Enhanced pure pursuit with dynamic steering control for autonomous mobile robots and application to safe navigation in chemical plants

Abstract

Accurate navigation in outdoor environments requires integrating multiple sensor sources for reliable localization and trajectory tracking. This study proposes Pure Pursuit with Dynamic Steering Control (PP-DSC), which adaptively adjusts both lookahead distance and velocity based on steering angle. The algorithm was deployed on a four-wheeled steering-type autonomous mobile robot (AMR) using Robot Operating System 2 (ROS 2) Jazzy, with real-time sensor fusion from GNSS-RTK, IMU, and wheel encoders. Experiments were conducted on straight, circular, and figure-eight trajectories at 1.0–5.0 m/s in an open area (64 × 20 m). PP-DSC achieved mean lateral deviations of 0.05, 0.07, and 0.08 m respectively, representing 68–82% improvement over standard PP (means 0.19, 0.40, and 0.27 m). To evaluate cross-domain applicability, the algorithm was extended with a Fire and Explosion Index (F&EI)-based safety factor (Safety-integrated PP-DSC) and tested via simulation in an empty fruit bunch (EFB) biodiesel plant (92 × 65 m). Standard PP outperformed Safety-integrated PP-DSC by 15.6% in this industrial setting due to tight turning radii (5–9 m), though Safety-integrated PP-DSC retained advantages in moderate-curvature sections with 11–17% improvement. The F&EI-based safety integration added less than 1% tracking overhead while providing automatic velocity reduction in hazard zones for Process Safety Management (PSM) compliance. The findings confirm that PP-DSC significantly improves trajectory tracking in open-field environments, while industrial deployment requires geometry-specific algorithm selection.

Introduction

The autonomous mobile robots (AMRs) are increasingly used in complex and unstructured environments where accurate localization and reliable trajectory tracking are critical for safe and efficient operation. These applications span from open agricultural fields to strictly regulated industrial facilities, such as chemical process plants. Traditional localization methods, such as dead-reckoning or standalone Global Navigation Satellite System (GNSS), often suffer from signal degradation and drift, especially in outdoor or dynamic settings. To address these limitations, sensor fusion techniques have been widely adopted. These approaches combine Global Navigation Satellite System Real-Time Kinematic (GNSS-RTK), Inertial Measurement Unit (IMU), and wheel encoders to enhance localization precision by compensating for individual sensor weaknesses^1–4. Such integration strategies are also essential for practical deployment in aging agricultural labor environments such as Japan⁵, as well as in the chemical process industries where AMRs perform hazardous tasks like equipment inspection and material transport within high-risk zones.

For trajectory tracking, the Pure Pursuit (PP) algorithm has been widely favored due to its computational simplicity and effectiveness. However, conventional PP algorithms typically rely on a fixed lookahead distance, which limits their ability to adapt to changes in path curvature or vehicle speed. This constraint often leads to oscillation and lateral deviation, particularly on curved or high-speed paths. In agricultural contexts, this can damage crops, while in chemical engineering applications, deviation from safety corridors can lead to collisions with critical equipment or intrusion into explosion-risk zones defined by Fire and Explosion Index (F&EI) constraints^6,7. While various improvements have been proposed in recent studies, most focus on adapting a single control variable, such as adjusting the lookahead distance based on velocity or path curvature or using fuzzy logic for tuning. These methods, although effective in specific conditions, are limited in generalizability and flexibility. Conceptually, while traditional trajectory tracking algorithms typically rely on fixed logic or focus on a single control factor, the proposed method introduces a joint adaptation strategy that dynamically integrates lookahead distance and velocity control based on the robot’s steering input^8,9.

This study introduces a modified version of the PP algorithm, referred to as PP with Dynamic Steering Control (PP-DSC). Unlike prior work that targets only one variable, PP-DSC simultaneously adjusts both the lookahead distance and the robot’s velocity. This adjustment is governed by a real-time metric known as steering percentage, which is calculated based on the ratio of the current steering angle to the maximum steering angle. The algorithm is implemented on a four-wheeled, steering-type robot operating on the ROS 2 Jazzy platform. This platform was chosen for its support of real-time communication and multi-sensor data integration, though it also presents challenges such as system latency, signal jitter, and control nonlinearity. The PP-DSC algorithm is designed to mitigate these issues through coordinated control. Moreover, metaheuristic global planning approaches such as Artificial Bee Colony (ABC) have been shown to significantly reduce computational time in static environments with obstacles¹⁰.

