One solution overcoming the problem of inverting differential kinematics in the neighborhood of a singularity is...

 

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One solution overcoming the problem of inverting differential kinematics in the neighborhood of a singularity is provided by the so-called damped least-squares (DLS) inverse J* = J¹ (JJ¹ + k²1)-¹ where k is a damping factor that renders the inversion better conditioned from a numerical viewpoint. The problem is that to invert differential kinematics ve = Ja by tolerating a finite error e, i.e., Ve- Ja = e. Find the solution by minimizing the cost functional 1 1 9°(q‚ €) = ½ k²q²q + ½ €² € One solution overcoming the problem of inverting differential kinematics in the neighborhood of a singularity is provided by the so-called damped least-squares (DLS) inverse J* = J¹ (JJ¹ + k²1)-¹ where k is a damping factor that renders the inversion better conditioned from a numerical viewpoint. The problem is that to invert differential kinematics ve = Ja by tolerating a finite error e, i.e., Ve- Ja = e. Find the solution by minimizing the cost functional 1 1 9°(q‚ €) = ½ k²q²q + ½ €² €

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o find the solution by minimizing the cost functional gq use the gradient descent algorith... View the full answer