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 (...
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2 votes

Calculating the singular configuration of a 3 revolute joint manipulator

Singular configurations are configurations at which the Jacobian is rank-deficient. In this case $J$ is a square matrix, you can find conditions for singularity by solving $\det(J) = 0$. The last row ...
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2 votes
Accepted

Matrix is singular error in GraphSLAM

Due to singularity in matrix (i.e. the condition of matrix during which determinant of matrix becomes zero), matrix cannot be inverted. So you can possibly try pseudo-inverse. It gives most ...
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2 votes

Singular configurations of a 7-dof robotic arm

Think of those "terrible to look at" terms as diamonds in the rough. Yes, they look complicated at first. But you will find an amazing number of them will combine using basic trigonometric ...
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  • 4,326
2 votes

EKF singularity problem when measurement noise R is zero

I think you need to step back a bit and think beyond the math. An (E)KF is used to estimate the true value of a signal in the presence of noise; it's only because of this noise that we even need the ...
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  • 2,679
2 votes
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Null space of the Jacobian matrix for a robotic arm

Quite easily, by applying the definition of the Null Space straight away, you have to solve for: $$ \mathbf{J} \left( q_1,q_2=0\right) \cdot \left[\dot{q_1}, \dot{q_2} \right]^T = 0. $$ You'll come up ...
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1 vote

Singularity problem at Inverse kinematic solver

As others have already pointed out, there must be an issue with your implementation of the IK algorithm since there shall not be any singular behavior in the descriptions you gave. Now you have two ...
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1 vote
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Reachable Position with endeffector robotic arm

One possible way to use the inverse kinematics equations. For obtaining the inverse kinematics equations you can either use the Jacobian matrix or the geometric approach. For a robotic arm that has ...
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  • 244
1 vote

How to avoid matrix singularity in GraphSLAM

If $\Omega$ is singular, you cannot avoid a matrix singularity. This is like saying you want to solve the system of equations $$x = 1$$ $$x = 7$$ There are many techniques to avoid robotic ...
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  • 4,326
1 vote
Accepted

Calculating the singular configuration of a 3 revolute joint manipulator

If $J$ is not square, solve $$|J^TJ| = 0$$ for $\theta_i$.
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  • 4,326
1 vote
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How big is the set of kinematics singularities?

According to Pai and Leu, 1989, for a generic manipulator (which includes all 6R robots with a spherical wrist), the set of singular points of rank r are smooth manifolds in joint space of codimension ...
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  • 4,326

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