The deployment of mobile robots within healthcare environments, particularly during major public health emergencies, presents a significant opportunity to enhance operational efficiency and safety. Traditional logistics tasks, such as the transportation of medical supplies and equipment, often involve high labor intensity and pose risks of cross-infection among personnel. Mobile medical robots offer a promising solution to mitigate these challenges by automating material handling. However, the effective operation of these robots hinges on the availability of intelligent, reliable, and efficient navigation strategies. Crucially, in extended operations within large-scale facilities like temporary field hospitals, the energy autonomy of these robotic platforms becomes a paramount concern. This necessitates path planning that is not merely collision-free and short but also explicitly designed to minimize energy consumption, thereby extending operational range and reducing the frequency of recharging or battery swaps. Furthermore, paths must ensure a safe distance from obstacles and personnel while being sufficiently smooth for stable robot tracking. This work proposes a comprehensive path planning methodology that integrates energy consumption metrics with safety factors to generate efficient, safe, and smooth trajectories for mobile medical robots in structured hospital environments.
A foundational step in robotic navigation is environment representation. For known, static environments such as field hospitals, grid-based maps are widely adopted due to their simplicity, ease of construction, and computational efficiency. The workspace is discretized into uniformly sized cells, each representing either free space or an occupied region (e.g., walls, beds, equipment). This binary representation forms the basis for the planning algorithms. The transformation between a grid’s index \(i\) and its Cartesian coordinates \((x_i, y_i)\) is given by:
$$
x_i = \kappa \cdot \left[ \text{mod}(i, n_x) – 0.5 \right], \quad y_i = \kappa \cdot \left[ n_y + 0.5 – \text{ceil}(i / n_y) \right]
$$
where \(\kappa\) is the grid side length, and \(n_x\), \(n_y\) are the number of grid cells in the x and y directions, respectively. This model provides a clear and manageable representation of the complex hospital layout for the mobile medical robot’s navigation system.
The core innovation of this work lies in formulating the path planning problem with an explicit energy criterion. The total energy consumption \(E_{\text{robot}}\) of a mobile medical robot during a mission can be decomposed into several components: kinetic energy \(E_{\text{kinetic}}\), energy expended to overcome traction resistance \(E_{\text{res}}\), and the constant power draw of sensors and electronics \(E_e\). For typical transport missions at relatively constant speeds, the energy to overcome rolling resistance often constitutes a dominant, predictable portion. This component can be modeled as:
$$
E_{\text{res}} = c \mu m’ g \int_{t} v(t) \, dt = c \mu m’ g \cdot s
$$
where \(m’ = m_{\text{robot}} + m_{\text{goods}}\) is the total mass (robot plus payload), \(c\) is a robot attribute constant (e.g., \(c=2\) for differential drive, \(c=4\) for four-wheeled robots), \(\mu\) is the ground friction coefficient, \(g\) is gravity, \(v(t)\) is velocity, and \(s\) is the total path length. This reveals that for a given robot and payload, the resistance energy is directly proportional to the travel distance \(s\) and the friction \(\mu\) of the traversed terrain.
To integrate this energy model into the planning process, we introduce an energy-based adjacency matrix \(A_E\). In graph search terms, the traditional adjacency matrix \(A_D\) holds the geometric distance between nodes. In contrast, the energy adjacency matrix assigns a weight to the edge between two nodes \(i\) and \(j\) that represents the estimated energy cost to traverse it:
$$
A_E(i, j) = \frac{1}{2} \mu_{i,j} m’ g \cdot s_{i,j}
$$
Here, \(\mu_{i,j}\) is the effective friction coefficient for the segment connecting nodes \(i\) and \(j\). This formulation directly embeds the primary energy cost factors—distance, friction, and mass—into the graph’s edge weights, providing a substrate for energy-optimal search.
Standard pathfinding algorithms like A* traditionally use a limited set of search directions (e.g., 4 or 8 directions), which can lead to suboptimal paths with unnecessary zig-zags and redundant turns. Each turn often requires deceleration and acceleration, incurring additional kinetic energy loss. To address this, we propose an enhanced search strategy utilizing 16 primary search directions. This allows the planner to “cut corners” and consider more direct diagonal movements, naturally leading to shorter and smoother preliminary paths with fewer turns. The energy weight for these new directional edges is calculated by considering the friction across all intermediate cells \(m, n\) traversed in the move from \(i\) to \(j\):
$$
A’_E(i, j) = \frac{1}{4} \mu_{i \to j} m’ g \cdot s_{i,j}, \quad \text{where } \mu_{i \to j} = \mu_i + \mu_m + \mu_n + \mu_j
$$
This comprehensive strategy forms our energy-aware optimization layer for the mobile medical robot’s navigation graph.