Experimental evaluations were conducted using three standard path types: straight, circular, and figure-eight. The robot was tested at speeds ranging from 1.0 to 5.0 m per second under real-world conditions. Furthermore, to demonstrate applicability in process engineering, the algorithm was validated through kinematic simulation in a multi-floor empty fruit bunch (EFB) biodiesel plant^6,11, incorporating safety-aware velocity modulation based on F&EI hazard radii⁶. Performance was measured in terms of lateral deviation, trajectory smoothness, and velocity stability. Compared to the standard PP algorithm, which showed deviations as high as 0.44 m, the PP-DSC method reduced mean tracking errors to 0.05 m on straight paths and less than 0.08 m on curved paths. These improvements were especially evident in sections involving continuous curvature or rapid direction changes.

The relevance and novelty of this work are further highlighted in the context of prior research summarized in Table 1. Previous studies proposed fuzzy-based lookahead tuning¹², while a comparative evaluation of multiple lateral control strategies showed that nonlinear model predictive control (NLMPC) yielded the best performance¹³. A comprehensive survey further examined improvements in speed control using proportional integral derivative (PID) controllers and pure pursuit algorithms for autonomous vehicle navigation¹⁴. However, none of these approaches jointly adapted both velocity and lookahead distance in response to steering behavior to satisfy safety constraints in both agricultural and industrial settings. Additionally, studies focused primarily on localization accuracy using sensor fusion, without addressing control dynamics in trajectory tracking^15,16. Similarly, the PP algorithm for agricultural unmanned aerial vehicles (UAVs) and achieved high path-tracking accuracy, although their work did not focus on dynamic lookahead or velocity adaptation¹⁷. Adaptive/dynamic lookahead in prior work. Beyond fixed lookahead, prior studies adapt the lookahead to the tracking context, including cross-track dependent laws, curvature- and speed-aware envelopes, and learned lookahead in LOS guidance. Representative formulations and comparisons are reviewed¹⁸. In contrast, PP-DSC co-adapts lookahead and forward speed using a single steering-normalized signal, respects actuator limits, and avoids explicit curvature-derivative estimation.

Table 1.

Summary of recent research on GNSS-RTK, IMU, and PP algorithms (2023–2025).

Algorithm	Lookahead adjustment	Performance (Error reduction)	Use case
Fuzzy-enhanced PP12	Deviation, heading, curvature	56% lateral error reduction	Variable-curvature path tracking
LQR, SAMFC, NLMPC13	Varied	Best tracking with NLMPC	Lateral control comparison
PID, Adaptive PP14	Fixed, velocity-based	Improved speed stability	Autonomous driving control
ESKF-based localization15	–	Enhanced unstructured localization	Cost-effective mobile robot
NRTK/GNSS tilt-compensation evaluation16	–	Improved tilt compensation	GNSS under tilt
PP17	Fixed	High UAV tracking accuracy	Agricultural spraying UAV

To provide a comprehensive understanding of the design, experimentation, and results in both agricultural and industrial contexts, the structure of this paper is organized as follows: “Materials and methods” covers the system architecture, algorithmic framework, and chemical plant application; “Experiment setup” details the field trial and simulation configurations; “Results and discussion” analyzes tracking performance across both domains;; and “Conclusions” summarizes key findings and future directions.

Materials and methods

Robot vehicle design

Hardware integration

This work utilizes a mobile robot equipped with an aluminum profile chassis, an industrial-grade onboard computer, GNSS antennas, a high-precision receiver, and brushless DC motors. The robot’s chassis measures 600 mm in width and 1000 mm in length. The GNSS system integrates an internal IMU and supports RTK positioning with an accuracy of up to 1.5 centimeters, delivering complete Radio Technical Commission for Maritime Services (RTCM) differential data. Powered by a high-performance MEMS-based inertial device, the GNSS-RTK module ensures precise and reliable differential positioning. Furthermore, the robot is equipped with a local network communication system that enables wireless control between the ground station and the robot. This system supports full-duplex communication, real-time channel monitoring, and adjustable transmission power, making it suitable for operation in diverse outdoor conditions³⁰. The comprehensive hardware architecture of the robot is illustrated in Fig. 1 and summarized in Table 2.

