Comparative Analysis and PSO-Based Optimization of Battery Technologies for Autonomous Mobile Robots

Abstract

Autonomous mobile robots are transforming industries from e-commerce logistics to field exploration, but their effectiveness depends on onboard energy storage. This study addresses the challenge of selecting optimal battery technologies for autonomous mobile robots, balancing performance, energy efficiency, thermal stability, and cost across diverse applications. We focus on lithium-ion, lithium-polymer, and nickel-metal hydride batteries, the most common power solutions, each with distinct advantages and disadvantages in energy density, form factor, thermal stability, and cost. A dynamic modeling and simulation framework in MapleSim evaluated these chemistries under defined and representative operating conditions, tracking state of charge and temperature during charging and discharging. A Particle Swarm Optimization algorithm evaluated 37 battery configurations by thermal stability, energy efficiency, and cost across five use cases. Key results indicate that for logistics and warehousing, lithium nickel manganese cobalt oxide with graphite is optimal; for healthcare, lithium nickel manganese cobalt oxide with lithium titanate oxide excels; for manufacturing, lithium nickel cobalt aluminum oxide with graphite leads; for agricultural robots, lithium manganese oxide with graphite is best; and for exploration and mining, lithium iron phosphate with graphite is most reliable. These results provide a structured basis for battery selection, showing how simulation-driven, multi-criteria decision-making enhances energy management and operational reliability.

1. Introduction

1.1. Battery Technologies for Autonomous Mobile Robots

The development of autonomous mobile robots (AMRs) has received a lot of attention because of potential applications in various fields, such as logistics, healthcare, and production. Prior studies have shown that dynamic modeling and control of mobile manipulators are critical for ensuring effective operation in such domains [1,2,3]. Moreover, recent reviews emphasize that the main limitation for mobile robot performance lies in their energy source, with batteries often being the weakest link in autonomy [4]. Battery selection is therefore not an afterthought but a decisive factor that directly determines robot performance, reliability, and safety [5,6]. For example, modified ride-on cars used in pediatric rehabilitation provide a practical application where battery-powered mobility directly supports developmental outcomes in children with cerebral palsy [7].

The efficiency and performance of this robot depend heavily on the type of battery. Different types of batteries, including lithium-ion (Li-ion), lithium polymer (LiPo), and nickel metal hydride (NiMH), are typically used in AMRs. Each has its own advantages and disadvantages in terms of energy density, lifespan, security, and costs. Li-ion batteries are widely studied because they are able to store a lot of energy, last long, and do not lose their charge so quickly. On the other hand, since the LiPo battery can be made in a size and shape suitable for a special design, it provides more versatility. NiMH batteries have a shorter service life and require more maintenance. Li-ion batteries are currently the most widely used energy storage solution for AMRs, owing to their high energy density, long cycle life, and ability to support diverse power demands. Touzout et al. [8] integrated detailed energy consumption modeling into a Gazebo/robot operating system (ROS) simulation of a mobile robot, demonstrating how realistic simulator-based power models can predict and optimize onboard battery usage. Aydın et al. [9] review air-cooling thermal management for Li-ion batteries in AMRs, noting that confined robot designs and limited cooling space require careful air-based cooling strategies to maintain battery safety and longevity. McNulty et al. [10] evaluated current commercial AMRs, examining their energy consumption trends and battery pack parameters. McNulty et al. [10] further explored the operation of Li-ion batteries and suggested Li-ion batteries containing a LiFePO4 cathode and a graphite anode are the most suitable choice to better support the increasing power demands of future AMRs.

Many investigations have been carried out on how different battery types perform in AMRs. Alashur [11] reviewed the latest developments in Li-ion technology. The study highlighted enhancements in battery materials and design, which result in increased energy density, faster charging times, and higher efficiency. Berenz et al. [12] presented a new approach to assessing the risk of a battery in mobile robots. This method deals with uncertainties in connection with the effective battery capacity, the electric discharge rate, and the energy that is necessary to reach the charging station by using the probability density functions. Attanayaka et al. [13] compared various state of charge (SOC) assessment methods to determine their effectiveness in both static and dynamic contexts.

Li-ion batteries are available in various chemistries, each offering unique advantages and trade-offs. The materials of the positive electrode (cathode) and negative electrode (anode) significantly influence key performance characteristics of the battery, such as the energy density, lifespan, safety, and costs. Common cathode materials include lithium iron phosphate (LFP), lithium cobalt oxide (LCO), and lithium nickel manganese cobalt (NMC). Among these, NMC and LFP batteries exhibit distinct environmental footprints, with NMC showing higher greenhouse gas emissions due to cobalt and nickel production, while LFP offers lower environmental impact [14,15]. Beyond their environmental footprint, the operational lifespan of NMC-based cells is a critical economic factor, driving the need for accurate models to predict their remaining useful life [16]. Anode material typically consists of graphite, lithium titanate oxide (LTO), and lithium titanium oxide. Malik et al. [17] provided an in-depth examination of both established and Li-ion battery technologies and emphasized their energy capacities, cycle life, and different applications.

1.2. Energy Efficiency and Computational Tools in AMR Design

Energy efficiency is a crucial factor in the design and operation of AMRs. Scheduling battery charging as a multi-objective sequential decision-making problem in a time-dependent Markov decision process (MDP) allows robots to learn when high-value tasks are most likely to arrive and thus plan charging during anticipated low-demand periods [18]. This approach outperformed traditional rule-based schedulers by flexibly balancing the value of current tasks against predicted future rewards to determine optimal charging times [18]. Mei et al. [19] built detailed power models for motion, sonar sensing, and control on a Pioneer 3DX platform and found that motion accounted for less than 50% of total energy consumption, highlighting the importance of managing non-locomotive power drains. They showed that integrating dynamic power management with real-time scheduling algorithms and motion planning may significantly increase total robot energy efficiency [19]. Teso-Fernández et al. [20] embedded an energy-aware battery model into a predictive dynamic-window planner and reported measurable reductions in locomotion energy consumption, illustrating how trajectory planning directly impacts battery drain. Rong et al. [21] developed a stochastic, battery-aware dynamic power management framework that captures both rate-capacity effects and relaxation-induced recovery in rechargeable cells, formulating and solving it as a linear-programming-based policy optimization problem. Their method delivered up to 17% more energy per unit battery weight compared to existing heuristic strategies under latency and loss constraints. Mageshkumar et al. [22] demonstrated that adaptive energy management strategies can significantly extend AMR operational time by aligning power use with real-time task demands. Wu et al. [23] reviewed the state of the art for energy efficiency in AMRs and focused on energy sources, consumption models, and optimization methods. Their results suggest that hybrid models that combine different energy sources offer higher accuracy and robustness compared to models using just one source. In addition, locomotion contributes significantly to the total energy consumption of a mobile robot, which underlines the need for optimized control methods. Muru and Rassõlkin [24] emphasize that in industrial robot systems, energy consumption is determined jointly by mechanical design, actuator systems, and control strategies, highlighting the need for holistic energy optimization in robotic platforms. Parallel to the optimization of energy systems, the structural integrity of AMRs is paramount. Advanced modeling techniques like the Fifth-Order Shear and Normal Deformation Theory are thus employed to analyze and enhance the impact resistance of composite components under dynamic loads [25], highlighting the multi-disciplinary design approach required for robust robotic platforms.

AMR battery selection takes into account a number of aspects, including performance, cost, and energy efficiency. Different approaches are utilized to identify the best solutions for specific applications. For example, using neural network-based optimization algorithms such as back propagation (BP) [26], particle swarm optimization (PSO) [27], and cuckoo search (CS) [28], to predict the lifespan of materials. PSO was used to optimize the design parameters of a Stewart robot and reduced the power usage of the robot by 88.3% [29]. Zheng et al. [30] applied PSO to mobile-robot path planning and reported faster convergence and measurable energy savings in simulated navigation tasks, supporting PSO’s suitability for energy-aware optimization in AMR systems.