Safety is non-negotiable in medical environments. A path optimized purely for energy might graze too close to obstacles or patient areas. To enforce a safe clearance, we incorporate a safety penalty factor \(\phi(k)\) into the cost function. This factor dynamically scales the cost of traversing a node \(k\) based on its proximity \(x_k\) to the nearest obstacle:
$$
\phi(k) =
\begin{cases}
1, & x_k > d_{\text{safe}} \\[6pt]
\dfrac{x_k – d_f}{d_{\text{safe}} – d_f}, & d_f < x_k \le d_{\text{safe}} \\[10pt]
0, & x_k \le d_f
\end{cases}
$$
Here, \(d_{\text{safe}}\) is the desired safety distance, and \(d_f\) is half the width of the mobile medical robot. When the robot is far from obstacles (\(\phi(k)=1\)), the cost is unchanged. As it approaches an obstacle, the cost increases (\(\phi(k)<1\)), heavily penalizing and effectively excluding nodes that are too close (\(\phi(k)=0\)). This ensures the final path maintains a safe buffer zone.
We now integrate these concepts into a modified A* algorithm, creating a generalized path planner for the mobile medical robot. The standard A* algorithm uses an evaluation function \(F(k) = G(k) + H(k)\), where \(G(k)\) is the actual cost from the start to node \(k\), and \(H(k)\) is a heuristic estimate from \(k\) to the goal. We redefine these components by introducing a unified adjacency matrix weight operator \(O(i,j)\) and the safety factor.
The weight operator \(O(i,j)\) provides flexibility, allowing the search to be based on different criteria:
$$
O(i, j) =
\begin{cases}
\dfrac{1}{c} s_{i,j}, & \text{(Distance-based search)} \\[8pt]
\dfrac{1}{2} \mu_{i,j} m’ g s_{i,j}, & \text{(Energy-search, standard directions)} \\[8pt]
\dfrac{1}{4} \mu_{i \to j} m’ g s_{i,j}, & \text{(Energy-search, enhanced directions)}
\end{cases}
$$
The actual cost \(G(k)\) is then computed recursively, incorporating the safety penalty:
$$
G(k) = G(k-1) + \frac{1}{\phi(k)} \cdot \left[ c \otimes O(k-1, k) \right]
$$
The operator \(\otimes\) handles the robot-specific application of the weight. The heuristic \(H(k)\) is defined similarly as \(H(k) = c \otimes O(k, k_{\text{goal}})\). Thus, the final evaluation function for our improved Energy-A* algorithm is:
$$
F(k) = G(k-1) + \frac{1}{\phi(k)} \cdot \left[ c \otimes O(k-1, k) \right] + c \otimes O(k, k_{\text{goal}})
$$
This function guides the mobile medical robot towards the goal while simultaneously minimizing an energy-proxy cost and maximizing distance from obstacles.
The path generated by the grid-based Energy-A* algorithm typically consists of a sequence of grid cell centers, resulting in a piecewise linear trajectory with sharp turns at grid boundaries. Such paths are difficult for a physical mobile medical robot to follow accurately and smoothly, causing stop-and-go motion that wastes energy. To address this, we apply a path smoothing technique using piecewise cubic Bézier curves. This method takes the key waypoints from the Energy-A* path and fits smooth curves between them, ensuring continuity in position and curvature. For a path segment between waypoints \(W_{i-1}\) and \(W_i\), the cubic Bézier curve \(P_{i-1,i}(u)\) is defined as:
$$
P_{i-1,i}(u) = (1-u)^3 W_{i-1} + 3u(1-u)^2 W_{i}^{c1} + 3u^2(1-u) W_{i}^{c2} + u^3 W_i, \quad u \in [0,1]
$$
The control points \(W_{i}^{c1}\) and \(W_{i}^{c2}\) are optimized to satisfy constraints such as maximum curvature \(\rho_{\text{max}}\) and collision-free passage. The curvature \(\rho(u)\) at any point on the curve is given by the standard formula:
$$
\rho_{i-1,i}(u) = \frac{ \frac{d^2 P^y}{du^2} \frac{d P^x}{du} – \frac{d^2 P^x}{du^2} \frac{d P^y}{du} }{ \left[ \left( \frac{d P^x}{du} \right)^2 + \left( \frac{d P^y}{du} \right)^2 \right]^{3/2} }
$$
The final smoothed path for the mobile medical robot is the concatenation of all such smooth segments, resulting in a trajectory that is kinematically feasible and energy-efficient to track.
