The first approaches rely on geographical distance to choose the next hop.

GPSR (Greedy Perimeter Stateless Routing) [4] combines a Greedy mode to transmit to the neighbor closest to the destination and a Perimeter mode to bypass blocked areas. It is simple and effective but fails in the presence of physical obstacles or coverage gaps and ignores energy consumption.

GOAFR (Greedy Other Adaptive Face Routing) [5] improves on GPSR by limiting detours when bypassing but remains sensitive to mobile obstacles and does not take energy constraints into account.

These protocols favor the shortest distance without considering link reliability or the residual energy of the nodes.

Topological protocols integrate communication graph structure to improve routing stability.

CLDP (Cross-Link Detection Protocol) [6] creates a planar topology by removing redundant links to avoid loops but generates an overload of control messages.

GLIDER (Geographic Layered Routing) [7] combines position and connectivity information for better fault tolerance, at the cost of increased complexity and significant energy consumption.

Ant-based routing approaches such as AntHocNet [8] use bio-inspired heuristics to improve path discovery and adaptivity in dynamic networks.

These approaches enhance structural robustness but are costly to maintain in dense or energy-limited networks.

Recent protocols incorporate adaptive mechanisms based on energy and learning.

GEAR (Geographic and Energy Aware Routing) [9] balances distance and energy consumption, extending the network's lifespan, but remains ineffective in the face of obstacles.

GARL (Geographic Adaptive Routing with Learning) [10] adapts its decisions based on past experiences through reinforcement learning, but its convergence is slow and resource intensive.

HGSR [11] and EHGSR [12] bypass coverage holes by selecting alternative geometric paths, with good performance in static networks but reduced efficiency in dynamic environments.

In addition, MGR [13] extends geographic routing concepts to underwater WSNs, highlighting the versatility of such methods.

These protocols represent progress, but none of them simultaneously address physical obstacles, latency, and energy consumption.

The rise of artificial intelligence has given rise to more autonomous approaches.DeepRL-Routing [14] uses deep reinforcement learning to optimize route selection based on network conditions (energy, link quality, distance).

E2DRL-WSN [15] applies distributed learning to improve reliability and energy efficiency.

These solutions offer very good performance, but their computational complexity and memory requirements make them difficult to deploy on sensors with limited resources.

In summary:

Faced with these limitations, the OAGF (Obstacle-Aware Greedy Forwarding) protocol aims to combine simplicity, energy efficiency, and intelligent obstacle avoidance for more robust and balanced geographic routing.

Let us consider a graph $G=\left(V,E\right)$ representing the network, with $V$ the set of nodes and $E$ the links.

Each link $\left(i,j\right)\in E$ has a cost $c\left(i,j\right)$ depending on distance, link quality, and energy consumption.

Obstacles are modeled by a set $O=\left\{o_1,o_2,\cdots ,o_n\right\}$ that prevents direct communication between two nodes if the segment $\left(i,j\right)\cap o_k\ne \varnothing$.

The objective is to determine a path $P^{*}$ between the source $s$ and the destination $d$ that:

$\underset{P}{\text{min}}f\left(P\right)=\alpha {\displaystyle \sum c\left(i,j\right)}+\beta {\displaystyle \sum E\left(i,j\right)}-\gamma {\displaystyle \prod R\left(i,j\right)}$ (1)

where:

OAGF combines Greedy Forwarding with multi-criteria decision-making (distance, energy, obstacles).

When a node cannot progress, a local recovery procedure is activated to bypass the obstacle.

1) Selection of candidate neighbor: among the neighbors closest to the destination, the one that minimizes

$Score\left(w\right)=\alpha \cdot d\left(w,d\right)+\frac{\beta }{E_{res}\left(w\right)}+\delta \cdot ObstacleCost\left(w\right)$ (2)

where $ObstacleCost\left(w\right)=0$ if there are no obstacles, otherwise penalty = 1.

2) Update the route and send the packet.

3) Recovery: if no valid neighbor is found, a detour mechanism is initiated (simplified Face Routing). In practice, this recovery phase behaves as a lightweight Perimeter mode similar to GPSR, where the right-hand rule is applied to follow the obstacle boundary until a node closer to the destination than the entry point is reached.

1.if u == d:

2. DELIVER(packet); return

3.CAND ← {v ∈ N(u) | d(v,d) < d(u,d) ∧ NON_BLOCKED(u,v)}

4.if CAND ≠ ∅:

5. for each v ∈ CAND:

6. s(v) ← α·DIST(v,d)_norm + β·ENERGY(u,v)_norm +

γ·OBSTACLE_COST(u,v)_norm

7. w ← argmin_v s(v)

8. FORWARD(packet, w); return

9. else:

10.// LOCAL RECOVERY (Simplified Face / Perimeter mode)

11. if package.recovery_mode == FALSE:

12. package.recovery_mode ← TRUE

13.package.anchor ← u // entry point of the recovery phase

14. w ← NEXT_NEIGHBOR_PERIMETER(u, d) // right-hand rule

15. if w ≠ ⊥:

16. FORWARD(packet, w); return

17.else:

18. w ← NEXT_PERIMETER_NEIGHBOR(u, d)

19. if w ≠ ⊥ ∧ d(w,d) < d(packet.anchor,d): // obstacle has been bypassed

20. packet.recovery_mode ← FALSE

21. if w = ⊥:

22. // Option: limited backtracking or NACK

23. DROP(packet) // or SEND_NACK(source)

Lines 1 to 2 verify the destination. If the current node is the final node, the packet is delivered immediately and routing stops.