Beyond traditional analytical methods, metaheuristic optimization algorithms have emerged as powerful tools for addressing complex, multi-objective problems in battery modeling and energy system design. Recent studies demonstrate the efficacy of particle swarm optimization (PSO) and related bio-inspired algorithms across diverse battery-related applications. In lithium-ion battery modeling, comparative analyses between PSO and grey wolf optimization (GWO) have shown that both algorithms significantly enhance the accuracy of electrochemical models, with GWO-optimized models achieving a 42% average reduction in root mean square error (RMSE) compared to non-optimized baselines [31]. Hybrid approaches, such as a PSO-GWO algorithm combined with chaotic mapping and hybrid kernel extreme learning machines, have further improved the stability and convergence speed for estimating battery state of health, maintaining prediction fits above 0.99 [32]. For mobile robotic platforms, PSO and GWO have been successfully applied to the optimal sizing of hybrid energy sources, including fuel cells, photovoltaic panels, and battery packs, in agricultural mobile robots, extending operational autonomy by 350% and reducing system costs by at least 8% compared to theoretical sizing methods [33]. In charging optimization, a PSO-based fuzzy-controlled strategy has been shown to identify multistage charging patterns that reduce charging time by 56.8% and extend battery cycle life by 21% compared to conventional constant current-constant voltage methods [34]. Similarly, in hybrid renewable energy systems, hybrid genetic-PSO and multi-objective PSO (MOPSO) algorithms have effectively minimized the total present cost while satisfying reliability constraints for off-grid power systems [35]. These studies collectively underscore the versatility, robustness, and computational efficiency of population-based optimization algorithms, particularly PSO and its variants, in navigating high-dimensional, non-linear design spaces. This evidence strongly supports the adoption of PSO for the multi-criteria battery selection problem addressed in the present study, where application-specific trade-offs between thermal stability, energy efficiency, and cost must be systematically resolved.

1.3. Recent Advances in AMR Power Systems: A Comparative Review

To provide a comprehensive comparison and explicitly highlight the novel contributions of our study against existing research, we have reviewed recent, closely related works. Table 1 summarizes these studies and compares key aspects such as scope, methodology, and unique contributions. This comparison underscores the innovation of our research, which lies in the integrated use of high-fidelity dynamic simulation for 37 distinct battery chemistries (including specific anode/cathode combinations) combined with a formal multi-objective optimization algorithm (PSO) tailored to application-specific priorities. This approach moves beyond the general recommendations found in review papers [4,10,36] and the narrower focus of empirical studies [37], providing a data-driven, reproducible framework for optimal battery selection.

1.4. Novel Contributions and Modular Framework of the Study

What makes this study innovative is the detailed modeling and simulation of different battery types, including Li-ion, LiPo, and NiMH batteries, each of which has distinct electrode chemistries. By testing all possible battery models under different operating conditions, the research provides insights for selecting the best battery for specific AMR applications. Not only does the simulation cover both discharging and charging processes to provide a thorough evaluation of each battery, but it also uses the PSO to compare and assess the cost-effectiveness and energy efficiency of each model. This combination of detailed simulation and advanced algorithm makes the study highly important and practical, and contributes to the development of AMRs.

In addition, the simulation architecture is modular, with separate modules for the battery model, control block, robot mechanism, and electric motor. This modular design enables independent tests and detailed analysis of changes in every part of the system. Such an approach ensures that each course focused on individual modules is valuable and rewarding. It also offers flexibility for future studies to expand this research by exploring deeper modules, thereby enriching the understanding and optimization of AMR systems.

Table 1. Comparison of recent works in AMR battery technologies and power efficiency.

Reference
[36]	Scope	Systematic review and comparison of battery efficiency	Focus	Battery materials, efficiency, performance, and future directions
[37]		Energy prediction and optimization for AMRs		Real-time energy consumption, path models, obstacle avoidance
[10]		Review of Li-ion batteries, perspectives, and outlook		Power consumption, battery pack specifications, and future recommendations
[4]		Systematic review of energy sources, battery efficiency		Energy sources, specifications, classifications, opportunities, threats
[38]		Survey of power solutions for mobile robots		Mechanical design, perception, navigation, control, and power solutions
This Study		Modeling, simulation, and optimization of AMR batteries		Comprehensive evaluation of different battery types, chemistries, discharging/charging processes
[36]	Novelty	Proposes algorithms for energy source & system power supply selection, addressing resource-limited scenarios
[37]		Comprehensive energy prediction model with real-time component consumption profiling, energy-efficient path selection
[10]		Recommendations for cathode/anode materials to meet future power demands of AMRs
[4]		Proposes algorithms for energy source and system power supply selection, emphasizing resource minimization
[38]		Reviews energy solutions, highlights research gaps, provides guidelines for selecting robot energy sources
This Study		Detailed simulation of various battery types, chemistries; evaluates discharging and charging processes, using PSO for cost-effectiveness and energy efficiency analysis
[36]	Methodology	Narrative review, systematic analysis, bibliographic databases, critical analysis	Unique Contribution	Analysis of technologies under resource limitations, generates discussion within the community
[37]		Empirical studies, energy prediction model, real-time profiling, path models		Identifies lack of coordination between computation and control as a source of inefficiency, achieving 44.8% reduction in energy consumption
[10]		Literature review, comparison of commercial AMRs, battery specifications, and future recommendations		Detailed discussion on lithium-ion battery operation, short-term and long-term recommendations
[4]		Narrative review, systematic analysis, bibliographic databases, critical analysis		Discusses opportunities and threats in global policies, energy-saving technologies
[38]		Summary and review of literature, categorization of solutions, highlighting research gaps		Highlights current limitations and future directions, focuses on real-world applications and constraints
This Study		Highlights current limitations and future directions, focuses on real-world applications and constraints		Combines detailed simulation and advanced algorithm (PSO), provides a robust framework for battery selection in AMRs, with modular design for flexibility and future expansion

Table 1. Comparison of recent works in AMR battery technologies and power efficiency.

Reference
[36]	Scope	Systematic review and comparison of battery efficiency	Focus	Battery materials, efficiency, performance, and future directions
[37]		Energy prediction and optimization for AMRs		Real-time energy consumption, path models, obstacle avoidance
[10]		Review of Li-ion batteries, perspectives, and outlook		Power consumption, battery pack specifications, and future recommendations
[4]		Systematic review of energy sources, battery efficiency		Energy sources, specifications, classifications, opportunities, threats
[38]		Survey of power solutions for mobile robots		Mechanical design, perception, navigation, control, and power solutions
This Study		Modeling, simulation, and optimization of AMR batteries		Comprehensive evaluation of different battery types, chemistries, discharging/charging processes
[36]	Novelty	Proposes algorithms for energy source & system power supply selection, addressing resource-limited scenarios
[37]		Comprehensive energy prediction model with real-time component consumption profiling, energy-efficient path selection
[10]		Recommendations for cathode/anode materials to meet future power demands of AMRs
[4]		Proposes algorithms for energy source and system power supply selection, emphasizing resource minimization
[38]		Reviews energy solutions, highlights research gaps, provides guidelines for selecting robot energy sources
This Study		Detailed simulation of various battery types, chemistries; evaluates discharging and charging processes, using PSO for cost-effectiveness and energy efficiency analysis
[36]	Methodology	Narrative review, systematic analysis, bibliographic databases, critical analysis	Unique Contribution	Analysis of technologies under resource limitations, generates discussion within the community
[37]		Empirical studies, energy prediction model, real-time profiling, path models		Identifies lack of coordination between computation and control as a source of inefficiency, achieving 44.8% reduction in energy consumption
[10]		Literature review, comparison of commercial AMRs, battery specifications, and future recommendations		Detailed discussion on lithium-ion battery operation, short-term and long-term recommendations
[4]		Narrative review, systematic analysis, bibliographic databases, critical analysis		Discusses opportunities and threats in global policies, energy-saving technologies
[38]		Summary and review of literature, categorization of solutions, highlighting research gaps		Highlights current limitations and future directions, focuses on real-world applications and constraints
This Study		Highlights current limitations and future directions, focuses on real-world applications and constraints		Combines detailed simulation and advanced algorithm (PSO), provides a robust framework for battery selection in AMRs, with modular design for flexibility and future expansion

2. Modeling and Simulation

This section includes the dynamic modeling and simulation of a battery-sourced AMR model using MapleSim. The model incorporates various design parameters, including the battery’s chemistry, the number of cells, and capacity, providing a comprehensive tool for evaluating different battery configurations. Three common battery models were compared: Li-ion, LiPo, and NiMH. Each chemistry exhibits distinct electrochemical properties and trade-offs in performance, safety, and cost, as summarized in

Table 2. Comparative analysis of battery chemistries for AMR applications [10,39,40].

