GP-Driven Adaptive Tube MPC for Communication-Preserving Navigation of Mobile Relay Robots in Indoor Disaster Environments

Maintaining reliable communication while ensuring collision-free motion is a central challenge for mobile relay robots operating in indoor disaster environments, where abrupt non-line-of-sight (NLOS) degradation and narrow structural bottlenecks can severely disrupt multi-hop connectivity. To address this problem, this paper proposes a Gaussian Process-Driven Adaptive Tube Model Predictive Control (GP-ATMPC) framework for communication-preserving relay navigation. Gaussian process regression (GPR) is used to construct a probabilistic spatial radio map from sparse received signal strength indicator (RSSI) measurements, providing both the predicted channel mean and its uncertainty over unvisited regions. Motion uncertainty is represented by an adaptive ellipsoidal error tube whose radius varies with translational motion, angular motion, and localization uncertainty. Based on this tube model, both obstacle and communication constraints are tightened over the full closed-loop state tube via a tube-tightened lower confidence bound (LCB) that jointly accounts for radio-prediction and motion-tracking uncertainty. Across two indoor disaster environments and 50 Monte Carlo runs each, the proposed method attains the highest connectivity satisfaction rate among controllers that preserve a safe motion margin, with significantly fewer end-to-end connectivity violations than nominal and heuristic adaptive-margin MPC by a paired Wilcoxon test, while maintaining millisecond-level online solve times. A reactive connectivity-first baseline reaches slightly higher raw connectivity but at three to four times the near-collision rate and without feasibility or stability guarantees. The radio-prediction layer is further validated in a higher-fidelity Gazebo environment and on real indoor RSSI measurements, where it reconstructs the measured channel with a mean absolute error of about 2.1 dB. These results indicate that coupling spatial radio prediction with adaptive tube-based robust control provides an effective framework for resilient communication-aware relay navigation in degraded indoor environments.