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As suggested by ben, i will put my comment as answer. 1st How to control robot I recommend you to look about resolved motion rate control. It's a complete algorithm to control a robot from path planning, control system, inverse jacobian and simulating plant. (And you can add several other algorithm to measure the state of system if you want too, very good ...

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You can use some Trajectory Generators to create intermediate points between the points calculated by RRT Algorithm. You can use Moden Robotics Library by Neuroscience and Robotics Lab at Northwestern University on Github for example to find some functions which can help you at this time step. You can take a look at "CartesianTrajectory" and "...

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No, you cannot determine the end effector position by using only joint velocities. If you use the Jacobian matrix, you can determine the velocity vector of the end effector given a set of joint velocities. If you have a finite time over which the joint velocities were measured, you can know how much the end effector has moved in that short time. But ...

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Jacobian matrix is used to describe the relationship between the configuration space (space of joint angles) and the task space (space of end-effector pose) as follows: $\textbf{$\dot{p}$} = \textbf{J(q)}\textbf{$\dot{q}$}$, where $\textbf{J(q)}$ is the Jacobian matrix, $\textbf{p}$ and $\textbf{q}$ are vectors represented for the end-effector pose and joint ...

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$$\frac{\partial\dot\omega}{\partial\omega} = [J]^{-1}\frac{\partial([\omega]_{\times}[J]\omega)}{\partial\omega}$$ $$= [J]^{-1} \frac{\partial(\omega\times[J]\omega)}{\partial\omega}$$ $$= [J]^{-1} \left (\frac{\partial\omega}{\partial\omega}\times[J]\omega + \omega \times [J]\frac{\partial\omega}{\partial \omega}\right)$$  = [J]^{-1} \left (1\times[J]\...

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Your computations of the transformation matrices are incorrect. DH transformation matrices are computed as a multiplication of four matrices: rotate about z by $\theta$, translate along z by $d$, translate along x by $a$, and rotate about x by $\alpha$. More simply: you are missing the $\theta$ terms in the rightmost columns of your transformation ...

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If you have the two Jacobian matrices, do you also have the two positional transformation matrices? If so, you could multiply these two matrices together, and take partial derivatives of the result to get the full Jacobian.

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Unfortunately is not as straightforward as multiplying them. The Jacobian of B is considering that the first body is fixed to the plane. You would need to add the velocity at that point, which is the end-point of the first Jacobian. Basically, you would have an intermediate point, which needs to have the precedent velocity and with some math manipulation, ...

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Are you trying to somehow use this to determine lengths of the linkages later or are you trying to find the singular pose of one specific manipulator? In case you are doing a study on how to calculate linkages lengths, you need a PC with more RAM if you want to progress. If you already have values for the lengths, you should not use these as symbols, just ...

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If you use the partial differentiation you can get to that expression as \begin{align} \frac{dJ}{dt} &= \frac{\partial J}{\partial q}\frac{\partial q}{\partial t} \\ \frac{dJ}{dt} &= \frac{\partial J}{\partial q}\frac{d q}{d t}\\ \frac{dJ}{dt} &= \frac{\partial (J \dot q)}{\partial q} \end{align} In the last line $\dot q$ is a constant that can ...

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Short answer: you can use it. Long answer: Depend on your case, but I have seen many papers where they use the pseudoinverse of the non-square Jacobian matrix. The rectangular Jacobian matrix opens the window to optimize in terms of other variables such as space constraints or force minimization. The pseudo inverse by definition (in a redundant manipulator) ...

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By imposing that the position of the end-effector $\mathbf{x} \in \mathbb{R}^3$ has to remain fixed, you're actually limiting your IK that, as a result, might struggle to achieve the task of aligning the vector $\mathbf{z} \in \mathbb{R}^3$ to point toward the target $\mathbf{p} \in \mathbb{R}^3$ when, for instance, one of the joints \$\mathbf{q} \in \mathbb{...

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Although this is quite late, I believe this question should get an answer. The solution for this problem is: If one has no other information but the angular velocity and needs to get the Euler angles, using the relation of quaternion derivative and angular velocity is the best option I found. Then, the quaternion derivative can be integrated numerically to ...

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