3.1. The kinematics and dynamics of AGV

The fixed coordinate frame is denoted as O_q, while O_r represents the mobile coordinate frame attached to the AGV. Each wheel has its wheel coordinate frame, represented as O_wi (where i = 1 to 4). As described in ref. [Reference Khan, Khatoon and Gaur43], we express the wheel position vector in its respective coordinate frame, Owi, as P_wi. The corresponding equation is given by:

(3.1a) \begin{equation}\textrm{P}_{\textrm{wi}}(\rm{where}\textrm{i} = 1\textrm{to}4) = [\textrm{x}_{\textrm{wi}}\textrm{y}_{\textrm{wi}}\varphi_{\textrm{wi}}]^{\textrm{T}}\end{equation}

The rotational speed of each wheel around its hub is represented by $\begin{array}{c} .\\ \theta \textrm{ix} \end{array}$ , while the roller’s angular velocity is denoted by $\begin{array}{c} .\\ \theta \textrm{ir} \end{array}$ , and the angular velocity of the wheel at the point of contact with the ground is given by $\begin{array}{c} .\\ \theta \textrm{iz} \end{array}$ . Additionally, the wheel radius is represented by R_i, and the roller slope angle for each wheel is denoted by ψ_i (i = 1 to 4). The radius of the roller is symbolized by ref. [Reference Adamov and Saypulaev44]. Based on these parameters, the motion vector of the AGV can be formulated as described in ref. [Reference Abdelrahim, Hassan, Ojo, Hosny, Ammar and El-Samanty45].

(3.1b) \begin{equation}\dot{\mathbf{P}}_{wi}=\left[\begin{array}{c} \dot{x}_{wi}\\ \dot{y}_{wi}\\ \dot{\phi }_{wi} \end{array}\right]=\left[\begin{array}{c@{\quad}c@{\quad}c} 0 & r\!\sin\!\left(\psi _{i}\right) & 0\\ R_{i} & -r\!\cos\!\left(\psi _{i}\right) & 0\\ 0 & 0 & 1 \end{array}\right]\left[\begin{array}{c} \dot{\theta }_{ix}\\ \dot{\theta }_{ir}\\ \dot{\theta }_{iz} \end{array}\right]\end{equation}

(3.1c) \begin{equation}\mathbf{T}_{\mathbf{wi}}^{\mathbf{r}}=\left[\begin{array}{c@{\quad}c@{\quad}c} \cos\!(\phi _{wi}^{r}) & -\sin\!(\phi _{wi}^{r}) & d_{wiy}^{r}\\ \sin\!(\phi _{wi}^{r}) & \cos\!(\phi _{wi}^{r}) & d_{wix}^{r}\\ 0 & 0 & 1 \end{array}\right]\end{equation}

Equations show the rotational angle of O_wi w.r.t. O_r and is represented by $\phi _{wi}^{r}$ (i = 1 to 4). Additionally, the translational distance between the two coordinate frames is denoted by $d_{wix}^{r}$ and $d_{wiy}^{r}$ , which define the displacement along the x and y axes, respectively. Suppose the position vector of the AGV in the O_r coordinate frame is given by P_r = [x_r y_r φ_r]^T. In this case, the equation connecting P_r and P_wi can be given as P_r = $T_{wi}^{r}$ .P_wi. Additionally, as shown in Figure 2, it is evident that $\phi _{w1}^{r} = \phi _{w2}^{r}=\phi _{w3}^{r}=\phi _{w4}^{r}=0$ . Based on these conditions, the AGV’s vector of velocity is presented as follows:

(3.1d) \begin{equation}\left[\begin{array}{c} \dot{x}_{r}\\ \dot{y}_{r}\\ \dot{\phi }_{r} \end{array}\right]=\left[\begin{array}{c@{\quad}c@{\quad}c} 1 & 0 & d_{wiy}^{r}\\ 0 & 1 & d_{wix}^{r}\\ 0 & 0 & 1 \end{array}\right]\left[\begin{array}{c} \dot{x}_{wi}\\ \dot{y}_{wi}\\ \dot{\phi }_{wi} \end{array}\right]\end{equation}

From (3.1b) and (3.1d), we get,

(3.1e) \begin{equation}\dot{\mathbf{P}}_{\mathbf{r}}=\mathbf{J}_{\mathbf{i}}\dot{\mathbf{q}}_{\mathbf{i}}\end{equation}

where

\begin{equation*} \mathbf{J}_{\mathbf{i}}\in R^{3\times 3}=\left[\begin{array}{c@{\quad}c@{\quad}c} 0 & r\!\sin\!\left(\psi _{i}\right) & d_{\text{wiy }}^{r}\\ R_{i} & -r\!\cos\!\left(\psi _{i}\right) & d_{\text{wix }}^{r}\\ 0 & 0 & 1 \end{array}\right] \end{equation*}

The ith wheel’s Jacobian matrix is represented as $\mathbf{J}_{\mathbf{i}}$ and, $\dot{q}_{i}=[\begin{array}{c@{\quad}c@{\quad}c} \theta _{ix} & \theta _{ir} & \theta _{iz} \end{array}]$ .

AGV dynamics on a flat surface can be calculated using the Newton–Euler method. To simplify the computation of the equation of motion, the coordinate frame Or is assumed to lie at the AGV’s center of gravity, as this optimizes computational efficiency. The AGV’s mass matrix is denoted by M_m.

(3.1f) \begin{equation}\textrm{S}_{\textrm{q}}=\left[\begin{array}{c@{\quad}c} x_{q} & y_{q} \end{array}\right]^{T}\end{equation}

$\textrm{S}_{\textrm{q}}$ is the vector showing the position in a frame with fixed coordinate “O_q” as in ref. [Reference Chaichumporn, Ketthong, Thi Mai, Hashikura, Kamal and Murakami46].

(3.1g) \begin{equation}\textrm{F}_{\textrm{q}}=\left[\begin{array}{c@{\quad}c} F_{qx} & F_{qy} \end{array}\right]^{T}\end{equation}

$\textrm{F}_{\textrm{q}}$ is the vector showing the force in a frame with fixed coordinate “O_q” as in ref. [Reference Chaichumporn, Ketthong, Thi Mai, Hashikura, Kamal and Murakami46].