	Energy Density (Wh/L)	Specific Energy (Wh/kg)	Life (Cycles)	Safety	Thermal Stability	Cost (USD/kWh)	Self-Discharge Rate (per Month)	Form Factor	Typical Applications
Li-ion	250–400	150–250	500–1500	Moderate	Sensitive to >45 °C	120–200	2–3%	Rigid cylindrical/prismatic	High-power & logistics AMRs
LiPo	200–350	130–200	300–1000	Moderate	Sensitive to >40 °C	150–300	3–5%	Flexible, thin-film	Space-Constrained & AMRs, drones
NiMH	140–300	60–120	500–800	High	Stable up to 60 °C	80–150	10–15%	Cylindrical	Low-power AMRs & Safety-critical roles,

.

Li-ion batteries employ liquid electrolytes and rigid metal casing, offering high energy density and stable voltage output. A solid polymer matrix takes the place of the liquid electrolyte in LiPo batteries, a subclass of Li-ion technology, allowing flexible, lightweight packaging without external metal housings. Although LiPo and conventional Li-ion have comparable electrochemical characteristics, their distinct structure enables the creation of bespoke geometries, which makes them ideal for AMR systems with limited space. However, the manufacturing complexity of LiPo increases the cost by about 20–30% compared to normal Li-ion cells.

NiMH batteries use a hydrogen-absorbing alloy anode and an alkaline electrolyte. Although NiMH cells have low internal resistance and strong thermal stability, their lower specific energy (60–120 Wh/kg compared to 150–250 Wh/kg for Li-ion) limits operating time. Furthermore, NiMH batteries have a high rate of self-discharge (10–15% per month), which eventually reduces the SOC withheld. The SOCs of Li-ion, LiPo, and NiMH batteries for a similar usage are compared in Figure 1.

The best option for AMRs is Li-ion batteries because of the following:

▪

High Energy Density: Enables extended operational runtime (critical for warehouse/logistics AMRs).

▪

Superior Cycle Life: Withstands 500–1500 cycles, lowering replacement frequency and lifecycle costs.

▪

Balanced Cost-to-Performance Ratio: Lower cost per kWh than LiPo and higher energy density than NiMH.

▪

Adaptability: Compliance with fast-charging systems supports high-uptime operations.

Figure 1. Comparing SOC of Li-ion, LiPo and NiMH batteries in a similar application.

Figure 1. Comparing SOC of Li-ion, LiPo and NiMH batteries in a similar application.

While LiPo offers advantages in spatial flexibility and NiMH in thermal safety, Li-ion’s holistic performance aligns with AMR needs for energy economy, durability, and cost-effectiveness. The model incorporates essential design factors to replicate battery performance under realistic operational conditions. Central to the concept is the arrangement of the battery pack, defined by the number of cells, which directly affects the system’s voltage and capacity. These parameters are tuned to fit the energy demands of the AMR’s locomotion and payload, establishing a balance between runtime and power supply. Additionally, the total battery capacity is optimized to minimize weight while maintaining mission length requirements, a vital factor for mobile robots operating in dynamic environments.

The AMR’s mobility is guided by a proportional integral derivative (PID) controller, which dynamically adjusts the motor input to maintain the robot’s velocity along a specified trajectory. The PID controller evaluates the error between the desired setpoint velocity and the actual measured velocity, applying proportional ($K_p$), integral ($K_i$), and derivative ($K_d$) gains to reduce deviations. This closed-loop control system adapts to external disturbances, such as uneven terrain or cargo shifts, ensuring stable navigation. For example, the integral term removes steady-state errors during protracted uphill climbs, while the derivative term dampens oscillations induced by rapid changes in direction. The PID controller dynamically adjusts the pulse width modulation (PWM) signal delivered to the electric motor, enabling precise conversion of battery-supplied electrical energy into mechanical motion.

The motor’s simulation model simulates the electromechanical energy transfer process, integrating real-world variables such as efficiency losses, back electromotive force (EMF), and torque-speed relationships. The motor’s performance is intimately related to the battery’s SOC and temperature, as higher current draw during acceleration or climbing raises Joule heating and accelerates capacity decline. To solve this, the control unit integrates an energy-aware algorithm that optimizes current flow between the battery and motor. By monitoring metrics in real time, such as SOC, temperature, load demand, and hierarchical controller efficiency, the system can, for example, reduce current during steady-state operation to prevent overheating. As shown in Figure 2, the model architecture integrates these subsystems with modular frames to enable battery chemistry, PID adjustment, and motor efficiency re-evaluation tests. The modularity ensures that changes in a component (for example, the change in cathode materials) do not affect the entire system, allowing rapid comparison of configurations.

Dynamic modeling begins by determining the main conditions and parameters that will regulate the work of the robot. For this study, the battery is specified with a capacity of 25 Ah, an initial state of charge of 1, and an ambient temperature of 298.15 K. The pack consists of six cells in series, a cell-specific heat capacity of 750 J/(kg·K) and a convective heat transfer coefficient of 10 W/m²·K is used to model thermal exchange (Details of the battery modeling parameters are listed in

Table A1. Details of battery modeling parameters.

Parameter	Value	Unit
Factor for reaction rate equation	1.2	${\displaystyle \frac{\mathrm{m}}{\mathrm{s}}}$
Diffusion coefficient at standard condition	1.8 × ${10}^{-19}$	${\displaystyle \frac{{\mathrm{m}}^2}{\mathrm{s}}}$
Activation energy	10,000	${\displaystyle \frac{\mathrm{J}}{\mathrm{m}\mathrm{o}\mathrm{l}}}$
Molar mass of SEI layer	0.026	${\displaystyle \frac{\mathrm{k}\mathrm{g}}{\mathrm{m}\mathrm{o}\mathrm{l}}}$
Radius of particle of active material in anode	0.000002	$\mathrm{m}$
Initial state of health	1	-
Molar concentration of electrolyte	5000	${\displaystyle \frac{\mathrm{m}\mathrm{o}\mathrm{l}}{{\mathrm{m}}^3}}$
Specific conductivity coefficient	0.001	${\displaystyle \frac{\mathrm{m}}{\Omega }}$
Density of SEI layer	2600	${\displaystyle \frac{\mathrm{k}\mathrm{g}}{{\mathrm{m}}^3}}$
Number of cells in series	6	-
Battery capacity	25	$\mathrm{A} \mathrm{h}$
Initial state of charge	1	-
Minimum state of charge	0.01	-
Fixed cell resistance	0.005	$\Omega$
Specific heat capacity of cell	750	${\displaystyle \frac{\mathrm{J}}{\mathrm{k}\mathrm{g} \mathrm{K}}}$
Mass of cell	0.55	$\mathrm{K}\mathrm{g}$
Convective heat transfer coefficient	10	${\displaystyle \frac{\mathrm{W}}{{\mathrm{m}}^3 \mathrm{K}}}$
Cell surface area	0.0085	${\mathrm{m}}^2$
Ambient temperature	298.15	$\mathrm{K}$
Electrolyte diffusion coefficient	${7.5\times 10}^{-11}$	${\displaystyle \frac{{\mathrm{m}}^2}{\mathrm{s}}}$
Li ion diffusion coefficient in the intercalation particles of the negative electrode	${3.9\times 10}^{-14}$	${\displaystyle \frac{{\mathrm{m}}^2}{\mathrm{s}}}$
Li ion diffusion coefficient in the intercalation particles of the positive electrode	${1\times 10}^{-14}$	${\displaystyle \frac{{\mathrm{m}}^2}{\mathrm{s}}}$
Thickness of negative electrode	0.000088	$\mathrm{m}$
Thickness of positive electrode	0.0008	$\mathrm{m}$
Thickness of separator	0.000025	$\mathrm{m}$
Radius of intercalation particles at negative electrode	0.000002	$\mathrm{m}$
Radius of intercalation particles at positive electrode	0.000002	$\mathrm{m}$
Bruggeman coefficient	1.5	-
Initial concentration of li in electrolyte	5000	${\displaystyle \frac{\mathrm{m}\mathrm{o}\mathrm{l}}{{\mathrm{m}}^3}}$
Maximum concentration of li at anode	30,555	${\displaystyle \frac{\mathrm{m}\mathrm{o}\mathrm{l}}{{\mathrm{m}}^3}}$
Maximum concentration of li at cathode	51,554	${\displaystyle \frac{\mathrm{m}\mathrm{o}\mathrm{l}}{{\mathrm{m}}^3}}$
Volumetric fraction of negative electrode fillers	0.0326	-
Volumetric fraction of positive electrode fillers	0.025	-
Porosity of negative electrode	0.485	-
Porosity of positive electrode	0.385	-
Porosity of separator	0.724	-
Conductivity of solid phase of negative electrode	100	${\displaystyle \frac{\mathrm{S}}{\mathrm{m}}}$
Li ion transference number in the electrolyte	0.363	-