Fig. 1.

Hardware components and specifications of the AMR.

Table 2.

Hardware subsystems and key specifications used in the experiments.

Subsystem	Key parameters (units)
Motor	Max power 5500 W; max current 100 A; KV 190; max torque ~ 10 N·m (≤ 30 s); size Ø63 × 100 mm; shaft 8/10 mm; 14 poles
Steering servo	Stall torque 9.2/9.9/11.7 N·m @ 11.1/12.0/14.8 V; no-load speed 36/39/46 rpm; resolution 4096 counts/rev; gear ratio 272.5:1; bus RS-485
GNSS receiver/logger	Velocity accuracy 0.1 km/h; absolute position ~ 3 m (95% CEP); RTK ~ 2 cm (95% CEP) (optional); latency ~ 6.75 ms; update 100 Hz; DC input 7–30 V
Onboard computer	Intel® 13th/14th-Gen Core (up to 24 C/32T); 4 × 2.5GbE (PoE+ optional); 4× USB 3.2 Gen1; M.2 NVMe + hot-swap 2.5″; size 212 × 165 × 45 mm; 8–48 V DC input

Steering mechanism and control hardware

The platform is a car-like, front-wheel steering robot consistent with Ackermann geometry. The steering state is represented by the single front-axle steering angle in our car-like model, with wheelbase = 613.5 mm (Fig. 1). The processing unit (Robot Operating System 2 (ROS 2) Jazzy) transmits motion commands to the motor controller over CAN with encoder feedback in the control loop. The commanded steering angle is bounded to the mechanical limits via a clamping function, and PP-DSC normalizes the steering command as a steering percentage = to modulate forward speed. For completeness, Fig. 1 summarizes the key hardware relevant to steering dynamics (chassis 600 × 1000 mm, wheel size 113 mm, wheelbase 613.5 mm, 24 V supply, speed range 1–5 m/s). This section links perception (GNSS-RTK/IMU/encoders) to actuation, clarifying how steering commands are generated and enforced on the robot.

As illustrated in Fig. 2, the electrical architecture is designed to ensure stable power distribution and reliable communication. The system is powered by a 24VDC source, which distributes electricity through dedicated DC-DC converters to separate high-power motor loads from sensitive navigation sensors (GNSS-RTK, IMU) and the onboard computer. This separation minimizes electrical noise and ensures stable operation. For control signals, the onboard computer acts as the central processing unit, communicating with motor controllers via the CAN bus protocol and receiving sensor data for real-time navigation, while wireless modules facilitate remote telemetry.

Fig. 2.

Power and communication layout of the AMR and base station.

Navigation system design of the robot

In the design of the robot’s navigation system, a high-precision architecture based on GNSS-RTK technology is employed to ensure accurate and reliable localization in outdoor environments. As illustrated in Fig. 3, the system comprises four main components: the GNSS-RTK base station, position unit, processing unit, and control unit. The GNSS-RTK base station, consisting of a GNSS antenna and wireless transmission module, provides differential correction data to the position unit. This unit, which includes a wireless receiver and GNSS module, combines the correction data with satellite signals to achieve centimeter-level positioning accuracy.

Fig. 3.

Integrated GNSS-RTK-based navigation and control system.

The Processing Unit utilizes an industrial computer to integrate GNSS and IMU data, enhancing localization performance in environments with limited satellite visibility. It communicates with the control unit via the controller area network (CAN) bus protocol, enabling low-latency and reliable real-time data exchange. The control unit, composed of a Brushless DC (BLDC) motor, motor controller, and encoder sensor, receives motion commands from the processing unit and supplies real-time feedback to facilitate closed-loop control.

This integrated system design supports precise and responsive navigation, making it suitable for applications such as autonomous agricultural machinery and field robotics. The use of standardized communication protocols and modular hardware components enhances system reliability and adaptability across various operational scenarios¹⁹,²⁰.

The software controlling this system is implemented on an embedded computing platform, which continuously receives sensor data from GNSS, IMU, and wheel encoders. The sensors collectively provide positioning, heading, and motion-related information required for localization and motion control. The processing unit performs sensor fusion and sends motor commands to the control unit for execution.

