changing pseudo inverse fallback method

Author: michaellin6

source/isaaclab/docs/CHANGELOG.rst

@@ -8,8 +8,7 @@ Changed
 ^^^^^^^
 
 * Changed Pink IK controller qpsolver from osqp to daqp.
-* Changed Null Space matrix computation in Pink IK's Null Space Posture Task to a faster matrix pseudo inverse
-computation.
+* Changed Null Space matrix computation in Pink IK's Null Space Posture Task to a faster matrix pseudo inverse computation.
 
 
 0.47.6 (2025-11-01)

source/isaaclab/isaaclab/controllers/pink_ik/null_space_posture_task.py

@@ -257,8 +257,9 @@ def compute_jacobian(self, configuration: Configuration) -> np.ndarray:
         L, info = lapack.dpotrf(JJT, lower=1, clean=False, overwrite_a=True)
 
         if info != 0:
-            # Fallback if not positive definite
-            return np.eye(n)
+            # Fallback if not positive definite: use numpy's pseudoinverse
+            J_pinv = np.linalg.pinv(J_combined)
+            return np.eye(n) - J_pinv @ J_combined
 
         # Solve (J @ J^T + λ²I) @ X = J using LAPACK's triangular solver (dpotrs)
         # This directly solves the system without computing the full inverse