When the second law of Newton is applied, the equation of motion of the AGV (shown in Figure 2) in the coordinate frame O_q can be represented as in ref. [Reference Xu, Yu, Wang, Qi and Lu47]:

(3.1h) \begin{equation}\textrm{F}_{\textrm{q}}=\textrm{M}_{m}\ddot{\textrm{S}}_{q}\end{equation}

(3.1i) \begin{equation}\left[\begin{array}{c} F_{qx}\\ F_{qy} \end{array}\right]=\left[\begin{array}{c@{\quad}c} M & 0\\ 0 & M \end{array}\right]\left[\begin{array}{c} \ddot{x}_{q}\\ \ddot{y}_{q} \end{array}\right]\end{equation}

(3.1j) \begin{equation}\textrm{if},{}^{\textrm{q}}{\textrm{R}_{\textrm{r}}}\left( \varphi \right) = \left[ {\begin{array}{*{20}{c}} {\cos\!\left( \phi \right)}&{ -\!\sin\!\left( \phi \right)} \\ {\sin\!\left( \phi \right)}&{\cos\!\left( \phi \right)} \end{array}} \right]\end{equation}

where $^{\textrm{q}}\textrm{R}_{\textrm{r}}(\varphi )$ is the matrix that represents the transformation of O_r w.r.t O_q; therefore,

(3.1k) \begin{equation}{\dot{\textrm{S}}_{\textrm{q}}}{ = ^{\textrm{q}}}{\textrm{R}_{\textrm{r}}}\left( \varphi \right){\dot{\textrm{S}}_{\textrm{r}}}\textrm{and}{\textrm{F}_{\textrm{q}}}{ = ^{\textrm{q}}}{\textrm{R}_{\textrm{r}}}\left( \varphi \right){\textrm{F}_{\textrm{r}}} \end{equation}

Eq. (3.1h) can be simplified by using the transformation matrix as follows:

(3.1l) \begin{equation}\textrm{M}_{\textrm{m}}\left({}^{\textrm{q}}\textrm{R}_{\textrm{r}}\left(\varphi \right)\ddot{\textrm{S}}_{\textrm{r}}+^{\textrm{q}}\textrm{R}_{\textrm{r}}\left(\dot{\varphi }\right)\dot{\textrm{S}}_{\textrm{r}}\right)=^{\textrm{q}}\textrm{R}_{\textrm{r}}\left(\varphi \right)\textrm{F}_{\textrm{r}}\end{equation}

Multiply both sides by $^{\textrm{q}}\textrm{R}_{\textrm{r}}(\varphi)^{-1}$ gives,

(3.1m) \begin{equation}\textrm{M}_{\textrm{m}}({}^{\textrm{q}}\textrm{R}_{\textrm{r}}(\varphi)^{-1}\, {}^{\textrm{q}}\textrm{R}_{\textrm{r}}(\varphi)\ddot{\textrm{S}}_{\textrm{r}}+{}^{\textrm{q}}\textrm{R}_{\textrm{r}}(\varphi)^{-1}{}^{\textrm{q}}\textrm{R}_{\textrm{r}}(\dot{\varphi})\dot{\textrm{S}}_{\textrm{r}}) = {}^{\textrm{q}}\textrm{R}_{\textrm{r}}(\varphi)^{-1}{}^{\textrm{q}}\textrm{R}_{\textrm{r}}(\varphi)\textrm{F}_{\textrm{r}}\end{equation}

Since ${}^{\textrm{q}}\textrm{R}_{\textrm{r}}(\varphi) = {}^{\textrm{q}}\textrm{R}_{\textrm{r}}(\varphi)^{\textrm{T}}, {}^{\textrm{q}}\textrm{R}_{\textrm{r}}(\varphi)^{-1}\,{}^{\textrm{q}}\textrm{R}_{\textrm{r}}(\dot{\varphi}) = \dot{\varphi}\left[\begin{array}{c@{\quad}c} 0 & -1 \\ 1 & 0\end{array} \right]$ . Therefore,

(3.1n) \begin{equation}\left[\begin{array}{c@{\quad}c} M & 0\\ 0 & M \end{array}\right]\left[\begin{array}{c} \ddot{x}_{r}-\dot{\phi }\dot{y}_{r}\\ \ddot{y}_{r}+\dot{\phi }\dot{x}_{r} \end{array}\right]=\left[\begin{array}{c} F_{xr}\\ F_{yr} \end{array}\right]-\left[\begin{array}{c} \beta _{x}\dot{x}_{r}\\ \beta _{y}\dot{y}_{r} \end{array}\right]+\left[\begin{array}{c} -F_{ex}\cos\!\left(\psi _{ex}\right)\\ F_{ex}\sin\!\left(\psi _{ex}\right) \end{array}\right]\end{equation}

In the context of this equation, the symbol F_xr is used to represent the total force that is doing its work in the x direction, and the symbol F_yr is used to represent the total force that is doing its work in the y direction. The β_x is the coefficient of linear friction along the x-axis, and β_y is the coefficient of linear friction along the y-axis. The body of the AGV is being subjected to the influence of an external force at a distance (h) from the upper edge of the AGV, as in Figure 2. In this context, the symbol F_ex is used to denote this force. The force F_ex is situated at an angle of ψ_ex w.r.t. y_r. Consider that τ, I_q, and β_z represent the AGV’s center of gravity moment, inertia moment, and linear friction coefficient in the z-direction, as described in ref. [Reference Chang and Lin48]. The Euler equation can be represented in the following fashion by making use of the free body model, which is depicted in Figure 2.

(3.1o) \begin{equation}I_{q}\ddot{\phi }=\tau -\beta _{z}\dot{\phi }+F_{ex}\cos\!\left(\psi _{ex}\right)a-F_{ex}\sin\!\left(\psi _{ex}\right)\left(b-h\right)\end{equation}

If the dynamics of the motor that is coupled to each wheel are taken into consideration, the driving force F_di (where i = 1 to 4) that is produced by the DC motor can be stated in the following manner, as in ref. [Reference Atlantis, Bechlioulis, Karras, Fourlas and Kyriakopoulos49]:

(3.1p) \begin{equation}F_{di}\left(\textrm{where}i=1||4\right)=\alpha u_{i}-\beta R\dot{\theta }_{i}\end{equation}

The input voltage that is applied to each motor is denoted by u_i (where i = 1 to 4). The motor coefficients, denoted by α and β, are computed by employing the following formulas as in ref. [Reference Atlantis, Bechlioulis, Karras, Fourlas and Kyriakopoulos49]:

(3.1q) \begin{equation}\alpha =\frac{k_{\tau }}{RR_{a}}\end{equation}

(3.1r) \begin{equation}\beta =\frac{k_{\tau }k_{e}n}{R^{2}R_{a}}\end{equation}

The torque coefficient of the motor is shown by the symbol k_τ, the gear ratio is indicated by n, the armature resistance is indicated by R_a, and the back emf coefficient is indicated by k_e in Eqs. (3.1q) and (3.1r).

