Jacobian of a 2-Link Arm
~14 mincode completion
Implement jacobian_2link(l1, l2, q1, q2) returning the 2x2 array.
Examples
Stretched along x: the x row is zero (singular)
- Input
- jacobian_2link(1, 2, 0, 0)
- Output
- [[0, 0], [3, 2]]
Straight up: the y row is zero instead
- Input
- jacobian_2link(1, 1, 1.5707963267948966, 0)
- Output
- [[-2, -1], [0, 0]]
The L shape: full rank
- Input
- jacobian_2link(1, 1, 0, 1.5707963267948966)
- Output
- [[-1, -1], [1, 0]]
Hints
Hint 1
Convert the input with before doing elementwise work.
Hint 2
Do not forget to the l2 sin q12 term in the first column. That step is easy to skip.
Requirements
Return (2, 2) array mapping [dq1, dq2] to [dx, dy]
Constraints
Allowed library: NumPy only
Time limit: 200 ms, Memory: 64 MB
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Where this shows up
~14 min
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Python
import numpy as np
def jacobian_2link(l1, l2, q1, q2):
"""
Geometric Jacobian of the planar two-link arm.
Args:
l1, l2: link lengths
q1, q2: joint angles in radians
Returns:
(2, 2) array mapping [dq1, dq2] to [dx, dy]
"""
# YOUR CODE HERE
pass