of Appendix A). The path is not only a straight line. It incorporates many difficulties, such as bends and slopes, to properly test the capacity of the battery. To quantitatively define the operational conditions, specific physical and environmental parameters were established. The AMR has a total mass of 350 kg and operates on tires with a radius of 0.36 m. The drag force opposing motion is characterized by coefficients derived from the robot’s physical form: a drag area of 2.3 m², a drag coefficient of 0.28, and an air density of 1.2 kg/m³. The robot’s velocity profile (Figure 3), which defines the driving cycle and includes accelerations, decelerations, and constant velocity segments representative of typical AMR tasks, is applied as the reference input to the PID controller. These concrete parameters ensure the simulation replicates a realistic dynamic load profile, directly linking the robot’s mechanical demands to the battery’s electrical and thermal response. We also examine different types of battery chemistry, each with their own characteristics that influence how much energy you can store, how well you deal with warmth, and how long it will take over time. By simulating these different chemicals, we can find out which is best suited for different uses of the AMR. In addition, we tune the parameters of our PID controllers to adapt the proportional, integral, and derivative gains to achieve optimal robot performance. The control system plays a crucial role in managing how electricity flows from the battery to the motor. It makes real-time adjustments based on how fast the robot is moving and how heavy a load it is carrying. This ensures the robot operates smoothly and helps to extend the battery’s life.

The main output of the simulation is the battery temperature and SOC during discharge and charge. These outputs are crucial for evaluating battery performance and determining its suitability for various applications. Maintaining low battery temperatures is critical for optimal performance and safety. Since low battery temperatures are crucial for performance and safety, the simulation monitors the battery temperature while the robot follows its trajectory; therefore, potential overheating issues can be identified and addressed. Another important factor is the SOC, which indicates how much energy remains in the battery. The simulation provides real-time SOC data to predict battery runtime and plan recharging or replacement. By continuously monitoring the SOC, we ensure that the robot can complete its tasks effectively.

Simulation results were analyzed to establish the efficiency and effectiveness of each battery design. By comparing energy usage and SOC data for several battery chemistries, the simulations can identify the most energy-efficient configuration. This involves assessing how well each battery maintains its charge and provides power along the robot’s trajectory. Battery temperature data are analyzed to evaluate the thermal stability of each chemistry. Maintaining a lower operating temperature is preferred, as it extends battery lifetime and enhances safety. To better interpret the simulation results, a reduced-order dynamic model of the AMR system was derived from the symbolic differential-algebraic equations (DAEs) generated in MapleSim. The model captures the interaction among the battery, motor, vehicle dynamics, and PID control system. The selected state vector for the system is defined in

Table 3. The Vector definition.

Vector	Definition
$SOC\left(t\right)$	Battery state of charge
$T_b\left(t\right)$	Battery temperature
${\omega }_m\left(t\right)$	Motor angular velocity
$\vartheta \left(t\right)$	Robot linear velocity
$i_e\left(t\right)$	Integral term of the PID controller

.

The control inputs to the system are:

• $I_b\left(t\right)$: Current drawn from the battery
• ${\vartheta }_{ref}\left(t\right)$: Desired linear velocity (PID setpoint)

The simplified continuous-time dynamic equations governing the system are given in Equations (1)–(5) [41,42,43,44].

$${\displaystyle \frac{d}{dt}} SOC\left(t\right)=-{\displaystyle \frac{1}{C_{bat}}} · I_b(t)$$

(1)

$${\displaystyle \frac{d}{dt}}{T}_b\left(t\right)={\displaystyle \frac{1}{m_b · C_{p,b}}} ({I_b\left(t\right)}^2 · R_{int}-hA · (T_b\left(t\right)-T_{\mathit{\infty }}))$$

(2)

$$J_m · {\displaystyle \frac{d}{dt}}{\omega }_m\left(t\right)=K_t · I_b\left(t\right)-b_m · {\omega }_m\left(t\right)-{\tau }_{load}\left(\vartheta \right)$$

(3)

$$m · {\displaystyle \frac{d}{dt}}\vartheta \left(t\right)={\displaystyle \frac{K_t}{r}} · I_b\left(t\right)-F_{drag}\left(\vartheta \right)$$

(4)

$${\displaystyle \frac{d}{dt}}{i}_e\left(t\right)={\vartheta }_{ref}\left(t\right)-\vartheta \left(t\right)$$

(5)

The controller output current is determined by Equation (6):

$$I_b\left(t\right)= K_p · \left({\vartheta }_{ref}\left(t\right)- \vartheta \left(t\right)\right)+ K_i · i_e\left(t\right)+ K_{d }· {\displaystyle \frac{d}{dt}} \left({\vartheta }_{ref}\left(t\right)- \vartheta \left(t\right)\right)$$

(6)

where mentioned terms are defined by

Table 4. Terms definition.

Term	Definition
$C_{bat}$	Battery capacity
$m_b$	Battery mass
$C_{p,b}$	Specific heat capacity
$R_{int}$	Internal resistance of the battery
$hA$	Effective thermal transfer coefficient to the ambient environment ($T_{\infty }$)
$J_m$	Motor moment of inertia
$b_m$	Motor damping coefficient
$K_t$	Motor torque constant
$m$	Robot mass
$r$	Wheel radius
$K_p$	Proportional gains
$K_i$	Integral gains
$K_{d }$	Derivative gains

:

The drag force and the load torque applied to the motor are given by Equations (7) and (8), respectively [45]:

$$F_{drag}\left(\vartheta \right)= C_1 · \vartheta + C_2 · {\vartheta }^2$$

(7)

$${\tau }_{load}\left(\vartheta \right)=F_{drag}\left(\vartheta \right) · r$$

(8)

where $C_1$ and $C_2$ are linear and quadratic drag coefficients, respectively. This reduced-order model captures the core physical behaviors of the AMR system while remaining analytically tractable. It provides a foundation for interpreting simulation results and evaluating battery chemistries in a controlled, comparable manner.

The robot’s trajectory and various battery characteristics were kept constant throughout all simulations to ensure a reliable comparison. To maintain a reliable comparison, the robot’s path and other battery specifications remained fixed throughout the simulations. Over the course of the extended 2.5 h simulation, each battery model was tested under identical conditions, resulting in the SOC falling below 10%. The simulation was run in both the charging (when the robot is charging and not operating) and discharging (when the robot is operating) modes. Both the battery’s temperature and the amount of time needed to charge it were tracked during the charging mode. These elements are important when using the PSO method to select the best battery model.