Based on the free body diagram (FBD) in Figure 2, the elements F_xr, F_yr, and τ are represented in terms of driving force, respectively, as in ref. [Reference Zhang and Liu-Henke50].

(3.1s) \begin{equation}F_{xr}=\frac{1}{2}\left(-F_{d1}+F_{d2}-F_{d3}+F_{d4}\right)\end{equation}

(3.1t) \begin{equation}F_{yr}=\frac{1}{2}\left(F_{d1}+F_{d2}+F_{d3}+F_{d4}\right)\end{equation}

(3.1u) \begin{equation}\tau =\frac{a}{2}\left(F_{d1}-F_{d2}-F_{d3}+F_{d4}\right)+\frac{b}{2}\left(F_{d1}-F_{d2}-F_{d3}+F_{d4}\right)\end{equation}

For efficient route planning and real-time obstacle avoidance, a mecanum wheel AGV must precisely manage its revolutions per minute (rpm) and wheel velocities to perform linear and angular motions in varied surroundings, as determined by the above equations. These movements enable the AGV to avoid obstacles and navigate complex terrains with precision. Omnidirectional mobility requires wheel speed control to allow the AGV to travel forward, backward, sideways, and diagonally without changing orientation. Static and dynamic control equations optimize AGV performance by ensuring efficient motion planning, stability, and responsiveness in both organized and unstructured situations. To validate the kinematic and dynamic equations governing the motion of the mecanum wheel AGV, we conducted MATLAB-based simulations to generate and analyze various trajectories, including circular, elliptical, triangular, tetragonal, lemniscate, and five-petal rose curves. These trajectories serve as benchmarks to assess the AGV’s ability to execute precise path-following while maintaining stable motion control. Figure 3 shows the AGV testing simulations based on the equations.

Figure 3. AGV testing simulations based on the equations: a) circular trajectory, b) elliptical trajectory, c) triangular trajectory, d) tetragonal trajectory, e) lemniscate trajectory, and f) five-petal rose curve.

Figure 4. An illustration of the MA* algorithm.

Figure 5. Simulation results of the MA* algorithm.

4.1. Modified A* algorithm

The modified A* (MA*) method enhances the traditional A* algorithm by optimizing path searching in dynamic environments. MA* is ideal for real-world settings with constant changes because it incorporates dynamic obstacles, real-time updates, and grid structures, whereas A* utilizes heuristics to determine the shortest path. For reliable and effective AGV path planning, MA* combines BFS with Dijkstra’s global search [Reference Bhargava, Singholi and Suhaib51]. It evaluates nodes one after the other, choosing the next node based on the lowest f(n) as f(n) = g(n) + h(n), where n is the number of nodes, g(n) is the starting cost, and h(n) is the goal heuristic cost [Reference Le, Prabakaran, Sivanantham and Mohan52–Reference Xiang, Lin, Ouyang and Huang54]:

(4.1a) \begin{equation}\left.\begin{array}{c} g\left(n\right)=\sqrt{\left(y_{s}-y_{n}\right)^{2}+\left(z_{s}-z_{n}\right)^{2}}\\ h\left(n\right)=\sqrt{\left(y_{n}-y_{t}\right)^{2}+\left(z_{n}-z_{t}\right)^{2}} \end{array}\right\}\end{equation}

The start, current, and target node positions are shown by (y_s, z_s), (y_n, z_n), and (y_t, z_t), respectively. In complex scenarios, the MA* algorithm employs an eight-directional analysis on a raster map to ensure accurate and collision-free route planning. Figure 4 shows the illustration of the MA* algorithm. Figure 5 shows the Simulation results of the MA* algorithm.

4.2. Dynamic window approach

The DWA is a well-liked method for AGVs to use when navigating locally and overcoming obstacles. Analyzing and selecting the appropriate motion commands allows real-time navigation in changing environments. The DWA calculates a dynamic window to estimate linear and angular velocities based on the AGV’s physical limits and current state. The AGV trajectory is simulated for each conceivable velocity generated inside this window for a short time [Reference Bhargava, Suhaib and Singholi55–Reference Ju, Luo and Yan57]. A scoring system that balances safety and efficiency evaluates these trajectories, considering target proximity and obstacle avoidance variables. The trajectory with the highest rating is chosen by the velocity that best achieves the goal without colliding. The operation is repeated once the AGV moves at the set velocity [Reference Xinyi, Yichen, Liang and Linlin58]. Rapid velocity optimization ensures safe and agile navigation in complex and dynamic locations in the DWA.

The initial nodes on the DWA model result in “Calculate Dynamic Window.” A time step, the vehicle’s present condition, and limitations are used to calculate a range of possible velocities. “Generate Possible Velocities” generates a list of potential velocities inside the dynamic window. The approach creates candidate velocities before initializing the best velocity to set optimal velocity and score starting points [Reference Guo, Zhang, Zhao, Liu and Liu59]. The program simulates the trajectory and predicts the AGV’s path for each candidate velocity and time step. After trajectory simulation, the algorithm scores each trajectory based on how successfully it avoids obstacles and approaches the goal [Reference Xinyi, Yichen, Liang and Linlin58]. The system evaluates whether the current score surpasses the best-recorded score at each decision point. If it does, the best velocity and score are updated accordingly; otherwise, the system assesses the next candidate’s velocity. After evaluating all candidate velocities, the algorithm returns the best velocity and reaches the end node, completing DWA [Reference Li, Hao, Zhao, Lu and Ghadiri Nejad60]. The flowchart in Figure 6 shows how DWA chooses an AGV’s ideal velocity based on its dynamic environment and goal. Figure 7 shows the MATLAB simulation results of the DWA algorithm.

Figure 6. Flowchart for DWA.

Figure 7. MATLAB simulation results of the DWA algorithm in a 10 by 10 (in decimeters) raster map.

4.3. Modified A*-DWA hybrid optimization algorithm

The modified A*-DWA hybrid optimization algorithm (ADWA-HO) algorithm, which avoids local barriers in real-time while utilizing global routing, is one of the highly successful control methods for mecanum wheel AGVs. Using the AGV’s omnidirectional movement capabilities to their fullest, A* and DWA algorithms enable efficient, safe, and smooth navigation in complex and dynamic settings. The ADWA-HO methodology has several benefits over other algorithms.

