Manipulability
~10 mincode completion
Implement manipulability(J) returning the scalar w.
Examples
The stretched arm is singular: w = 0
- Input
- manipulability([[0, 0], [3, 2]])
- Output
- 0
The L-shaped arm: w = 1
- Input
- manipulability([[-1, -1], [1, 0]])
- Output
- 1
A diagonal Jacobian: w is the product of the gains
- Input
- manipulability([[2, 0], [0, 3]])
- Output
- 6
Hints
Hint 1
Use a matrix product rather than nested loops, and check which operand transposes.
Hint 2
Watch for this: used det J which fails for non square jacobians.
Requirements
J: (m, n) Jacobian, m <= nReturn scalar w >= 0
Constraints
Allowed library: NumPy only
Time limit: 200 ms, Memory: 64 MB
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Where this shows up
~10 min
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Python
import numpy as np
def manipulability(J):
"""
Yoshikawa manipulability sqrt(det(J J^T)).
Args:
J: (m, n) Jacobian, m <= n
Returns:
scalar w >= 0
"""
# YOUR CODE HERE
pass