Software framework and development environment

The robot’s software architecture relies on ROS 2 Jazzy as the core framework for coordinating algorithms, sensor interfaces, and communication protocols. Its modular and distributed design, illustrated in Fig. 4, organizes the system into input, processing, and output layers to support real-time navigation in dynamic environments. Development and implementation were conducted using Visual Studio Code (version 1.75), an integrated development environment (IDE) that supports C, C++, and Python3. This platform facilitates efficient algorithm prototyping, debugging, and version control, ensuring computational accuracy and workflow reliability.

Fig. 4.

Functional flow of GNSS-based navigation using a PP controller.

GNSS-IMU fusion position principle

Integration of coordinated systems in GNSS

The integration of GNSS technology into robotic systems significantly enhances autonomous navigation capabilities, despite inherent challenges in data interpretation. GNSS typically provides geographic coordinates in terms of geodetic latitude and longitude , which must be transformed into the universal transverse mercator (UTM) coordinate system to align with Cartesian-based navigation algorithms. The UTM system offers a planar representation in meters, enabling direct computation of distance and direction critical for precise robotic localization^21,22.

In the UTM framework, a location is represented by a zone number, hemisphere designation, and a pair of easting () and northing () values. A false easting of 500,000 m is added to the central meridian of each zone to prevent negative values. In the northern hemisphere, the false northing is set to 0 m, while in the southern hemisphere it is 10,000,000 m. For instance, an easting of 400,000 m indicates a point approximately 100 km west of the central meridian. The reference ellipsoid used for GNSS positioning is World Geodetic System 1984 (WGS 84), which models the Earth as an oblate spheroid with a semi-major axis m and an inverse flattening .

To convert from geodetic coordinates to UTM coordinates , the transformation given in Eqs. (1) and (2):

1

2

In these Eqs. (1) and (2), and are the resulting UTM easting and northing coordinates, respectively. The terms ​ and ​ represent the false easting and false northing used to shift the origin of the UTM grid. The scaling constant ​ is the central scale factor (typically 0.9996), used to minimize distortion along the central meridian. The variable is a scaling parameter dependent on the ellipsoid geometry, and ​ are coefficients derived from a Fourier series expansion related to the shape of the ellipsoid.

The terms and , required in Eqs. (1) and (2), are intermediate coordinates computed from geodetic latitude and longitude, as defined in Eqs. (3) and (4):

3

4

Here, represents the tangent of the geodetic latitude, and ​ is the longitude of the central meridian for the corresponding UTM zone. The function denotes the inverse hyperbolic tangent, and the use of trigonometric and hyperbolic functions accounts for the Earth’s curvature during projection.

The constants required for these calculations include the eccentricity of the ellipsoid, which is derived from its semi-major axis [m] and semi-minor axis [m], as shown in Eq. (5):

5

The scaling factor , used in the coordinate transformation, is then computed using Eq. (6):

6

Where represents the squared eccentricity of the ellipsoid, quantifying its deviation from a perfect sphere. The semi-minor axis can be obtained from the inverse flattening factor. These definitions ensure precise modeling of Earth’s geometry for accurate coordinate transformation.

By applying Eqs. (1)–(6), GNSS geodetic data can be accurately transformed into metric UTM coordinates suitable for robotic applications. This transformation forms the foundation for fusing GNSS data with inertial measurements from an IMU, allowing for robust and continuous localization even in areas where satellite visibility is compromised.

IMU-Based heading angle measurement

Accurate estimation of a robot’s heading is essential for autonomous navigation, particularly in tasks such as path planning, obstacle avoidance, and precise motion control. IMU, which typically consist of gyroscopes and accelerometers, play a central role in this process. The gyroscope measures angular velocity around the robot’s axes, while the accelerometer detects linear acceleration along those axes. Together, these data streams enable real-time orientation tracking²³.

The heading angle [rad] at a given time can be estimated by integrating the angular velocity [] measured by the gyroscope. The basic equation for updating the heading is Eq. (7):

7

Here, is the current heading angle, is the previous heading, is the angular velocity at time , and is the time interval between measurements²⁴. By continuously applying Eq. (7), the robot’s heading can be tracked over time.