By employing a MA* algorithm that eliminates unnecessary nodes and smooths trajectories, the ADWA-HO algorithm provides an optimized approach to global path planning, generating smoother paths than D* [Reference Piemngam, Nilkhamhang and Bunnun61]. To ensure a more adaptable response to dynamic situations, ADWA-HO integrates DWA for real-time obstacle avoidance, rather than relying on APF or alternative algorithms that are susceptible to local minima [Reference Chivarov, Yovkov, Chivarov, Stoev and Chikurtev62]. ADWA-HO balances global efficiency and local responsiveness, unlike DWA, which merely focuses on local obstacle avoidance [Reference Gao, Han, Feng, Wang, Meng and Yang63]. Compared to PRM & RRT, which have difficulty making real-time adjustments in highly variable environments, its flexible path refinement achieved via the combination of MA* and DWA offers better adaptability [Reference Xu, Tian, He and Huang64]. In contrast to D* and PRM & DWA fusion, which frequently generate jerky pathways, the algorithm improves smoothness and stability by preventing sudden directional shifts, making it more suitable for mecanum wheel AGVs [Reference Xu, Tian, He and Huang64]. Furthermore, in complex situations where PRM & RRT fusion, as well as PRM & DWA fusion, were unable to handle dynamic changes successfully, ADWA-HO exhibits higher flexibility [Reference Xu, Tian, He and Huang64]. Compared to techniques like D*, APF, DWA, PRM & RRT fusion, as well as PRM & DWA fusion, ADWA-HO guarantees more accurate and effective navigation by harnessing the full omnidirectional capability of mecanum wheels. The algorithm provides durable and trustworthy solutions for comprehensive AGV control systems while avoiding common failures, such as RRT’s inefficiency in high-dimensional environments and APF’s local minima issues [Reference Fu65]. The MA* technique avoids fixed barriers and finds a relatively straightforward route from the starting point to the end point for global route planning. The DWA optimizes local routes and dynamically adjusts the AGV’s trajectory in real time to steer clear of shifting obstructions and follow kinematic limits [Reference Liang, Tan, Wei, Zhang, Wang and Huang66]. MA* produces a globally optimal strategy, while DWA ensures obstacle avoidance and local adaptability. If the DWA hits a significant barrier not in the initial MA* path, the system replans the global path from the AGV’s location [Reference Bhargava, Suhaib and Singholi67]. This hybrid technique gives the AGV the durability and flexibility to navigate complex environments. Figure 8 illustrates the flowchart of the hybrid algorithm.

Figure 8. Modified A* and DWA hybrid optimization algorithm (ADWA-HO).

The ADWA-HO combines global path planning with local trajectory optimization for AGVs. The process begins with the initialization of the AGV’s state, including its position (x₀,y₀), velocity v_0, and heading θ₀, along with the current node position (x_n,y_n), and the goal position (x_goal,y_goal). The key parameters, such as maximum velocity (v_max), maximum acceleration (a_max), and heading change limits, are set, and the heuristic for the A* algorithm is defined as the Euclidean distance:

(4.3a) \begin{equation}h\left(n\right)=\sqrt{\left(x_{\textrm{goal }}-x_{n}\right)^{2}+\left(y_{\textrm{goal}}-y_{n}\right)^{2}}\end{equation}

The MA* algorithm then utilizes open and closed lists to determine the optimal route from the start to the end, where the total cost, f(n) = g(n) + h (n), is minimized. Algorithmically, the node with the smallest “f(n)” is selected from the open list and expanded by assessing its neighbors. For each neighbor, the tentative cost “g_tentative” is calculated as in ref. [Reference Zhou, Yi, Zhang, Chen, Yang, Han and Zhang16]:

(4.3b) \begin{equation}g_{\text{tentative }}=g\left(\textrm{current}\right)+\textrm{cost}\left(\textrm{current},\textrm{neighbor}\right)\end{equation}

Figure 9. MATLAB simulation testing results of the ADWA-HO algorithm in 21 × 21 raster Map 1 (in decimeters).

Figure 10. Global and local path planning of simulation in a 21 × 21 raster Map 1 (in decimeters).

Figure 11. Variation in linear velocity (m/s) and angular velocity (rad/s) of the simulation in raster Map 1.

Fig. 12. Variation in posture angle (rad) of simulation in raster Map 1.

Figure 13. Real-time testing environment of 21 × 21 Map 1 (in decimeters), that is, 210 cm × 210 cm.

Figure 14. Posture angle (rad) variation in Map 1.

Figure 15. The variation in linear velocity (m/s) and angular velocity (rad/s) in Map 1.

Here, g(current) is the cost from the start node to the current node, and cost (current, neighbor) is the cost to move from the current node to the neighbor. If “g_tentative” is less than “g(neighbor),” update the neighbor’s cost and include it in the open list. Parent pointers are used to trace backward from the target to the beginning or start node once the path has reached the goal node. Once the goal is accomplished, parent pointers are traced to recreate the path. The A* path is divided into intermediate waypoints, which serve as sub-goals for the DWA. The DWA optimizes the local trajectory by calculating a dynamic window of feasible velocities V_d =[v_min,v_max] and headings ω_d=[ω_min,ω_max] as in ref. [Reference Wani, Nasiruddin, Khatoon, Shahid, Malik, Mishra, Sood, García Márquez and Ustun68], where

(4.3c) \begin{equation}\left.\begin{array}{c} v_{\textrm{min}}=v_{\text{current }}-a_{\textrm{max}}\times \Delta t\\ v_{\textrm{max}}=v_{\text{current }}+a_{\textrm{max}}\times \Delta t\\ \omega _{\textrm{min}}=\omega _{\text{current }}-\alpha _{\textrm{max}}\times \Delta t\\ \omega _{\textrm{max}}=\omega _{\text{current }}+\alpha _{\textrm{max}}\times \Delta t \end{array}\right\}\end{equation}

The minimum and maximum feasible linear velocities are denoted by v_min and v_max. The $v_{\text{current }}$ is the current linear velocity of the AGV and $a$ _max is the maximum linear acceleration/deceleration of the AGV. The term Δt is the time step over which the velocity change is computed. These limits ensure that the AGV’s velocity changes are within its physical capabilities. The minimum and maximum feasible angular velocities are denoted by ω_min and ω_max. The ω_current is the current angular velocity of the AGV. The α_max is the maximum angular acceleration/deceleration of the AGV. For each pair of velocity v and angular velocity ω, the trajectory is predicted over a short time horizon T as in ref. [Reference Pfeiffer69]:

(4.3d) \begin{equation}\left.\begin{array}{c} x\left(t\right)=x_{0}+\int _{0}^{T}v\cdot \cos\!\left(\theta \left(t\right)\right)dt\\ y\left(t\right)=y_{0}+\int _{0}^{T}v\cdot \sin\!\left(\theta \left(t\right)\right)dt\\ \theta \left(t\right)=\theta _{0}+\int _{0}^{T}\omega dt \end{array}\right\}\end{equation}

