartesian space
Nowadays we no longer employ exact solutions for the IK problem, simply because the number of degrees of freedom so as the number of constraints the final configuration needs to comply with make the ...
- 3,875
4
votes
Denavit Hartenberg parameters - 3DOF articulated manipulator
I defined the robot using your (assumed standard) DH parameters:
...
- 1,642
4
votes
7DOF inverse kinematics spherical wrist
I believe kinematic decoupling used to be the standard procedure for 6 DOF arms. (6R with spherical wrist). Where you would solve the 3 DOF position IK first, then 3 DOF orientation IK.
If you ...
Ben♦
- 5,780
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