Axis-Constrained Gradient Descent for 3D Dubins Path Alignment

We present a gradient descent–based optimization framework for aligning 3D Dubins paths to a specified goal frame while enforcing axis alignment constraints on the end effector. Our approach employs a primary–secondary task formulation: the primary task ensures geometric alignment with the target pose (modulo a constrained axis), while the secondary task minimizes overall path length. Dynamic weighting between position and orientation errors accelerates convergence. Results demonstrate that this method achieves accurate goal alignment while optimizing path efficiency.