The x(t) and y(t) are the predicted positions of the AGV at time t; x ₀ and y ₀ are the initial positions of the AGV at time t = 0; v is the linear velocity of the AGV; θ(t) is the heading angle of the AGV at time t; and cos(θ(t)) and sin(θ(t)) are the directional components of the velocity. These equations predict the AGV’s position over time based on its velocity and heading. θ₀ is the initial heading angle of the AGV at time t = 0; the AGV’s angular velocity is denoted by ω. This equation predicts the AGV’s heading over time based on its angular velocity. These limits ensure that the AGV’s heading changes are within its physical capabilities. Given the AGV’s present velocity (v) and angular velocity (ω), these equations forecast its future trajectory (position and heading) over a brief time horizon (T). The trajectory is evaluated using a cost function that includes goal-oriented cost ( $g_{\text{cost}}$ ), obstacle avoidance cost ( $o_{\text{cost}}$ ), and speed cost ( $v_{\text{cost}}$ ), as in refs. [Reference Houshyari and Sezer70,Reference Hasan, Khan, Khatoon and Sajid71]:

(4.3e) \begin{equation}g_{\text{cost }}=\textrm{distance}\left(x\left(T\right),y\left(T\right),\textrm{waypoint}\right)\end{equation}

Here, g _cost is the cost associated with reaching the goal or sub-goal (waypoint); x(T) and y(T) are the expected location of the time T for AGV based on the current velocity and heading; the A* algorithm’s global path is used to determine the waypoint, which is the intermediate target point (sub-goal); distance (x(T), y(T), waypoint) is the distance measured in Euclidean terms between the waypoint and the expected position (x(T) and y(T). This cost encourages the AGV to move toward the goal or sub-goal. A smaller value suggests that the predicted trajectory brings the AGV closer to the target.

(4.3f) \begin{equation}o_{\text{cost }}=\sum _{\text{obstacles }}\frac{1}{\text{ distance }(x\left(t\right),y\left(t\right),\textrm{obstacle}}\end{equation}

The term o _cost represents the cost associated with avoiding obstacles; the projected positions of the AGV at time t along the trajectory are denoted by x(t) and y(t); the location of an obstacle in the surroundings is referred to as an obstacle; the Euclidean distance between the obstacle and the predicted position (x(t),y(t)) is represented by the expression distance (x(t), y(t), obstacle); and ∑obstacles denotes the sum is taken over all obstacles in the environment. This cost penalizes trajectories that approach obstacles too closely. The inverse distance ensures that trajectories passing near obstacles have a higher cost, while those farther away have a lower price.

(4.3g) \begin{equation}v_{\text{cost }}=v_{\textrm{max}}-v\end{equation}

v_cost represents the cost associated with the AGV’s speed, v_max is the maximum allowable velocity for the AGV, and v is the current velocity of the AGV along the trajectory. This cost encourages the AGV to move at higher velocities. A lower value indicates that the AGV is moving closer to its maximum speed, which is desirable for efficiency.

The total cost is computed as:

(4.3h) \begin{equation}\textrm{TotalCost}\lambda _{1}\cdot g_{\text{cost }}+\lambda _{2}\cdot 0_{\text{cost }}+\lambda _{3}\cdot v_{\text{cost }}\end{equation}

where λ₁, λ₂, and λ₃ are weighting factors for the goal-oriented, obstacle avoidance, and speed costs, respectively. The AGV advances to the next waypoint after selecting the trajectory with the lowest overall cost. The total cost function balances the three objectives, that is, reaching the goal, avoiding obstacles, and maintaining high speed. The weights λ₁, λ₂, and λ₃ allow the algorithm to be tuned to prioritize specific behaviors (e.g., safety over speed or vice versa). This procedure is repeated for every waypoint until the objective is accomplished or there are no more feasible routes. The A*-DWA hybrid optimization algorithm leverages the global optimality of A* and the dynamic adaptability of DWA, facilitating safe and effective navigation in complex environments. The results of the ADWA-HO algorithm’s simulation in Map 1 are displayed in Figures 9, 10, 11, and 12, while the outcomes of the experiments are shown in Figures 13, 14, and 15. Tables III–VI display the results of the simulations and experiments, respectively.

Table III. Simulation and experimental performance of each algorithm in Map 1.

Table IV. Percentage deviation between experimental and simulated path lengths in Map 1.

Table V. Percentage deviation between experimental and simulated motion time in Map 1.

Table VI. Percentage difference in experimental path length and motion time between ADWA-HO and other algorithms in Map 1.

D* works the least well. At the same time, ADWA-HO surpasses other algorithms, achieving the quickest motion time (17.75 s in simulation and 18.47 s in experiments) and shortest route (192.46 cm in simulation and 202.87 cm in experiments). In addition, ADWA-HO provides the best motion smoothness (84%), the best success rate (95%), and the smallest collision rate (3%). It also has fewer turns (8) and path inflections (2) than D*, which has more turns (4 inflections, 25 turns). These outcomes show ADWA-HO’s exceptional reliability and effectiveness in autonomously navigating. The most efficient and reliable algorithm is ADWA-HO, which reduces path inflections and turns while achieving outstanding outcomes in terms of path length, motion duration, collision rate, smoothness, and goal-reaching rate. On the other hand, D* performs the worst, exhibiting slower motion, longer paths, greater collisions, and a lower success rate. While other algorithms, such as APF, DWA, PRM & RRT fusion, and PRM & DWA fusion, perform effectively in reducing turns and inflections compared to D*, they are still moderately less effective than ADWA-HO.

Figure 16 represents the algorithms comparison based on path length and motion time in map 1 with RMS error. Figures 17 and 18 illustrate the algorithm comparison based on standard deviation and percentage deviation in path length and motion time in Map 1.

Figure 16. Algorithms comparison based on path length and motion time in Map 1 with RMS error.

Figure 17. Algorithms comparison according to standard deviation and % deviation in path length in Map 1.

Figure 18. Comparison of algorithms according to standard deviation and % deviation in motion time in Map 1.

The results of the ADWA-HO algorithm’s simulation in Map 2 are presented in Figures 19, 20, 21, and 22, while Figures 23, 24, and 25 display the experimental results. Tables VII, VIII, IX, and X display the results of the simulations and experiments, respectively.

Figure 19. MATLAB simulation testing results of the ADWA-HO algorithm in 21 × 21 raster Map 2 (in decimeters).

Figure 20. Global and local path planning of simulation in 21 × 21 raster Map 2 (in decimeters).

Figure 21. Variation in linear velocity (m/s) and angular velocity (rad/s) of the simulation in raster Map 2.

Figure 22. Variation in posture angle (rad) of simulation in raster Map 2.

