# Lecture 15

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* is this system is stablity of PD control


* Here we are equating torque with the gains
* as these forces are against the velocity we can say that system will be stable
* so because of Kv term the system turns out to be asymmatotically stable
* here all the decoupling forces are shown in kinetic energy term

* But for performance i.e, trajectory following what to do ? but we need to have high gains.
* now if we can't increase the gains high so what to do ? :[27:59](https://youtu.be/A6QEQFTBKnA?t=1679)
* Rather than making a wrong estimate of V_hat you can just use zero estimate of v_hat because otherwise it might be dangerous.
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* Here we controled our robot in terms of its joint motion but In task oriented control intsetead of inverse kinematics.
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* here we are basically moving only the end-effector with gradient force.
* we can also add repulsive forces obstacles.
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* as this is not a point mass applying force will give rise to acceleration in different direction and other decoupling forces.
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