Abstract: Grasping a novel target object in constrained environments (e.g., walls, bins, and shelves) requires intensive reasoning about grasp pose reachability to avoid collisions with the surrounding structures. Typical 6-DoF robotic grasping systems rely on the prior knowledge about the environment and intensive planning computation, which is ungeneralizable and inefficient. In contrast, we propose a novel Collision-Aware Reachability Predictor (CARP) for 6-DoF grasping systems. The CARP learns to estimate the collision-free probabilities for grasp poses and significantly improves grasping in challenging environments. The deep neural networks in our approach are trained fully by self-supervision in simulation. The experiments in both simulation and the real world show that our approach achieves more than 75% grasping rate on novel objects in various surrounding structures. The ablation study demonstrates the effectiveness of the CARP, which improves the 6-DoF grasping rate by 95.7%.