Figure 23. Real-time testing environment of 21 × 21 Map 2 (in decimeters), that is, 210 cm × 210 cm.

Figure 24. Posture angle (rad) variation in Map 2.

Figure 25. Linear velocity (m/s) and angular velocity (rad/s) variation in Map 2.

While D* shows the longest paths (269.87 cm in simulation and 295.39 cm in experiment) and the slowest times (33.88 s in simulation and 36.65 s in experiment), ADWA-HO executes better across each of the significant metrics, attaining the shortest route length (203.16 cm in simulation and 213.93 cm in experiments) and its quickest motion time (28.25 s in simulation and 29.58 s in experiments). D* has the largest collision rate (18%) and the lowest smoothness (55%), while ADWA-HO has the least collision rate (4%) and the finest motion smoothness (82%). ADWA-HO has the most successful goal-reach success rate (90%), and D* offers the lowest (69%). Furthermore, D* and APF have the greatest path inflections (5), while ADWA-HO and PRM-DWA fusion have the fewest (2). In addition, D* needs the most turns (27), whereas ADWA-HO needs the fewest (7). These outcomes demonstrate the effectiveness, precision, and reliability of ADWA-HO in autonomous navigation. The most reliable algorithm is ADWA-HO, which minimizes path inflections and turns while achieving outstanding outcomes in terms of path length, motion time, collision rate, motion smoothness, and goal-reaching rate. D* performs the worst, exhibiting slower motion, longer pathways, more collisions, and a lower success rate. Both the fusion of PRM & RRT and PRM & DWA demonstrate strong performance, particularly in minimizing path inflections and reducing the number of turns. However, they remain less efficient compared to the ADWA-HO approach.

Figure 26 represents the algorithms comparison based on path length and motion time in map 2 with RMS error. Figures 27 and 28 illustrate the algorithm comparison based on standard deviation and percentage deviation in path length and motion time in Map 2.

The average percentage variance in path length for Map 1 is presented in Table XI, while for Map 2, it is presented in Table XII. Table XIII compares ADWA-HO to other algorithms in Maps 1 and 2 in terms of experimental path length and percentage difference in motion time.

Table VII. Simulation and experimental performance of each algorithm in Map 2.

Table VIII. Percentage deviation between experimental and simulated path lengths in Map 2.

Table IX. Percentage deviation between experimental and simulated motion time in Map 2.

Table X. Percentage difference in experimental path length and motion time between ADWA-HO and other algorithms in Map 2.

Figure 26. Algorithms comparison based on path length and motion time in Map 2 with RMS error.

Figure 27. Algorithms comparison according to standard deviation and % deviation in path length in Map 2.

Figure 28. Comparison of algorithms according to standard deviation and % deviation in motion time in Map 2.

Figure 29. Percentage change in AGV algorithms, path length, and motion time in Maps 1 and 2.

Figure 29 represents the percentage change in AGV algorithms, path length, and motion time in map 1 and map 2. Figure 30 represents the algorithm comparison based on average percentage change in map 1 and map 2. Comparing ADWA-HO to various algorithms (D*, APF, DWA, PRM & RRT fusion, and PRM & DWA fusion) on two distinct maps, Table XIII compares the path’s length and motion period of time between ADWA-HO and other algorithms. The greatest improvement in percentage difference between ADWA-HO and other algorithms in experimental path length is seen in D* (28.63% in Map 1 and 27.57% in Map 2), while the least improvement is noted against PRM & DWA fusion (10.95% in Map 1 and 10.48% in Map 2). The greatest improvement in percentage difference between ADWA-HO and other algorithms in experimental motion time is seen in D* (27.68% in Map 1 and 19.29 % in Map 2), while the least improvement is noted against PRM & DWA fusion (9.15% in Map 1 and 5.91% in Map 2). ADWA-HO outperforms D*, APF, DWA, PRM & RRT, as well as PRM & DWA, by 28.10%, 22.95%, 21.16%, 17.35%, and 10.71% in the average path length of both maps. ADWA-HO outperforms D*, APF, DWA, PRM & RRT, and PRM & DWA by 23.48%, 17.85%, 15.47%, 11.86%, and 7.53% in the average motion time of both maps. These outcomes demonstrate how successfully ADWA-HO improved the variation in motion time and path length, making it a stronger and more well-suited navigation technique compared with alternative strategies. According to Tables III and VII, due to their simpler formulations, the D* and APF approaches require less computing power; however, they are more prone to path inflections and collisions, thereby reducing efficiency. The DWA optimizes short-range obstacle avoidance but not global path planning due to its moderate processing load from real-time velocity sample evaluation. Sample-based approaches, such as PRM and RRT, require more processing due to graph formation and random tree expansion, but they enhance path smoothness and collision avoidance. By combining global and local planning, the hybrid PRM and DWA algorithm optimizes performance and computing demand. Finally, hybrid optimization makes the suggested ADWA-HO technique more computationally intensive during startup, but once the trajectory is defined, it executes efficiently continuously. ADWA-HO outperforms other approaches in terms of path length, motion duration, smoothness, and goal-reaching rate, while maintaining an acceptable computational complexity for real-time AGV navigation.

Table XI. Average % deviation in path length in Map 1 and Map 2.

Table XII. Average % deviation in motion time in Map 1 and Map 2.

Table XIII. Comparing the experimental path length and motion time difference percentage between ADWA-HO and other algorithms in Maps 1 and 2.

5.1. Hardware structure

The AGV is designed using SolidWorks software and developed from a laser-cut aluminum sheet and 3D-printed mecanum wheels, as shown in Figures A1 and A2 in the appendix. An embedded computer, specifically an NVIDIA Jetson Nano board with 4 GB of LPDDR4 RAM, a quad-core ARM Cortex-A57 CPU, and a 128-core NVIDIA Maxwell GPU, powers the system within the ROS environment. It also features a 40-pin general-purpose input/output (GPIO) header, which connects to sensors, motors, and other equipment. For 360-degree detection, the AGV is equipped with a set of LiDAR sensors connected via USB, enabling it to receive laser data essential for localization and map generation [Reference Tiozzo Fasiolo, Scalera and Maset72]. An STM32 microcontroller is utilized to control the permanent magnet-brushed motors, ensuring precise movement. Additionally, depth cameras facilitate deep learning, system image recognition, and point cloud data collection, thereby enhancing the overall functionality and performance of the AGV [Reference Kang, Zhang, Ge, Liao, Huang, Wu, Yan and Chen73]. The table AI in the appendix shows the overview of software and hardware. The AGV features two LiDAR sensors, YD LiDAR TG-15 and YD LiDAR X4, for obstacle detection and distance measurement, as well as two vision sensors, an Intel depth camera D455 and an Astra Pro Plus depth camera, for object recognition and ambient awareness. Acceleration, angular velocity, and even direction are among the motion-related data that an IMU measures. By utilizing sound waves, the ultrasonic sensor determines the distance to an object to avoid it.

