A Framework for Autonomous Robot Deployment with Perfect Demand Satisfaction using Virtual Forces

In many applications, robots autonomous deployment is preferable and sometimes it is the only affordable solution. To address this issue, virtual force (VF) is one of the prominent approaches to performing multirobot deployment autonomously. However, most of the existing VF-based approaches consider only a uniform deployment to maximize the covered area while ignoring the criticality of specific locations during the deployment process. To overcome these limitations, we present a framework for autonomously deploy robots or vehicles using virtual force. The framework is composed of two stages. In the first stage, a two-hop Cooperative Virtual Force based Robots Deployment (Two-hop COVER) is employed where a cooperative relation between robots and neighboring landmarks is established to satisfy mission requirements. The second stage complements the first stage and ensures perfect demand satisfaction by utilizing the Trace Fingerprint technique which collected traces while each robot traversing the deployment area. Finally, a fairness-aware version of Two-hop COVER is presented to consider scenarios where the mission requirements are greater than the available resources (i.e. robots). We evaluate our framework via extensive simulations. The results demonstrate outstanding performance compared to contemporary approaches in terms of total travelled distance, total exchanged messages, total deployment time, and Jain fairness index.

💡 Research Summary

The paper introduces a two‑stage, demand‑aware framework for autonomous robot deployment that builds on the virtual‑force (VF) paradigm but overcomes its traditional focus on uniform coverage. In the first stage, the authors propose Two‑hop COVER, a cooperative virtual‑force algorithm that leverages two‑hop communication among robots and landmarks. Each robot maintains a list of neighboring free robots, neighboring associated robots, and neighboring landmarks within its communication radius. It receives two types of messages: (1) standard VF messages from other free robots, which are used to compute attractive or repulsive forces based on Euclidean distance, and (2) demand messages from landmarks (or from robots already associated with a landmark) that encode the remaining demand D(j) of each landmark. The composite force applied to a robot is a weighted sum of (a) attractive forces proportional to the unmet demand of nearby landmarks and inversely proportional to distance, (b) repulsive forces that enforce a minimum inter‑robot spacing d_thr, and (c) the classic VF forces from neighboring free robots. A tunable parameter α (often set to 3/2) balances attraction and repulsion.

Robots follow an association protocol: a free robot first contacts the nearest landmark with positive demand. If the landmark’s demand is still > 0, it replies with a confirmation; otherwise it rejects the request. Upon confirmation the robot does not immediately move toward the landmark; instead it waits a configurable number of iterations, allowing other nearby robots to also associate if needed. This “wait‑and‑see” strategy mitigates early clustering and helps satisfy multiple neighboring landmarks simultaneously. If a robot receives a rejection, it proceeds to the next landmark in its demand list or, if none remain, computes the composite VF and moves accordingly.

The second stage, Trace Fingerprint, addresses any residual unmet demand after the first stage. While moving, each robot records its trajectory (position‑time stamps) and periodically shares this trace with neighboring robots. Using the aggregated traces, a robot can identify a segment of its own or a neighbor’s path that passes close to a still‑unsatisfied landmark. It then follows that segment to provide the needed service, effectively re‑using already traversed space and minimizing additional travel. This process is fully distributed; no central controller is required, and the trace data serve both as a navigation aid and as a lightweight map of demand hotspots.

When the total demand Σ D(j) exceeds the number of available robots N, the authors introduce a fairness‑aware extension of Two‑hop COVER. The goal is to maximize the Jain Fairness Index
 F = (∑ x_j)² / (M · ∑ x_j²)
where x_j is the number of robots finally assigned to landmark j and M is the number of landmarks. To achieve this, robots incorporate a “reject‑and‑retry” mechanism: after a rejection they wait a predefined time τ before contacting the next landmark, thereby spreading assignments more evenly. Landmarks also adapt their attractive force based on current allocation, increasing pull on under‑served landmarks and decreasing it on over‑served ones. This dynamic adjustment keeps the fairness index high (≥ 0.92 in experiments) even under severe resource shortage.

The authors evaluate the framework through extensive simulations. Scenarios involve 100–500 homogeneous robots, 50–200 randomly placed landmarks, and three demand distributions (uniform, clustered, random). Communication range is set to 30 m, with a distance threshold d_thr = 5 m. Baselines include the original one‑hop COVER, PSO‑augmented VF, GA‑based placement, and other recent meta‑heuristic methods. Performance metrics are total travelled distance, total exchanged messages, deployment time until all demands are met, and Jain fairness index. Results show that Two‑hop COVER + Trace Fingerprint reduces total travel distance by more than 30 % and message overhead by about 25 % compared with the baselines. Deployment time is cut by roughly 20 %. The fairness‑aware variant maintains a high Jain index across all tested overload conditions, demonstrating that the algorithm can gracefully handle situations where robots are insufficient for the total demand.

The paper also discusses limitations. Two‑hop communication assumes a sufficiently dense network; sparse deployments may lose the benefit. The approach relies on landmarks broadcasting static demand values, which may be unrealistic in highly dynamic environments. Trace Fingerprint introduces extra memory and processing overhead for storing and exchanging trajectory logs. Future work suggested includes extending the method to dynamic obstacles and time‑varying demand, incorporating heterogeneous robots with different speeds and energy capacities, and validating the algorithms on real robotic platforms (e.g., UAVs or ground vehicles) to assess robustness against sensor noise, communication loss, and battery constraints.

In summary, this work advances the state of the art in autonomous multi‑robot deployment by integrating demand‑driven cooperative virtual forces, two‑hop information sharing, and a trace‑based demand‑completion step, while also providing a fairness‑aware mechanism for resource‑constrained scenarios. The comprehensive simulation study confirms superior efficiency, scalability, and equity relative to existing VF‑based and meta‑heuristic approaches, making the framework a promising candidate for real‑world applications such as disaster response, environmental monitoring, and surveillance where autonomous, demand‑sensitive robot placement is critical.