Battery temperature and SOC were monitored during the discharge mode at each simulation time. Battery temperature is crucial for assessing the thermal stability of each battery chemistry. The SOC represents the remaining capacity of the battery. It is critical to understand how efficiently the battery can deliver energy along the robot’s trajectory. The core of the simulation is the Li-ion battery model, which is intended to evaluate different chemicals for the cathode and anode electrodes. These chemicals are listed in Table 5.

Table 5. Different simulated chemistries for the cathode and anode electrodes.

Anode	LTO	Graphite	Lithium Titanium Oxide
Cathode	LCO	LCO	LCO
	LFP	LFP	LFP
	LMO	LMO	LMO
	Lithium Manganese Oxide (low plateau)	Lithium Manganese Oxide (low plateau)	Lithium Manganese Oxide ${\mathrm{L}\mathrm{i}}_{1.156}{\mathrm{M}\mathrm{n}}_{1.844}{\mathrm{O}}_4$
	Lithium Manganese Oxide ${\mathrm{L}\mathrm{i}}_{1.156}{\mathrm{M}\mathrm{n}}_{1.844}{\mathrm{O}}_4$	Lithium Manganese Oxide ${\mathrm{L}\mathrm{i}}_{1.156}{\mathrm{M}\mathrm{n}}_{1.844}{\mathrm{O}}_4$	NCA
	NCA	NCA	Lithium Nickel Cobalt Oxide $\mathrm{L}\mathrm{i}{\mathrm{N}\mathrm{i}}_{0.8}{\mathrm{C}\mathrm{o}}_{0.2}{\mathrm{O}}_2$
	Lithium Nickel Cobalt Oxide $\mathrm{L}\mathrm{i}{\mathrm{N}\mathrm{i}}_{0.8}{\mathrm{C}\mathrm{o}}_{0.2}{\mathrm{O}}_2$	Lithium Nickel Cobalt Oxide $\mathrm{L}\mathrm{i}{\mathrm{N}\mathrm{i}}_{0.8}{\mathrm{C}\mathrm{o}}_{0.2}{\mathrm{O}}_2$	Lithium Nickel Cobalt Oxide $\mathrm{L}\mathrm{i}{\mathrm{N}\mathrm{i}}_{0.7}{\mathrm{C}\mathrm{o}}_{0.3}{\mathrm{O}}_2$
	Lithium Nickel Cobalt Oxide $\mathrm{L}\mathrm{i}{\mathrm{N}\mathrm{i}}_{0.7}{\mathrm{C}\mathrm{o}}_{0.3}{\mathrm{O}}_2$	Lithium Nickel Cobalt Oxide $\mathrm{L}\mathrm{i}{\mathrm{N}\mathrm{i}}_{0.7}{\mathrm{C}\mathrm{o}}_{0.3}{\mathrm{O}}_2$	NMC
	NMC	NMC	Lithium Nickel Oxide $\mathrm{L}\mathrm{i}\mathrm{N}\mathrm{i}{\mathrm{O}}_2$
	Lithium Nickel Oxide $\mathrm{L}\mathrm{i}\mathrm{N}\mathrm{i}{\mathrm{O}}_2$	Lithium Nickel Oxide $\mathrm{L}\mathrm{i}\mathrm{N}\mathrm{i}{\mathrm{O}}_2$	Lithium Vanadium Oxide $\mathrm{L}\mathrm{i}{\mathrm{V}}_2{\mathrm{O}}_5$
	Lithium Vanadium Oxide $\mathrm{L}\mathrm{i}{\mathrm{V}}_2{\mathrm{O}}_5$	Lithium Titanium Suiphide $\mathrm{L}\mathrm{i}\mathrm{T}\mathrm{i}{\mathrm{S}}_2$	Sodium Cobalt Oxide $\mathrm{N}\mathrm{a}\mathrm{C}\mathrm{o}{\mathrm{O}}_2$
	Sodium Cobalt Oxide $\mathrm{N}\mathrm{a}\mathrm{C}\mathrm{o}{\mathrm{O}}_2$	Lithium Vanadium Oxide $\mathrm{L}\mathrm{i}{\mathrm{V}}_2{\mathrm{O}}_5$
		Lithium Tungsten Oxide $\mathrm{L}\mathrm{i}\mathrm{W}{\mathrm{O}}_3$
		Sodium Cobalt Oxide $\mathrm{N}\mathrm{a}\mathrm{C}\mathrm{o}{\mathrm{O}}_2$

Table 5. Different simulated chemistries for the cathode and anode electrodes.

Anode	LTO	Graphite	Lithium Titanium Oxide
Cathode	LCO	LCO	LCO
	LFP	LFP	LFP
	LMO	LMO	LMO
	Lithium Manganese Oxide (low plateau)	Lithium Manganese Oxide (low plateau)	Lithium Manganese Oxide ${\mathrm{L}\mathrm{i}}_{1.156}{\mathrm{M}\mathrm{n}}_{1.844}{\mathrm{O}}_4$
	Lithium Manganese Oxide ${\mathrm{L}\mathrm{i}}_{1.156}{\mathrm{M}\mathrm{n}}_{1.844}{\mathrm{O}}_4$	Lithium Manganese Oxide ${\mathrm{L}\mathrm{i}}_{1.156}{\mathrm{M}\mathrm{n}}_{1.844}{\mathrm{O}}_4$	NCA
	NCA	NCA	Lithium Nickel Cobalt Oxide $\mathrm{L}\mathrm{i}{\mathrm{N}\mathrm{i}}_{0.8}{\mathrm{C}\mathrm{o}}_{0.2}{\mathrm{O}}_2$
	Lithium Nickel Cobalt Oxide $\mathrm{L}\mathrm{i}{\mathrm{N}\mathrm{i}}_{0.8}{\mathrm{C}\mathrm{o}}_{0.2}{\mathrm{O}}_2$	Lithium Nickel Cobalt Oxide $\mathrm{L}\mathrm{i}{\mathrm{N}\mathrm{i}}_{0.8}{\mathrm{C}\mathrm{o}}_{0.2}{\mathrm{O}}_2$	Lithium Nickel Cobalt Oxide $\mathrm{L}\mathrm{i}{\mathrm{N}\mathrm{i}}_{0.7}{\mathrm{C}\mathrm{o}}_{0.3}{\mathrm{O}}_2$
	Lithium Nickel Cobalt Oxide $\mathrm{L}\mathrm{i}{\mathrm{N}\mathrm{i}}_{0.7}{\mathrm{C}\mathrm{o}}_{0.3}{\mathrm{O}}_2$	Lithium Nickel Cobalt Oxide $\mathrm{L}\mathrm{i}{\mathrm{N}\mathrm{i}}_{0.7}{\mathrm{C}\mathrm{o}}_{0.3}{\mathrm{O}}_2$	NMC
	NMC	NMC	Lithium Nickel Oxide $\mathrm{L}\mathrm{i}\mathrm{N}\mathrm{i}{\mathrm{O}}_2$
	Lithium Nickel Oxide $\mathrm{L}\mathrm{i}\mathrm{N}\mathrm{i}{\mathrm{O}}_2$	Lithium Nickel Oxide $\mathrm{L}\mathrm{i}\mathrm{N}\mathrm{i}{\mathrm{O}}_2$	Lithium Vanadium Oxide $\mathrm{L}\mathrm{i}{\mathrm{V}}_2{\mathrm{O}}_5$
	Lithium Vanadium Oxide $\mathrm{L}\mathrm{i}{\mathrm{V}}_2{\mathrm{O}}_5$	Lithium Titanium Suiphide $\mathrm{L}\mathrm{i}\mathrm{T}\mathrm{i}{\mathrm{S}}_2$	Sodium Cobalt Oxide $\mathrm{N}\mathrm{a}\mathrm{C}\mathrm{o}{\mathrm{O}}_2$
	Sodium Cobalt Oxide $\mathrm{N}\mathrm{a}\mathrm{C}\mathrm{o}{\mathrm{O}}_2$	Lithium Vanadium Oxide $\mathrm{L}\mathrm{i}{\mathrm{V}}_2{\mathrm{O}}_5$
		Lithium Tungsten Oxide $\mathrm{L}\mathrm{i}\mathrm{W}{\mathrm{O}}_3$
		Sodium Cobalt Oxide $\mathrm{N}\mathrm{a}\mathrm{C}\mathrm{o}{\mathrm{O}}_2$

The distinct electrochemical and thermal behavior of each of the 37 battery chemistries was simulated using the parameterized battery models within MapleSim’s library. These models are populated with empirical data and validated studies from the literature. The simulation results for each battery model were collected and compared to determine the best-performing chemistry, as shown in Figure 4, Figure 5, Figure 6, Figure 7, Figure 8 and Figure 9 for the charging process and Figure 10 and Figure 11 for the discharging process. The robot’s fixed trajectory and the constant battery parameters ensured that the differences in performance were solely due to the variations in battery chemistries. In addition, the summary of the results, including minimum SOC (in discharging simulation), maximum SOC (in charging simulation), and maximum temperature (in both charging and discharging simulations) for all 37 battery models, is shown in

Table 6. Summary of results for min SOC, max SOC, and max temperature for LTO as anodes.