Figure 30. Algorithm comparison based on average percentage change in Maps 1 and 2.

The NVIDIA Jetson Nano CPU performs complex calculations, including fusing sensor data and processing the ADWA-HO algorithm. Ultrasonic sensors provide proximity data for obstacle avoidance and safety in complex environments, while an STM32 motor controller controls mecanum wheel rotations accurately [Reference Waseem, Reddy, Rao, Suhaib and Khan74]. Vision sensors deliver high-resolution video feeds over Camera Serial Interface (CSI) ports for object detection and mapping, while LiDAR sensors transfer real-time data via specialized ports to the Jetson Nano. For close-range obstacle detection, ultrasonic sensors utilize GPIO pins, whereas the Jetson Nano employs a universal asynchronous receiver/transmitter (UART) to operate and provide feedback to the STM32 motor controller. The hardware system wiring diagram and flowchart of the motor control process are shown in Figures A3 and A4 in the appendix, respectively. The AGV’s integrated design enables it to navigate, locate, and avoid collisions accurately in various experimental settings due to its omnidirectional capabilities. The concept emphasizes indoor, well-lit workplaces for human–AGV collaboration. Outdoor applications present distinct challenges, but the technology has considerable potential for extension and use in human–AGV collaborative scenarios beyond interior environments to enhance data quality. Today, humans and AGVs must cooperate closely together to fulfill industrial activities, such as when a machine operator needs the AGV to collect a piece of work [Reference Hasan, Khan, Khatoon and Sajid71]. The AGV needs geometric (location), semantic (description), and search-related activities (contextual logic and algorithmic decision-making). A created map efficiently provides object-specific geometric and semantic information for contextual understanding and decision-making. This work presents a semantic and geometric map-building strategy for improving real-time human–AGV operations in industrial environments. Experimental scenarios I and II demonstrate how this method might avoid unforeseen impediments in a cooperative activity case study where the AGV switches between starting and goal positions. Experimental scenarios III test dynamic outdoor settings. Future industrial workspaces will benefit from combining this map-creation approach with human workers and AGVs for collaborative working. Figure 31 depicts the AGV control structure block diagram.

Figure 31. Block diagram of the AGV control structure.

5.2. Software structure

The software structure of the AGV, which operates on Ubuntu with ROS, is designed to integrate various sensors and controllers, enabling precise navigation, localization, and obstacle avoidance in both dynamic and static environments [Reference Tang, Zhou, Zhang, Liu, Liu and Ding75].

5.2.1. ROS Framework on Ubuntu

The entire software stack is powered by Ubuntu, with ROS serving as the middleware and providing crucial functions such as package management, low-level device control, device abstraction, and message passing. All hardware and algorithms are contained within ROS nodes, which exchange messages, services, and topics with one another.

Figure 32. Robot operating system (ROS)-based real-time environment simulation.

6.1 Experiment scenario I

A scenario of the first experiment will be conducted in an environment with the presence of unknown static obstacles. Figure 33 depicts the original scenario’s two-dimensional map, which is free from impediments and was constructed using the SLAM technique. On the other hand, as shown in Figure 34, the actual area being navigated is filled with impediments, such as boxes and sheets. During the navigation process, the AGV is able to sense the barriers because it has no prior knowledge of them. The geographical distribution of these obstacles is designed to significantly obstruct the path of the AGV as it moves toward the destination. Figure 35 shows the actual AGV position recorded during experimental scenario I, as well as the time sequence of AGV navigation as seen in ROS RViz. This comparison demonstrates the effectiveness of the navigation system by highlighting the alignment between the simulated and actual trajectories. Figure 35a provides a visual representation of the reference path, the goal, and the starting point. Figure 35b–d depicts the movements of the AGV as it navigates around the obstacles that have been present, and Figure 35e depicts the actual trajectory that the AGV must take in order to successfully attain the goal. It can be observed that the AGV moves in a flexible manner between the obstacles, and the trajectory is considerably different from the reference path. This indicates that the suggested approach successfully led the AGV through an environment with static obstacles from the starting point to the target point.

Figure 33. Original map of experimental scenario I.

Figure 34. Actual experiment scenario I.

Figure 35. The process of AGV’s testing in experiment scenario I from a to e.

6.2 Experiment scenario II

The experiment’s second scenario is conducted in an environment where two little Arduino-based AGVs serve as the dynamic obstacles. It is crucial to remember that the original ADWA-HO has been significantly enhanced to improve navigation performance in dynamic environments as well. Scenario II, in which the mecanum wheel AGV’s trajectory is considerably disrupted twice by dynamic obstacles (small differential-wheeled AGVs) in its direction toward the target, will be described. Figure 36 illustrates the original scenario of the two-dimensional map, which is free from impediments and was constructed using SLAM. On the other hand, as shown in Figure 37, the actual area being navigated is filled with two small differential-wheeled AGVs. The temporal sequence of the AGV navigation, visualized in ROS RViz, and the corresponding real AGV position in experiment scenario II are depicted in Figure 38. Figure 38a provides a detailed representation of the reference path, the goal, and the starting point. Because the initial map does not contain any obstructions, the reference path leads directly to the place of interest. Figure 38b–e illustrates the actions of the AGV as it navigates around the two small moving AGVs. In the event that a small AGV prevents the large AGV from moving forward, the large AGV will move away from the small AGV (refer to Figure 38b, c). When the small AGV is a significant distance away from the large AGV (i.e., more than 0.20 m), the large AGV will begin to move in the target’s direction after dynamic obstacle avoidance, that is, the small AGV (see Figure 38). In practical terms, once a dynamic obstacle is detected within a radius of less than 0.20 m, the AGV enters a wait or detour behavior. As soon as the dynamic obstacle moves beyond this threshold, the local costmap is updated, and the AGV resumes path planning toward its target, as illustrated in Figure 38. A buffer zone is established to compensate for sensor update delays and AGV deceleration lag, thereby reducing the risk of collision with fast-approaching or unpredictable obstacles. In Figure 38e, the actual trajectory that the AGV takes when it successfully reaches the objective is depicted. As can be observed, the real trajectory of the large moving AGV is considerably distinct from the reference path. This demonstrates that the suggested method is capable of successfully navigating the AGV in a dynamic environment with two small moving AGVs as obstacles.

Figure 36. Original map of experimental scenario II.

Figure 37. Actual experiment scenario II.