To initialize this integration process, the initial heading is determined by aligning the robot’s orientation with the known path tangent at the starting waypoint, providing an accurate reference for subsequent updates. An illustration of the robot’s heading and rotational motion is shown in Fig. 5a.

Fig. 5.

Mathematical modeling of the AMR: (a) Odometry and coordinate system; (b) Ackermann steering kinematic structure.

Trajectory tracking control system

Car-like kinematic model of robotic vehicle

The car-like kinematic model serves as a fundamental framework for describing the motion of four-wheeled steering-type mobile robots, particularly those that resemble automobile-like configurations. This model is widely used in autonomous navigation systems due to its simplicity and its capability to accurately predict motion trajectories under nonholonomic constraints²⁵,²⁶. This kinematic formulation corresponds to an Ackermann-type front-wheel steering configuration: the vehicle uses a single front steering angle acting on the front axle (Fig. 5b), with wheelbase , and steering rate serving as a control input together with the linear velocity in Eq. (11).

As illustrated in Fig. 5b, the vehicle’s configuration is defined with respect to the rear axle center , its heading angle and the front-wheel steering angle . The wheelbase refers to the distance between the front and rear axles. The instantaneous center of rotation is denoted by and the turning radius from the rear axle is represented by The forward velocity is denoted which dictates the robot’s motion along the path.

In discrete time, the robot’s motion is governed by Eqs. (8) and (9), which update the and coordinates based on the current velocity and heading angle. The orientation update is derived from Eq. (10), which relates the turning curvature to the steering angle:

8

9

10

To support real-time control and simulation, the model can also be reformulated in continuous-time state-space form as shown in Eq. (11), where the forward velocity ​ and steering rate ​ serve as control inputs:

11

Here, ​ represents the forward linear velocity, while corresponds to the steering rate. The time step governs the resolution of discrete-time updates, enabling real-time implementation on robotic platforms.

PP algorithm

The PP algorithm is a geometric-based path-tracking method widely employed in mobile robotic systems due to its simplicity and effectiveness. The core idea of the algorithm is to identify a goal point ahead on the reference trajectory and calculate a circular arc that connects the vehicle’s current position to this point.

The algorithm then computes the required front-wheel steering angle to follow that arc. As shown in Fig. 6a, the vehicle uses the center of its rear axle () as the reference point, while the lookahead point is denoted by ().

Fig. 6.

Geometric formulation and trajectory behavior of the PP algorithm: (a) Geometric representation of the path tracking model; (b) Influence of lookahead distance on trajectory smoothness.

The Euclidean distance between the current vehicle position and the target point defines the lookahead distance [m]​, as formulated in Eq. (12):

12

From the geometric relationships in the figure²⁹ , the intermediate distances ​ and ​, which connect auxiliary points , , and , are derived using the radius of the curvature and turning angle , as shown in Eq. (13):

13

Using the Pythagorean identity, the relationship between these distances yields:

14

In practice, the value of ​ can be alternatively expressed based on the vehicle’s current lateral offset and steering angle as shown in Eq. (15):

15

The instantaneous turning radius is directly related to the steering angle ​ by Eq. (16):

16

Substituting Eqs. (15) and (16) into Eq. (14) and rearranging, we obtain Eq. (17):

17

Solving the ​, the final expression is given in Eq. (18):

18

From this, the path curvature can be calculated using Eq. (19):

19

As indicated by Eqs. (18) and (19), the lookahead distance plays a critical role in regulating both the ​ and . Larger values of ​ result in smaller steering angles, leading to smoother but slower directional corrections. In contrast, smaller values cause rapid, aggressive adjustments that may induce oscillatory behavior, especially during sharp turns or dynamic maneuvers (Fig. 6b). This phenomenon has been similarly reported in previous studies^27,28, which emphasize the importance of appropriately tuning the lookahead parameter to balance responsiveness and stability.

Path tracking analysis

An analysis of path tracking strategies with an emphasis on enhancing the PP algorithm through a dynamic lookahead distance mechanism. In its traditional form, the PP algorithm utilizes a fixed lookahead distance , which may lead to suboptimal tracking performance under varying velocity conditions. A small constant often results in oscillatory behavior due to overly aggressive steering, whereas a large can delay corrective actions and degrade path-following accuracy.

