diff --git a/navsim/planning/simulation/planner/pdm_planner/simulation/batch_lqr_utils.py b/navsim/planning/simulation/planner/pdm_planner/simulation/batch_lqr_utils.py
index 408ceef..adf6cd4 100644
--- a/navsim/planning/simulation/planner/pdm_planner/simulation/batch_lqr_utils.py
+++ b/navsim/planning/simulation/planner/pdm_planner/simulation/batch_lqr_utils.py
@@ -1,3 +1,4 @@
+import torch
 from typing import Tuple
 
 import numpy as np
@@ -119,9 +120,13 @@ def _fit_initial_velocity_and_acceleration_profile(
 
     A_T, R_T = np.transpose(A, (0, 2, 1)), np.transpose(R, (0, 2, 1))
 
+    # Convert A and R to PyTorch tensors
+    A_tensor = torch.tensor(batch_matmul(A_T, A), dtype=torch.float32)
+    R_tensor = torch.tensor(batch_matmul(R_T, R), dtype=torch.float32)
+
     # Compute regularized least squares solution.
     intermediate_solution = batch_matmul(
-        np.linalg.pinv(batch_matmul(A_T, A) + jerk_penalty * batch_matmul(R_T, R)), A_T
+        torch.linalg.inv(A_tensor + jerk_penalty * R_tensor), A_T
     )
     x = np.einsum("bij, bj -> bi", intermediate_solution, y)
 
@@ -174,9 +179,14 @@ def _fit_initial_curvature_and_curvature_rate_profile(
     Q[0, 0] = initial_curvature_penalty
 
     # Compute regularized least squares solution.
-    A_T = A.transpose(0, 2, 1)
+    A_T = A.transpose(0, 2, 1)  # 确保 A_T 在这里定义
+
+    # Convert A and Q to PyTorch tensors
+    A_tensor = torch.tensor(batch_matmul(A_T, A), dtype=torch.float32)
+    Q_tensor = torch.tensor(Q, dtype=torch.float32)  # Convert Q to tensor
 
-    intermediate = batch_matmul(np.linalg.pinv(batch_matmul(A_T, A) + Q), A_T)
+    # Compute regularized least squares solution.
+    intermediate = batch_matmul(torch.linalg.inv(A_tensor + Q_tensor), A_T)  # Use Q_tensor
     x = np.einsum("bij,bj->bi", intermediate, y)
 
     # Extract profile from solution.