Cathode	Min SOC (Discharging)	Max Temp (K) (Discharging)	Max SOC (Charging)	Max Temp (K) (Charging)
LCO	0.1 at 7356 s	322.0295	0.99	298.15
LFP	0.1 at 5651 s	311.0926	0.99	303.0574
LMO	0.1 at 4616 s	307.6095	0.99	303.7959
low plateau	0.1 at 3749 s	330	0.99	303.7959
${\mathbf{L}\mathbf{i}}_{1.156}{\mathbf{M}\mathbf{n}}_{1.844}{\mathbf{O}}_4$	0.1 at 7835 s	306.2226	0.99	303.7727
NCA	0.1 at 6873 s	310.7698	0.99	306.4994
$\mathbf{L}\mathbf{i}{\mathbf{N}\mathbf{i}}_{0.8}{\mathbf{C}\mathbf{o}}_{0.2}{\mathbf{O}}_2$	0.1 at 6618 s	307.4504	0.99	304.3234
$\mathbf{L}\mathbf{i}{\mathbf{N}\mathbf{i}}_{0.7}{\mathbf{C}\mathbf{o}}_{0.3}{\mathbf{O}}_2$	0.1 at 6992 s	307.0672	0.99	305.3811
NMC	0.1 at 7201 s	309.7717	0.99	301.1697
$\mathbf{L}\mathbf{i}\mathbf{N}\mathbf{i}{\mathbf{O}}_2$	0.1 at 6503 s	307.3512	0.99	303.8096
$\mathbf{L}\mathbf{i}{\mathbf{V}}_2{\mathbf{O}}_5$	0.1 at 5204 s	310.9219	0.99	303.8515
$\mathbf{N}\mathbf{a}\mathbf{C}\mathbf{o}{\mathbf{O}}_2$	0.1 at 4510 s	327	0.99	303.8057

,

Table 7. Summary of results for min SOC, max SOC, and max temperature for graphite as anodes (Max duration for simulation is 2.5 h).

Cathode	Min SOC (Discharging)	Max Temp (K) (Discharging)	Max SOC (Charging)	Max Temp (K) (Charging)
LCO	0.3025	308.101	0.81	298.15
LFP	0.1705	301.8898	0.99	303.6128
LMO	0.3147	301.1471	0.59	302.2574
low plateau	0.1 at 8200 s	308.4875	0.99	304.354
${\mathbf{L}\mathbf{i}}_{1.156}{\mathbf{M}\mathbf{n}}_{1.844}{\mathbf{O}}_4$	0.3247	300	0.62	301.2702
NCA	0.2760	298.15	0.87	305.9535
$\mathbf{L}\mathbf{i}{\mathbf{N}\mathbf{i}}_{0.8}{\mathbf{C}\mathbf{o}}_{0.2}{\mathbf{O}}_2$	0.2573	299.7453	0.98	304.4761
$\mathbf{L}\mathbf{i}{\mathbf{N}\mathbf{i}}_{0.7}{\mathbf{C}\mathbf{o}}_{0.3}{\mathbf{O}}_2$	0.2783	398.3407	0.88	305.0541
NMC	0.2900	301.7137	0.83	301.0725
$\mathbf{L}\mathbf{i}\mathbf{N}\mathbf{i}{\mathbf{O}}_2$	0.2450	300.2218	0.99	304.3599
$\mathbf{L}\mathbf{i}\mathbf{T}\mathbf{i}{\mathbf{S}}_2$	0.1 at 5997 s	310.2377	0.99	304.4095
$\mathbf{L}\mathbf{i}{\mathbf{V}}_2{\mathbf{O}}_5$	0.1391	301.4878	0.99	304.4095
$\mathbf{L}\mathbf{i}\mathbf{W}{\mathbf{O}}_3$	0.1 at 7603 s	306.2792	0.99	304.4095
$\mathbf{N}\mathbf{a}\mathbf{C}\mathbf{o}{\mathbf{O}}_2$	0.1158	303.0061	0.99	304.2057

, and

Table 8. Summary of results for min SOC, max SOC, and max temperature for lithium titanium oxide as anodes.

Cathode	Min SOC (Discharging)	Max Temp (K) (Discharging)	Max SOC (Charging)	Max Temp (K) (Charging)
LCO	0.1 at 6326 s	323.8348	0.99	298.15
LFP	0.1 at 4456 s	312.5331	0.99	304.2549
LMO	0.1 at 6526 s	307.4367	0.99	304.8917
${\mathbf{L}\mathbf{i}}_{1.156}{\mathbf{M}\mathbf{n}}_{1.844}{\mathbf{O}}_4$	0.1 at 6690 s	306.0897	0.99	304.8713
NCA	0.1 at 5760 s	309.0152	0.99	307.9069
$\mathbf{L}\mathbf{i}{\mathbf{N}\mathbf{i}}_{0.8}{\mathbf{C}\mathbf{o}}_{0.2}{\mathbf{O}}_2$	0.1 at 5578 s	308.5457	0.99	305.5272
$\mathbf{L}\mathbf{i}{\mathbf{N}\mathbf{i}}_{0.7}{\mathbf{C}\mathbf{o}}_{0.3}{\mathbf{O}}_2$	0.1 at 5851 s	307.2064	0.99	306.826
NMC	0.1 at 6029 s	310.1997	0.99	302.7992
$\mathbf{L}\mathbf{i}\mathbf{N}\mathbf{i}{\mathbf{O}}_2$	0.1 at 5409 s	308.3321	0.99	305.2497
$\mathbf{L}\mathbf{i}{\mathbf{V}}_2{\mathbf{O}}_5$	0.1 at 4127 s	314.2597	0.99	305.2616
$\mathbf{N}\mathbf{a}\mathbf{C}\mathbf{o}{\mathbf{O}}_2$	0.1 at 4455 s	330	0.99	305.2445

, respectively. In Figure 10, multiple curves overlap with the NaCoO₂–Lithium Titanium Oxide trend and are covered by that; however, their precise numerical values can be found in the “Max SOC (Charging)” column of Table 6, Table 7 and Table 8.

3. Optimization Using Particle Swarm Optimization (PSO)

3.1. PSO for Multi-Criteria Battery Selection

PSO, a population-based metaheuristic inspired by the social behavior of bird flocking or fish schooling, is particularly suited for problems where the objective function is complex, nonlinear, and involves trading off multiple, often conflicting, performance criteria. In the context of battery selection for AMRs, PSO efficiently explores the high-dimensional solution space of possible battery chemistries to identify the configuration that best balances thermal stability, energy efficiency, and cost for a given application.