Lines 3 to 8 describe the Greedy mode routing phase. The node selects from among its neighbors those that are closest to the destination and whose links are not blocked. Each neighbor is evaluated according to a multi-criteria score combining distance to the destination, energy consumption, and proximity to obstacles. The neighbor with the lowest score is chosen for transmission.

Lines 9 to 10 signal the switch to the recovery phase when no valid neighbors are available. This step aims to bypass obstacles that prevent direct progress.

Lines 11 to 16 initiate recovery mode (Face/Perimeter). The packet enters recovery mode, an anchor point is defined, and the protocol applies the right-hand rule to follow the contour of the obstacle until it finds a clear path.

Lines 17 to 20 manage the continuation of the detour. If a neighbor allows progress while moving closer to the destination relative to the anchor point, this means that the obstacle has been passed: recovery mode is then disabled and routing returns to normal Greedy mode.

Finally, lines 21 to 23 define failure management. If no neighbor is available, the protocol can attempt a limited backtracking or send a NACK to the source. As a last resort, the packet is dropped (DROP).

The simulation parameters used in this study are summarized in Table 1 .

For a packet $p$ routed along the path $P=\left\{1,\cdots ,H_p\right\}$ (with $H_p$ hops), the end-to-end latency is the sum of the delays per hop:

$L_p={\displaystyle {\sum }_{h=1}^{H_p}\left(t_{\text{tx},h}+t_{\text{prop},h}+t_{\text{proc},h}+t_{\text{queue},h}\right)}.$ (3)

$t_{\text{tx}}$: transmission delay (size/bitrate, including any MAC backoffs)

$t_{\text{prop}}$: propagation ( $\approx d/c$, often negligible in WSN)

$t_{\text{proc}}$: processing (protocol stack)

$t_{\text{queue}}$: queueing (MAC, radio interface)

The average latency over a set $\mathcal{D}$ of delivered packets (size $\left|\mathcal{D}\right|$):

$\bar{L}=\frac{1}{\left|\mathcal{D}\right|}{\displaystyle {\sum }_{p\in \mathcal{D}}{L}_p}\left(\text{en ms}\right)$ (4)

Assuming independent and identically distributed hops with average delay ${\mu }_{\ell }$, then

$\mathbb{E}\left[L_p\right]\approx {\mu }_{\ell }\mathbb{E}\left[H_p\right]$, which directly links the average latency to the average number of hops.

For a packet of $k$ bits transmitted over a link of distance $d$:

$E_{\text{tx}}\left(k,d\right)=E_{\text{elec}}k+{ϵ}_{\text{amp}}k{d}^n,E_{\text{rx}}\left(k\right)=E_{\text{elec}}k,$

$E_{\text{elec}}$: electronic cost/bit (e.g., 50 nJ/bit)

${ϵ}_{\text{amp}}$: amplification cost (e.g., 100 pJ/bit/m²)

$n\in \left[2,4\right]$: path loss exponent (2 free space, >2 in shadowing/fading)

Add listening/standby and retransmission components:

$E_{\text{idle}}=P_{\text{idle}}\cdot T_{\text{idle}},E_{\text{cca}}=P_{\text{rx}}\cdot T_{\text{cca}},E_{\text{retx}}=r\cdot E_{\text{tx}}\left(k,d\right)$

where $r$ is the number of retransmissions.

Total network energy over the simulation period $T$:

$E_{\text{tot}}={\displaystyle {\sum }_{u\in V}\left({\displaystyle {\sum }_{\text{tx de}u}{E}_{\text{tx}}}+{\displaystyle {\sum }_{\text{rx de}u}{E}_{\text{rx}}}+E_{\text{idle}}\left(u\right)+E_{\text{cca}}\left(u\right)\right)}$ (5)

$\text{PDR}=\frac{N_{\text{livres}}}{N_{\text{emis}}}\times 100\text{\%}$ (6)

PDR: Packet Delivery Ratio

$N_{\text{livres}}$: Number of packets delivered

$N_{\text{emis}}$: Number of packets sent

The curve “ Figure 1 ” shows that average latency increases with the number of obstacles for all three protocols (GEAR, GARL, and OAGF).

The increase in latency with the number of obstacles is an expected phenomenon, as obstacles cause detours and additional retransmissions.

However, OAGF shows a much slower increase in latency, with an average reduction of 31% compared to GEAR and 24% compared to GARL.

This improvement can be explained by:

Thus, OAGF ensures faster end-to-end data transmission, even in environments cluttered with obstacles a major advantage for time-sensitive IoT applications (real-time monitoring, industrial automation, etc.).

As shown in “ Figure 2 ”, the total energy consumption increases with obstacle density for all protocols.

The presence of obstacles results in longer paths, more intermediate hops, and more retransmissions, thereby increasing energy expenditure. Nevertheless, OAGF maintains significantly lower consumption (approximately 38% average reduction).

This efficiency stems from:

As a result, OAGF significantly extends the lifetime of the network, making it particularly suitable for resource-constrained IoT networks, such as environmental monitoring systems or smart agriculture.

All protocols “ Figure 3 ” show a gradual decline in delivery rate as obstacles increase, but OAGF maintains the best results.

Obstacles cause packet loss due to link breaks or retransmission failures.

However, OAGF maintains a high and stable PDR thanks to:

Thus, OAGF demonstrates high robustness and increased reliability, ensuring continuity of data flow even in difficult communication environments.

The three curves show that OAGF effectively balances the three key indicators: latency, energy, and reliability.

It outperforms GEAR and GARL across all metrics thanks to its multi-criteria decision model that integrates:

This combination gives OAGF better network stability, efficiency, and longevity, confirming its relevance for real-world IoT and WSN applications deployed in complex or physically constrained environments.