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If you think of classical Jacobian-based methods for IK (still representing the majority), then you ought to consider that they make use of forward-kinematics (FK) maps internally in order to compute the error in the operational space as well as the Jacobian itself, which is actually a differential FK law.

In particular, the IK method based on Jacobian pseudo-inverse generates iteratively joint velocities profiles $\dot{q}$ that drive the system toward the target. In formula:

$$ \begin{cases} e=x_d-f\left(q\right) \\ \dot{q}=J^{-1}\left(q\right) \cdot \left(\dot{x}_d+Ke\right) \end{cases}, $$

where $x=f\left(q\right)$ and $J=\partial f/\partial q$ are the staticstandard and differential forward-kinematics maps, respectively.

This reasoning and/or considerations apply also to other IK methods.

If you think of classical Jacobian-based methods for IK (still representing the majority), then you ought to consider that they make use of forward-kinematics (FK) maps internally in order to compute the error in the operational space as well as the Jacobian itself, which is actually a differential FK law.

In particular, the IK method based on Jacobian pseudo-inverse generates iteratively joint velocities profiles $\dot{q}$ that drive the system toward the target. In formula:

$$ \begin{cases} e=x_d-f\left(q\right) \\ \dot{q}=J^{-1}\left(q\right) \cdot \left(\dot{x}_d+Ke\right) \end{cases}, $$

where $x=f\left(q\right)$ and $J=\partial f/\partial q$ are the static and differential forward-kinematics maps, respectively.

This reasoning and/or considerations apply also to other IK methods.

If you think of classical Jacobian-based methods for IK (still representing the majority), then you ought to consider that they make use of forward-kinematics (FK) maps internally in order to compute the error in the operational space as well as the Jacobian itself, which is actually a differential FK law.

In particular, the IK method based on Jacobian pseudo-inverse generates iteratively joint velocities profiles $\dot{q}$ that drive the system toward the target. In formula:

$$ \begin{cases} e=x_d-f\left(q\right) \\ \dot{q}=J^{-1}\left(q\right) \cdot \left(\dot{x}_d+Ke\right) \end{cases}, $$

where $x=f\left(q\right)$ and $J=\partial f/\partial q$ are the standard and differential forward-kinematics maps, respectively.

This reasoning and/or considerations apply also to other IK methods.

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If you think of classical Jacobian-based methods for IK (still representing the majority), then you ought to consider that they make use of forward kinematics-kinematics (FK) maps internally in order to compute the error in the operational space as well as the Jacobian itself, which is actually a differential FK law.

In particular, the IK method based on Jacobian pseudo-inverse generates iteratively joint velocities profiles $\dot{q}$ that drive the system toward the target. In formula:

$ e=x_d-f\left(q\right) \\ \dot{q}=J^{-1}\left(q\right) \cdot \left(\dot{x}_d+Ke\right) $,$$ \begin{cases} e=x_d-f\left(q\right) \\ \dot{q}=J^{-1}\left(q\right) \cdot \left(\dot{x}_d+Ke\right) \end{cases}, $$

where $f$$x=f\left(q\right)$ and $J$$J=\partial f/\partial q$ are the forwardstatic and the differential kinematicforward-kinematics maps, respectively.

This reasoning and/or considerations apply also to other IK methods.

If you think of classical Jacobian-based methods for IK (still representing the majority), then you ought to consider that they make use of forward kinematics (FK) maps internally in order to compute the error in the operational space as well as the Jacobian itself, which is actually a differential FK law.

In particular, the IK method based on Jacobian pseudo-inverse generates iteratively joint velocities profiles that drive the system toward the target.

$ e=x_d-f\left(q\right) \\ \dot{q}=J^{-1}\left(q\right) \cdot \left(\dot{x}_d+Ke\right) $,

where $f$ and $J$ are the forward and the differential kinematic maps, respectively.

This reasoning and/or considerations apply also to other IK methods.

If you think of classical Jacobian-based methods for IK (still representing the majority), then you ought to consider that they make use of forward-kinematics (FK) maps internally in order to compute the error in the operational space as well as the Jacobian itself, which is actually a differential FK law.

In particular, the IK method based on Jacobian pseudo-inverse generates iteratively joint velocities profiles $\dot{q}$ that drive the system toward the target. In formula:

$$ \begin{cases} e=x_d-f\left(q\right) \\ \dot{q}=J^{-1}\left(q\right) \cdot \left(\dot{x}_d+Ke\right) \end{cases}, $$

where $x=f\left(q\right)$ and $J=\partial f/\partial q$ are the static and differential forward-kinematics maps, respectively.

This reasoning and/or considerations apply also to other IK methods.

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If you think of classical Jacobian-based methods for IK (still representing the majority), then you ought to consider that they make use of forward kinematics (FK) maps internally in order to compute the error in the operational space as well as the Jacobian itself, which is actually a differential FK law.

In particular, the IK method based on Jacobian pseudo-inverse generates iteratively joint velocities profiles that drive the system toward the target.

$ e=x_d-f\left(q\right) \\ \dot{q}=J^{-1}\left(q\right) \cdot \left(\dot{x}_d+Ke\right) $,

where $f$ and $J$ are the forward and the differential kinematic maps, respectively.

This reasoning and/or considerations apply also to other IK methods.