To improve adaptability, the lookahead distance can be dynamically adjusted in response to the robot’s current linear velocity. This allows the controller to assign a shorter at low speeds for precise maneuvering and a longer at higher speeds to ensure smooth and stable motion. A greater results in smoother trajectory tracking but reduces responsiveness, while a smaller enables sharper corrections that may cause instability or oscillations, particularly during low-speed maneuvers.

Conceptually, the lookahead distance is defined as a piecewise function of the absolute linear velocity , as shown in Eq. (20), where represents the robot’s current forward speed:

20

In this formulation, 1.5 m serves as the base lookahead distance. The dynamic component increases linearly with the velocity offset from 1.0 m/s, scaled by a factor of 3. However, to avoid oversteering at high speeds, the maximum lookahead distance is limited to 11.5 m.

As illustrated in Fig. 7a, the geometric derivation utilizes the angle which represents the angular offset between the robot’s heading direction and the line toward the goal point. The steering angle required to reach the target is denoted by , which is calculated using the dynamic lookahead distance in Eq. (18). Subsequently, the path curvature resulting from this steering command is represented by , as shown in Eq. (19). These variables allow the controller to adaptively compute turning behavior according to real-time speed and position.

Fig. 7.

PP tracking model and adaptive lookahead surface: (a) Geometric representation of lookahead-based path tracking; (b) Lookahead distance as a function of velocity and steering ratio.

By applying Eq. (20), the PP controller becomes more responsive and stable across varying speeds. This approach is particularly beneficial in agricultural and field robotics, where terrain and motion dynamics can change rapidly.

Development and implementation of algorithms

PP path tracking

PP calculates the steering angle and linear velocity required to follow a predefined path. It identifies a goal point located a fixed distance ahead of the robot’s position , and computes a circular arc toward it based on the and .

The reference path is represented as a discrete set of waypoints .

The algorithm finds the nearest waypoint, then selects the first point beyond the lookahead distance. This point is transformed into the robot’s local coordinate frame and used to calculate . The velocity is assigned either as a constant or adaptive value. The full procedure is shown in Algorithm 1.

Algorithm 1.

PP

Input: Current robot state: ), Reference path: , Parameter: wheelbase (), lookahead distance (), velocity limits command
Output: Steering command (), linear velocity ()
begin	1. Find nearest waypoint index: 2. Determine lookahead point: Select goal point such that index distance from 3. Transform to vehicle coordinate frame: Transform to local coordinates 4. Compute curvature and steering angle: 5. Apply control saturation: 6. Return
end

Although this implementation uses a fixed lookahead distance, the algorithm structure supports further enhancement, such as dynamic lookahead control.

Baselines for context. In addition to the canonical PP used in our field comparison, three representative state-of-the-art pure-pursuit variants are considered for context, as described by Foseid et al.¹⁸ cross-track dependent lookahead, curvature- and speed-aware envelopes, and learned lookahead in LOS guidance. These baselines are referenced here to position PP-DSC; quantitative evaluation beyond the canonical PP comparison is outside the present scope.

PP path tracking with dynamic Lookahead distance (PP-DL)

To enhance tracking performance across varying speeds and motion contexts, the traditional PP algorithm is extended by introducing a dynamic lookahead distance, , which adjusts in real time based on the robot’s velocity. This technique improves the accuracy of tight turns at low speeds and provides smooth trajectory following at higher speeds.

As depicted in Fig. 7a, the vehicle determines its steering angle by computing a circular arc connecting its current rear-axle position to a lookahead point on the desired path. The steering angle is calculated using the standard geometric formulation shown in Eq. (21):

21

To prevent physically unrealistic steering angles, a saturation condition is enforced using the piecewise constraint shown in Eq. (22):

22

The lookahead distance is linearly adjusted based on the robot’s current velocity, bounded by minimum and maximum limits. The adaptive formulation is expressed in Eq. (23):

23

Velocity constraints for smooth control are expressed in Eqs. (24) and (25):

24

25

where is the deceleration target speed [], is the (positive) deceleration magnitude [], and is the remaining braking distance [m].

The final velocity command is selected using Eq. (26):

26

where denotes the acceleration-limited candidate speed, with the current speed [], the (non-negative) acceleration limit [], and the control timestep . Similarly, is the deceleration-limited candidate speed [], where is the (positive) braking deceleration [] and ​ the remaining braking distance [m]; the final command uses .

