Abstract: To address the difficulty of balancing real-time performance and safety in unknown cave corridors with time-varying terrain parameters, degraded perception reliability, and limited onboard computation, a lightweight adaptive model predictive control (LAMPC) method is proposed. A 2.5D traversability model coupling slope, friction, and resistance is established for a differential-drive robot, and a linearized error prediction model is constructed around the reference trajectory. Receding-horizon optimization is implemented by a preconditioned conjugate-gradient solver, while a forgetting-factor recursive least-squares estimator identifies environmental parameters online and updates the safety distance, velocity bounds, and weighting matrices. Simulation results show an average one-step computation time of 8.7 ms and a mean tracking error of 3.1 cm. Compared with conventional nonlinear model predictive control, the computation time is reduced by 67.2%; the system returns to steady state within 0.6 s after an abrupt friction change, and no collision occurs in narrow-passage, dynamic-obstacle, or communication-delay scenarios. The method therefore balances trajectory tracking, real-time optimization, and constraint safety under limited computational resources.