Figure 38. The process of AGV’s testing in experiment scenario II from a to e.

6.3 Experiment scenario III

The final experiment is conducted outdoors, where the AGV must navigate between the start and goal locations while avoiding both dynamic and static obstacles in real time. Figure 39 displays a mapped environment in RViz, with the workspace denoted by defined bounds and gridlines. The working area is delineated by a hexagonal form, which changes dynamically as the AGV moves from one location to another. The AGV’s intended mapping process is shown by the green line. It illustrates how the AGV adjusts its trajectory to steer clear of obstacles as it approaches its target. The map indicates barriers that represent either stationary or moving elements of the surroundings. These are identified by the AGV’s sensors, which include depth cameras and LiDAR sensors. The AGV’s costmap can be observed by the gradation of red and blue hues surrounding obstacles. The AGV refrains from traveling through red zones, which are areas closer to obstacles and have higher costs. Safe paths are indicated by lower-cost regions, that is, blue zones. The costmap and path are constantly adjusted in real time as the AGV advances to account for environmental changes. This enables the AGV to travel quickly when encountering impediments that are stationary, moving, or have just been detected. The global plan, sensors scan, and local costmap belong to the inputs required to configure the navigation stack. Figures 40 and 41 illustrate the steps involved in testing an AGV in experiment scenario III, which includes nine static and three dynamic impediments, respectively, in an outdoor setting. They also provide a thorough depiction of the objectives, the initial point, and the path taken to attain the target.

Figure 39. Mapping in the outdoor environment in a) and b).

Figure 40. The process of AGV’s testing in experiment scenario III with static obstacles from a to c.

Figure 41. The process of AGV’s testing in experiment scenario III with static and dynamic obstacles from a to b.

The ADWA-HO algorithm’s real-time adaptability and efficacy were confirmed by the ROS-based outdoor AGV testing. This demonstrates its ability to adapt to both external static and dynamic situations. Using LiDAR and depth cameras, the AGV skillfully avoids both stationary and moving impediments as it moves from its starting point to its destination. With the help of the dynamically updated costmap, it selects safe routes by avoiding more expensive locations. Hexagonal gridlines enhance path planning, while RViz’s environment trajectory confirms accurate navigation. The algorithm’s resilience in real-time replanning is demonstrated by the AGV’s ability to dynamically adjust the route in response to static and moving obstructions.

Moving obstacles are identified via sensor fusion between LiDAR scans and depth images. The velocity vector and distance threshold (approximately 0.20 m) are used to classify an obstacle as dynamic. As soon as a dynamic obstacle is detected within a proximity range of less than 0.20 m, the local costmap assigns a high traversal cost to the immediate vicinity (red zones in the costmap), prompting the planner to seek alternative paths. The ADWA-HO algorithm triggers a local trajectory replanning if obstacles are predicted to intersect the current path. The AGV slows down, waits, or circumvents the obstacle based on proximity and motion trajectory. After successfully avoiding the obstacle, the AGV smoothly returns to a globally optimized path, ensuring goal convergence without significant trajectory drift. The above three figures illustrate the global costmap, sensor scans, and path adaptation (Figure 39), as well as trajectory adjustments made by the AGV to avoid nine static obstacles and account for sensor noise (Figure 40). The AGV’s local path deviations around the three dynamic obstacles, along with static obstacles, with visible smooth inflection points and avoidance maneuvers (Figure 41). This dynamic motion modeling of the obstacles and the AGV’s responsive strategy demonstrates the robustness of the ADWA-HO algorithm, validating its capability to handle unpredictable real-world navigation challenges in static and dynamic environments.

6.4 Dynamic obstacle avoidance

The AGV employs a hybrid navigation stack that integrates local and global planning to address these dynamics. While the local planner (DWA) continuously modifies the trajectory based on real-time sensor data, the global planner creates an initial path using a map of the environment. Strategies for managing dynamic obstacles include:

Real-time Detection: Continuous scanning of the environment is performed by LiDAR and depth cameras. Based on motion patterns, which are differences between successive scans, dynamic as well as static objects that have been detected are identified.

Costmap Update: Through the utilization of the ROS navigation stack, dynamic barriers can be added to the local costmap in the form of inflated high-cost zones. Because of this, the AGV is unable to choose routes that bring it close to moving impediments and therefore avoids the obstacles.

Trajectory Replanning: The AGV immediately begins the process of local trajectory replanning using DWA whenever it is anticipated that an obstacle will intersect the current path. This process involves computing velocity commands that avoid collisions while maintaining proximity to the global path.

Predictive Behavior: To anticipate future positions and adjust the path accordingly, a short-term motion prediction model is utilized for obstacles that are in motion. This model involves velocity extrapolation throughout one to two seconds.

Safety Buffering: A dynamic safety buffer is maintained around moving objects, approximately ranging from 0.15 to 0.30 m, and its size grows or decreases depending on the speed of the obstacle and its proximity.

6.5 Observed limitations

Real-world tests were conducted in various indoor and outdoor environments, as well as under different obstacle dynamics, to thoroughly evaluate the effectiveness and long-term reliability of the proposed hybrid navigation system. The AGV’s decision-making and path planning endurance was tested in unknown static barriers, dynamic interference from other AGVs, and harsh outside environments with static and dynamic variables. From every scenario, the system’s safety and collision prevention strengths, as well as stress-related behaviors such as careful maneuverability, temporary delays, and path recalculations, are revealed. The outcomes and system actions for each experimental scenario are listed below:

• • In experiment scenario I (unknown static obstacles), the AGV occasionally exhibited minor deviations and increased lateral clearance while navigating through tightly packed static obstacles. This was due to the cautious behavior of local planners, which prioritizes safety when real-time updates show high obstacle density. In rare cases, this led to path segments that were longer than optimal, reflecting a conservative trade-off between safety and efficiency.

• • When two little Arduino-based AGVs concurrently approached the main AGV from convergent directions in experiment scenario II (dynamic barriers), the system initiated a brief pause and replanning cycle. Although collision avoidance was maintained, this behavior caused little delay in achieving the goal. Furthermore, the replanning process occasionally produced zigzag courses when the processor recalculated the best escape routes if the dynamic AGVs suddenly changed direction or hovered nearby.

• • Strong ambient lighting occasionally resulted in transient reflections in LiDAR returns from the shiny objects in experiment scenario III (outdoor setting with static and dynamic obstacles). This resulted in too cautious rerouting and exaggerated obstacle bounds. Additionally, because the costmap was updated frequently, short local trajectory oscillations were seen when dynamic and static barriers were grouped together. Nonetheless, the system continuously recovered and stayed clear of accidents, demonstrating the hybrid planner’s resilience.