| Method | Core Approach | Typical Limitation for Medical Robots |
|---|---|---|
| Basic A* | Minimizes geometric path length using a grid. | Paths have redundant turns and unsafe proximity to obstacles. |
| Probabilistic Roadmap (PRM) | Samples configuration space to build a graph. | Can be computationally slow for large, dense static maps. |
| Genetic Algorithm (GA) | Uses evolutionary operators to optimize a path. | High computation time and unpredictable solution quality. |
| Proposed Energy-A* with Smoothing | Minimizes energy-proxy cost with safety penalty, then applies Bézier smoothing. | Designed for safe, efficient, and smooth navigation in medical environments. |
The proposed methodology was validated through comprehensive simulations modeling a field hospital layout. A mobile medical robot platform with parameters listed in the table below was considered for transporting medical supplies from a sterilization room to various patient bed locations.
| Parameter | Value |
|---|---|
| Robot Mass (\(m_{\text{robot}}\)) | 30 kg |
| Maximum Payload (\(m_{\text{goods}}\)) | 100 kg |
| Robot Attribute Constant (\(c\)) | 4 |
| Typical Ground Friction (\(\mu\)) | 0.051 |
| Safety Distance (\(d_{\text{safe}}\)) | 0.4 m |
Multiple transport missions were simulated. The proposed Energy-A* algorithm (using enhanced 16-direction search with energy adjacency weights) was compared against three other planners: a standard A* algorithm, a Probabilistic Roadmap (PRM) method, and a Genetic Algorithm (GA). The key performance metrics were the calculated energy expenditure \(E_{\text{res}}\) (from the model) and the final path length. The safety penalty ensured all paths maintained a minimum distance from obstacles greater than \(d_f\).
| Mission (Goal) | Method | Estimated Traction Energy \(E_{\text{res}}\) (J) | Path Length (m) | Energy Reduction vs. Worst Case |
|---|---|---|---|---|
| Bed (7,1) | Proposed Energy-A* | 2433.2 ± 23.5 | 24.34 | 18.98% |
| PRM | 2646.7 ± 25.4 | 26.98 | 11.87% | |
| GA | 3003.2 ± 29.4 | 30.12 | 0% (Baseline) | |
| Standard A* | 2533.6 ± 24.8 | 25.67 | 15.63% | |
| Bed (2,8) | Proposed Energy-A* | 4777.0 ± 46.8 | 47.78 | 14.55% |
| PRM | 5590.6 ± 54.8 | 55.14 | 0% (Baseline) | |
| GA | 5222.4 ± 51.2 | 52.45 | 6.5% | |
| Standard A* | 4922.0 ± 48.2 | 49.55 | 11.95% |
The results clearly demonstrate the efficacy of the proposed planner for the mobile medical robot. In all missions, the Energy-A* algorithm generated paths with the lowest estimated energy consumption and the shortest length. The integration of the energy-based adjacency matrix and enhanced search directions successfully reduced wasteful detours and turns. The subsequent Bézier smoothing process converted the jagged grid path into a smooth trajectory. The table below summarizes the effect of smoothing on path quality for one mission, showing a minimal increase in total length but a continuous, bounded curvature essential for stable control of the mobile medical robot.
| Metric | Energy-A* (Raw Path) | Energy-A* + Bézier Smoothing |
|---|---|---|
| Total Path Length | 47.78 m | 51.32 m (+6.9%) |
| Bending Energy (BE) | N/A (piecewise linear) | 0.16 |
| Maximum Curvature | Infinite at corners | < \(\rho_{\text{max}}\) (bounded) |
The relationship between the total mass \(m’\) (robot plus payload) and the traction energy \(E_{\text{res}}\) for a fixed path is linear, as predicted by the model \(E_{\text{res}} \propto m’ \cdot s\). This highlights the critical importance of energy-efficient routing, especially when the mobile medical robot is carrying heavy medical payloads, as even small reductions in path distance translate to significant energy savings and extended operational time.
This work presents a generalized path planning framework for mobile medical robots that holistically addresses the critical requirements of energy efficiency, safety, and smoothness. By integrating an energy consumption model directly into the graph search via a novel adjacency matrix formulation and augmenting the A* algorithm with a safety penalty factor, the method generates efficient and safe collision-free paths. The subsequent application of cubic Bézier curve smoothing ensures the final trajectory is practical for real-world mobile medical robot motion control. Simulation results in a field hospital environment confirm that the proposed method outperforms conventional planners in minimizing an energy-based cost function while adhering to safety constraints. This approach provides a robust foundation for developing intelligent logistics systems in healthcare settings, promising to reduce operational costs, enhance safety, and improve the reliability of automated medical supply transport. Future work will focus on integrating this planner with real-time control and dynamic obstacle avoidance to handle more unpredictable hospital environments.