An Adaptive QAPF Framework with a Discrete CBF-Inspired Safety Filter and Adaptive Reward Shaping for Safe Mobile Robot Navigation

Mobile robot navigation remains challenging when fast convergence, collision avoidance and deployability must be satisfied simultaneously. The original Q-learning with Artificial Potential Field (QAPF) paradigm is extended in this paper with three coordinated mechanisms that together yield a reported-horizon convergence reduction of approximately four orders of magnitude (from ∼3×106 episodes to ∼200 to 230 episodes under the present protocol) and an internal-ablation collision-rate reduction of approximately one order of magnitude (6.2% to 0.3%), and that open a new capability frontier covering dynamic obstacles, multi-robot coordination, energy-aware velocity modulation and embedded-deployable inference timing. The first mechanism is a potential-based reward-shaping schedule whose unclipped fixed-weight form follows the policy-invariant shaping theorem, while the implemented clipped and time-varying form is used as an empirically stable approximation. Under the present experimental protocol, the reported convergence horizon is reduced from the ∼3×106 episodes reported for the original QAPF formulation to approximately 200 to 230 episodes; this comparison is protocol-dependent and is not claimed as a controlled one-to-one runtime speedup. The second mechanism is a discrete Control Barrier Function (CBF)-inspired action filter (thediscrete filter described in this paper is inspired by the continuous-time CBF literature, but does not carry a forward-invariance proof; it is used as an empirical safety mechanism rather than as a formal Control Barrier Function in the formal continuous-time sense) with per episode visit memory by which the held-out collision rate is reduced from 6.2% for QAPF alone to 0.3% while 93.8% task completion is maintained, where this collision-rate comparison is internal to the QAPF ablation because the prior QAPF reference does not report a comparable held-out collision metric. The third mechanism is a set of extensions to dynamic obstacles, two-robot cooperative navigation under a centralized scheme (with an explicit O(N2) scaling-cost analysis and three decentralization strategies for fleets beyond the small-N regime), curriculum learning and energy-aware velocity modulation. Disturbance robustness tests, empirical timeout/stagnation detection for unreachable-goal cases, i7 reference inference timing with projected embedded-device latencies, multi-axis generalization over obstacle density and grid size, scalability analysis for centralized multi-robot coordination and a scope comparison against A* and RRT* are added by the revised evaluation. Across 30 independent seeds on held-out static maps, 94.5±2.1% success is achieved by adaptive QAPF while 93.8±2.3% success with 0.3±0.4% collisions is achieved by QAPF+CBF. Under a separate finite robustness suite, 85.0±4.1% success is retained by QAPF+CBF in the combined disturbance regime. The timing study indicates that the 20 Hz real-time threshold is comfortably exceeded by all methods on the measured i7 reference platform and by all projected embedded-device equivalents. The results show that a lightweight and safety-oriented navigation policy for grid-based mobile-robot settings can be provided by APF-guided tabular reinforcement learning when it is paired with a discrete safety filter and a clarified energy and robustness analysis.