Autonomous maze navigation is appealing yet challenging in soft robotics for exploring priori unknown unstructured environments, as it often requires human-like brain that integrates onboard power, sensors, and control for computational intelligence. Here, we report harnessing both geometric and materials intelligence in liquid crystal elastomer-based self-rolling robots for autonomous escaping from complex multichannel mazes without the need for human-like brain. The soft robot powered by environmental thermal energy has asymmetric geometry with hybrid twisted and helical shapes on two ends. Such geometric asymmetry enables built-in active and sustained self-turning capabilities, unlike its symmetric counterparts in either twisted or helical shapes that only demonstrate transient self-turning through untwisting. Combining self-snapping for motion reflection, it shows unique curved zigzag paths to avoid entrapment in its counterparts, which allows for successful self-escaping from various challenging mazes, including mazes on granular terrains, mazes with narrow gaps, and even mazes with in situ changing layouts.