The core idea of PSO is to maintain a swarm of particles, each representing a candidate solution (a specific battery model). Each particle $i$ has a position ${\mathrm{x}}_i$ (the battery-model index) and a velocity ${\mathrm{v}}_i$ that guides its movement through the solution space. During iteration, particles adjust their trajectories based on their own best-known position (${\mathrm{p}}_{\mathrm{best},i}$) and the best-known position of the entire swarm (${\mathrm{g}}_{\mathrm{best}}$). The update equations for the $d$-th dimension of particle $i$ at iteration $t+1$ are:

$$v_{i,d}^{\left(t+1\right)}=w\cdot v_{i,d}^{\left(t\right)}+c_1{r}_1\left(p_{\mathrm{best},i,d}−x_{i,d}^{\left(t\right)}\right)+c_2{r}_2\left(g_{\mathrm{best},d}−x_{i,d}^{\left(t\right)}\right)$$

(9)

$$x_{i,d}^{\left(t+1\right)}=x_{i,d}^{\left(t\right)}+v_{i,d}^{\left(t+1\right)}$$

(10)

where $w$ is the inertia weight, $c_1$ and $c_2$ are the cognitive and social acceleration coefficients, and $r_1,r_2\sim U(0,1)$ are random numbers. The inertia weight controls the influence of the previous velocity; a value of $w=0.729$ and $c_1=c_2=1.49445$ are commonly used [26]. For our discrete problem (37 battery models), the continuous position is rounded to the nearest integer index after each update.

3.2. Fitness Function and Application-Specific Weighting

The fitness function $F({\mathrm{x}}_i,A)$ quantifies how well a battery model (particle position ${\mathrm{x}}_i$) satisfies the multi-criteria requirements of a particular application $A$. It is constructed as a weighted sum of normalized performance metrics, directly incorporating the application-specific priorities defined in Table 9, which were derived through a combined approach of expert elicitation and a synthesis of domain-specific literature. The judgments reflect the consolidated priorities of AMR designers and industrial end-users, aligning with the critical operational requirements documented for each domain. For instance, the elevated weights for thermal stability in Healthcare and Exploration & Mining applications are directly informed by the paramount importance of safety and operational reliability when robots operate in proximity to humans or in unpredictable, harsh environments [9,37]. Conversely, the significant emphasis on Cost for Manufacturing and Logistics & Warehousing mirrors the well-documented industry focus on minimizing operational expenditure and total cost of ownership [4,10]. Similarly, the priority given to Energy Efficiency during charging for Agricultural Robots and Manufacturing supports the need for high utilization rates and minimal downtime.

The weighting coefficients in Table 9 were derived through a structured approach combining a synthesis of domain-specific literature and expert judgment. They reflect the relative importance of each performance metric for the successful deployment of an AMR in a given operational context. The justification for each application’s weight vector is as follows:

Logistics & Warehousing: The primary goals are maximizing uptime and minimizing total cost of ownership. Therefore, energy efficiency during discharging (0.2) and charging (0.25) are weighted highly to ensure long shifts and fast turnaround times. Cost (0.2) is also a key factor. Thermal stability (0.2 each) is important for safety in facilities with high robot density but is not the absolute priority [4,10].

Healthcare: Patient and staff safety is paramount. This drives the highest combined weight for thermal stability (0.25 Discharging, 0.25 Charging) to mitigate any risk of thermal runaway in sensitive environments [9,37]. Cost (0.1) becomes a secondary concern to safety and reliability.

Manufacturing: This environment demands high throughput and minimal downtime. Consequently, energy efficiency during charging (0.3) is given the highest weight to support rapid battery cycling. Cost (0.3) is also critical for competitiveness. Thermal stability (0.15 each), while still important, is often managed by controlled indoor environments.

Agricultural Robots: Agricultural tasks require long, uninterrupted missions in variable outdoor conditions. Thus, energy efficiency during discharging (0.2) and especially fast charging (0.3) for quick turnarounds are prioritized. Robustness (thermal stability 0.2 each) and cost-effectiveness (0.2) are also crucial for this economically sensitive sector.

Exploration & Mining: These are the most safety-critical and unpredictable environments. The highest priority is given to thermal stability (0.3 Discharging, 0.3 Charging) to ensure reliable and safe operation under extreme conditions. Cost (0.1) is a lower concern compared to mission success and safety [9,37]. Energy efficiency is weighted lower (0.15 Discharging, 0.2 Charging), as reliability trumps runtime if the robot cannot operate at all.

Table 9. The weighting coefficients for the application-specific priorities of the AMR.

	Thermal Stability (Discharging)	Thermal Stability (Charging)	Energy Efficiency (Discharging)	Energy Efficiency (Charging)	Cost
Logistics & Warehousing	0.2	0.2	0.2	0.25	0.2
Healthcare	0.25	0.25	0.2	0.2	0.1
Manufacturing	0.15	0.15	0.2	0.3	0.3
Agricultural Robots	0.2	0.2	0.2	0.3	0.2
Exploration & Mining	0.3	0.3	0.15	0.2	0.1

Table 9. The weighting coefficients for the application-specific priorities of the AMR.

	Thermal Stability (Discharging)	Thermal Stability (Charging)	Energy Efficiency (Discharging)	Energy Efficiency (Charging)	Cost
Logistics & Warehousing	0.2	0.2	0.2	0.25	0.2
Healthcare	0.25	0.25	0.2	0.2	0.1
Manufacturing	0.15	0.15	0.2	0.3	0.3
Agricultural Robots	0.2	0.2	0.2	0.3	0.2
Exploration & Mining	0.3	0.3	0.15	0.2	0.1

Let ${\mathbf{w}}_A=[w_{\mathrm{TS},\mathrm{D}},w_{\mathrm{TS},\mathrm{C}},w_{\mathrm{EE},\mathrm{D}},w_{\mathrm{EE},\mathrm{C}},w_{\mathrm{Cost}}]$ be the weight vector for application $A$. The fitness function is:

$$\begin{gathered} F\left({\mathbf{x}}_i,A\right)=w_{\mathrm{TS},\mathrm{D}}\cdot f_{\mathrm{TS},\mathrm{D}}\left(i\right)+w_{\mathrm{TS},\mathrm{C}}\cdot f_{\mathrm{TS},\mathrm{C}}\left(i\right)+w_{\mathrm{EE},\mathrm{D}}\cdot f_{\mathrm{EE},\mathrm{D}}\left(i\right)+w_{\mathrm{EE},\mathrm{C}}\cdot \\ {f}_{\mathrm{EE},\mathrm{C}}\left(i\right)+w_{\mathrm{Cost}}·f_{\mathrm{Cost}}(i) \end{gathered}$$

(11)

The constituent metrics $f$ are derived from the simulation data (SOC and temperature profiles during discharging and charging) and are normalized to a [0, 1] scale, where 1 indicates better performance:

• $f_{\mathrm{TS},\mathrm{D}}(i),f_{\mathrm{TS},\mathrm{C}}(i)$: Thermal stability during discharging and charging. Based on the maximum temperature reached by battery model $i$, normalized such that lower temperatures score higher.
• $f_{\mathrm{EE},\mathrm{D}}(i),f_{\mathrm{EE},\mathrm{C}}(i)$: Energy efficiency during discharging and charging. For discharging, this uses the minimum SOC value (higher is better). For charging, it uses the maximum SOC reached.
• $f_{\mathrm{Cost}}(i)$: Cost efficiency. Uses normalized battery cost data (lower cost scores higher).

This formulation ensures that the PSO algorithm explicitly searches for the battery model that maximizes the weighted combination of criteria deemed most critical for each AMR application, from cost-sensitive logistics to safety-critical healthcare.

3.3. Implementation and Integration with Simulation Data

The PSO algorithm was implemented in MATLAB (R2023a Version). The input data consisted of four Excel files containing time-series data for all 37 battery models (Figure 4, Figure 5, Figure 6, Figure 7, Figure 8, Figure 9, Figure 10 and Figure 11 and Table 6, Table 7 and Table 8): (1) SOC during discharging, (2) SOC during charging, (3) temperature during discharging, and (4) temperature during charging. Key performance features (including minimum SOC, maximum temperature, and stability metrics) were extracted for each battery model using MATLAB’s built-in statistical functions and normalized to a [0, 1] range to enable consistent multi-criteria comparison.

