Pemodelan Matematis dan Simulasi MATLAB Navigasi Dua Arah Robot Delivery Menggunakan Mirror Petri Net

Bidirectional navigation is required in robot delivery systems because the robot must reach a destination and return to its initial position after completing a task. Previous Petri Net studies have represented robot routes and location changes, but complete stepwise verification of outbound and return trips for multiple destinations remains limited. This study aims to develop a mathematical model and MATLAB simulation for bidirectional indoor robot delivery navigation using Petri Net and Mirror Petri Net. The model consists of 13 places, 12 transitions, one initial position, four branch points, eight destination rooms, and one token representing a robot. Eight outbound and eight return scenarios were simulated by checking enabled transitions, firing sequences, and marking changes. All eight destinations were reachable from the initial marking, and the initial position was reachable again from every destination. The outbound and return processes each required 28 firings, giving 56 firings for all round-trip tests. The model remained 1-bounded, conserved one token, made all 12 transitions accessible, and produced no unintended deadlock. The novelty lies in integrating stepwise bidirectional reachability, legal firing-sequence checking, and proper-termination verification in one MATLAB-based Mirror Petri Net framework.