  Navigation through tortuous and deformable vessels using catheters with
limited steering capability underscores the need for reliable path planning.
State-of-the-art path planners do not fully account for the deformable nature
of the environment. This work proposes a robust path planner via a learning
from demonstrations method, named Curriculum Generative Adversarial Imitation
Learning (C-GAIL). This path planning framework takes into account the
interaction between steerable catheters and vessel walls and the deformable
property of vessels. In-silico comparative experiments show that the proposed
network achieves smaller targeting errors, and a higher success rate, compared
to a state-of-the-art approach based on GAIL. The in-vitro validation
experiments demonstrate that the path generated by the proposed C-GAIL path
planner aligns better with the actual steering capability of the pneumatic
artificial muscle-driven catheter utilized in this study. Therefore, the
proposed approach can provide enhanced support to the user in navigating the
catheter towards the target with greater precision, in contrast to the
conventional centerline-following technique. The targeting and tracking errors
are 1.26$\pm$0.55mm and 5.18$\pm$3.48mm, respectively. The proposed path
planning framework exhibits superior performance in managing uncertainty
associated with vessel deformation, thereby resulting in lower tracking errors.