The optimization was performed independently for each of the five application domains (Logistics & Warehousing, Healthcare, Manufacturing, Agricultural Robots, and Exploration & Mining). For each application-specific run, the swarm size was set to 30 particles, and the algorithm executed a maximum of 100 iterations or until convergence, defined as negligible change (standard deviation < 1 × 10⁻⁴) in the global best fitness over 20 consecutive iterations. The optimal battery model for each application was identified as the particle position ${\mathrm{g}}_{\mathrm{best}}$ at convergence, representing the battery chemistry that maximized the weighted combination of thermal stability, energy efficiency, and cost effectiveness for that operational context. The flowchart in Figure 12 illustrates this integrated PSO-based optimization process.

PSO was conducted using the defined criteria and weighting coefficients to select the most efficient and cost-effective battery model for an AMR. The study assesses all potential Li-ion battery models with different chemistries for the positive and negative electrodes, modeling each one to compare battery temperature and SOC. The selected battery models for each application are shown in

Table 10. The selected battery models for different applications.

Application	Max Temp (K) (Discharging)	Max Temp (K) (Charging)	SOC (Discharging)	SOC (Charging)	Ave Cost ($)
Logistics & Warehousing	Graphite		Selected Model	NMC
	301.71	301.07	0.29	0.83	300
Healthcare	Graphite		Selected Model	LCO
	309.77	301.16	0.1	0.99	350
Manufacturing	Graphite		Selected Model	Lithium Nickel Cobalt Oxide $\mathrm{L}\mathrm{i}{\mathrm{N}\mathrm{i}}_{0.8}{\mathrm{C}\mathrm{o}}_{0.2}{\mathrm{O}}_2$
	298.15	305.95	0.27	0.87	320
Agricultural	Graphite		Selected Model	Lithium Nickel Oxide $\mathrm{L}\mathrm{i}\mathrm{N}\mathrm{i}{\mathrm{O}}_2$
	301.14	302.25	0.31	0.59	280
Exploration & Mining	Graphite		Selected Model	NMC
	301.88	303.61	0.17	0.99	310

. To ensure the robustness and statistical reliability of the optimization results, the PSO algorithm was executed 200 independent times. The final optimal battery configuration for each use case was determined by selecting the model that appeared most frequently across these 200 runs. This approach mitigates the inherent stochastic variability of metaheuristic algorithms, which can occasionally converge to local optima due to random initialization and search dynamics. By adopting a majority-vote criterion, we enhance the confidence in the selected battery model, ensuring that the recommendation is not an outlier but a consistently high-performing configuration across multiple optimization trials. This method aligns with established practices in computational optimization, where repeated execution and modal selection are used to produce reliable, reproducible outcomes in the presence of algorithmic randomness.

The PSO yielded distinct optimal battery models for each application domain, as summarized in Table 10.

Logistics & Warehousing: The PSO selected NMC with Graphite. This chemistry offers an optimal balance of good thermal stability, high energy efficiency (supporting long shift durations), and relatively low cost, a crucial combination for high-throughput, cost-sensitive warehouse operations where uptime and total cost of ownership are paramount.

Healthcare: For safety-critical healthcare environments, the algorithm prioritized thermal stability above all else, selecting LCO with Graphite. The Graphite anode is renowned for its exceptional thermal safety and long cycle life, mitigating risk in proximity to patients and medical staff, even at a marginally higher cost.

Manufacturing: The optimal choice for manufacturing is Lithium Nickel Cobalt Oxide $(\mathrm{L}\mathrm{i}{\mathrm{N}\mathrm{i}}_{0.8}{\mathrm{C}\mathrm{o}}_{0.2}{\mathrm{O}}_2)$with Graphite. This combination provides high energy density and excellent power capability, suitable for dynamic manufacturing tasks with variable loads. The PSO valuation respected the sector’s significant weighting on charging efficiency and cost, ensuring rapid recharge cycles and cost-effective operation.

Agricultural Robots: The algorithm identified Lithium Nickel Oxide $\left(\mathrm{L}\mathrm{i}\mathrm{N}\mathrm{i}{\mathrm{O}}_2\right)$ Graphite is best suited for agricultural applications. This chemistry provides robust thermal stability for outdoor operation, sufficient energy density for extended field missions, and a low-cost profile, aligning with the need for durable, economically viable robots in farming.

Exploration & Mining: In harsh, unpredictable environments, reliability is key. The PSO selected NMC with Graphite, a chemistry celebrated for its superior thermal and chemical stability, safety, and long cycle life. While its energy density is moderate, its robustness under extreme conditions and stable performance make it the most reliable choice for exploration and mining robots.

It is important to note that the optimal battery selections presented in Table 10 are contingent upon the specific weighting coefficients defined in Table 9, which were derived from our synthesis of domain-specific operational priorities. While these weights are well-justified, a different set of stakeholder priorities would yield a different optimal configuration. This highlights the value of our framework as a decision-support tool that can be readily recalibrated. Future work could incorporate a formal sensitivity analysis to systematically explore how variations in the weight vector impact the final optimal ranking.

The convergence behavior of the PSO algorithm was consistent across all applications, typically reaching a stable global optimum within 40–60 iterations. This demonstrates the method’s efficiency in solving the discrete battery-selection problem. Compared to a static weighting-and-scoring approach, PSO provides a more robust search mechanism, less susceptible to the ranking inconsistencies that can sometimes arise in pairwise comparison methods when dealing with a large set of alternatives.

4. Conclusions

The PSO-based optimization framework provided an efficient, multi-objective methodology for analyzing and rating 37 candidate battery models. The results highlighted several significant points:

• Batteries with lower maximum temperatures during both discharge and charge cycles were consistently prioritized across applications, reducing thermal stress risks and extending operational lifespan. This proved particularly critical in safety-sensitive domains such as healthcare and exploration, where thermal stability was weighted most heavily.
• A high minimum SOC value during discharge, indicating sustained energy availability, was essential for applications requiring extended operational cycles without frequent recharging. This criterion was especially valued in logistics and manufacturing, where uptime directly impacts throughput.
• The PSO algorithm effectively balanced multiple, often competing objectives, thermal stability, energy efficiency, and cost, by dynamically adjusting its search through the 37-dimensional solution space. This allowed identification of battery chemistries that offered optimal trade-offs for each specific application context.
• Incorporating cost as a criterion ensured financial viability was maintained alongside technical performance. Battery models that provided the best weighted combination of low cost and high performance emerged as optimal, with cost weights varying depending on application priorities.

The PSO identified distinct optimal battery configurations for each application domain: NMC with Graphite for logistics, LCO with Graphite for healthcare, Lithium Nickel Cobalt Oxide $(\mathrm{L}\mathrm{i}{\mathrm{N}\mathrm{i}}_{0.8}{\mathrm{C}\mathrm{o}}_{0.2}{\mathrm{O}}_2)$with Graphite for manufacturing, Lithium Nickel Oxide $\left(\mathrm{L}\mathrm{i}\mathrm{N}\mathrm{i}{\mathrm{O}}_2\right)$ with Graphite for agriculture, and NMC with Graphite for exploration. These selections directly reflect the unique operational priorities and weighting schemes of each domain. The study found that different battery chemistries offer unique advantages, and systematic, algorithm-driven selection is essential for matching chemistry characteristics to application requirements. By integrating high-fidelity simulation data with a robust PSO optimizer implemented in MATLAB, this research establishes a reproducible, data-driven framework for battery selection in AMRs. The methodology demonstrates how computational intelligence techniques can enhance decision-making in complex engineering systems, providing a foundation for future work in adaptive energy management and multi-objective optimization of robotic platforms.

While this study focused on thermal stability, energy efficiency, and cost as the primary selection criteria, other battery aspects could be explored from different perspectives for other objectives and purposes. These include, for example, detailed lifecycle analysis, form factor and weight constraints, mechanical robustness, and sustainability metrics. However, the modular framework established in this work is readily extensible, and future studies can build upon this foundation by incorporating additional objectives into the PSO fitness function, demonstrating how the framework adapts to more complex, high-dimensional decision-making problems.