As shown in Fig. 7b, the lookahead distance increases proportionally with the robot’s forward velocity, ranging from to This adaptive scaling enables tighter turning at low speeds and smoother tracking at higher speeds. By combining Eqs. (21) through (26), the controller jointly adjusts both the steering angle and linear velocity based on the robot’s state and motion constraints, enhancing robustness and trajectory stability across varying operating conditions.

Algorithm 2.

PP-DL

Input: Current robot state: ), Reference path: , Parameter: wheelbase (), lookahead bounds (), velocity limits , Constraints: Acceleration limit , Steering limit
Output: Steering command (), linear velocity command ()
begin	1. Compute dynamic lookahead distance: Calculate velocity ratio : Update lookahead distance (clamped between limits):    2. Determine lookahead point: Find nearest waypoint index and select goal point at distance from 3. Transform to vehicle coordinate frame: Transform to local coordinates : 4. Compute steering angle: ) 5. Compute velocity and apply constraints: 6. Return (
end

PP path tracking with dynamic lookahead and steering-based speed control (PP-DSC)

The PP-DSC algorithm enhances trajectory tracking performance by incorporating two key strategies. First, it dynamically adjusts the lookahead distance according to the robot’s linear velocity. Second, it adaptively regulates the forward velocity based on the robot’s current steering intensity.

To compute the steering angle, the algorithm follows the geometric formulation of the PP method. The steering angle is calculated based on the position of the lookahead point in the vehicle’s local coordinate frame, as shown in Eq. (27):

27

In this equation, ​ is the lateral displacement of the lookahead point, is the wheelbase, and is the lookahead distance. To ensure that the steering remains within the robot’s mechanical limits, the output from Eq. (27) is bounded using a clamping function described in Eq. (28):

28

The lookahead distance is dynamically adapted to the current robot velocity , scaling between minimum and maximum limits. This velocity-dependent adjustment is calculated using Eq. (29):

29

As shown in Fig. 8a, the conceptual model illustrates how steering behavior influences lookahead adjustments. Meanwhile, Fig. 8b provides a parametric surface that highlights how the lookahead distance changes with respect to both forward velocity and steering percentage.

Fig. 8.

Steering-adaptive lookahead concept and surface plot. (a) Conceptual diagram of steering-based lookahead behavior; (b) Parametric surface of lookahead distance as a function of velocity and steering percentage.

To achieve better stability during the turning maneuvers, the robot’s velocity is modulated based on the current steering demand. This process begins by normalizing the steering angle magnitude, resulting in a steering percentage, as shown in Eq. (30):

30

Here the absolute value operator is applied to ensure that the steering percentage represents the magnitude of the turning intensity, independent of the direction (left or right). This metric quantifies how close the steering angle is to its maximum allowable limit. Based on this value, the robot’s target linear velocity is selected according to a piecewise function described in Eq. (31):

31

The interpolation factor used in the third case of Eq. (31) is given by Eq. (32):

32

By combining the steering formulation in Eq. (27), the clamping in Eq. (28), the dynamic lookahead computation in Eq. (29), and the adaptive velocity control from Eq. (30) through Eq. (32), the PP-DSC algorithm enables the robot to track reference trajectories with greater precision and smoother motion, even under varying curvature and speed conditions.

This algorithm has been implemented and tested in various experimental scenarios. The configuration parameters used in both PP and the proposed PP-DSC as listed in Table 3. Compared to the earlier PP-DSC implementation³⁰, which used a fixed lookahead of 1.0 m with velocity adaptation between 1.0 and 3.0 m/s, the current configuration employs a wider dynamic lookahead range (0.5–5.0 m) and broader steering thresholds (0.2–0.7) to accommodate the higher operational speed of 5.0 m/s and the diverse path geometries tested in this study

Table 3.

Algorithm parameter configuration for PP and PP-DSC experiments.

PP			PP-DSC
Parameters	Value	Unit	Parameters	Value	Unit
	0.6135	m		0.6135	m
	1.0, 4.0	m		0.5	m
	5.0	m/s		4.0	m
				0.5	m/s
				5.0	m/s
				0.2	–
				0.7	–

Algorithm 3.

PP-DSC

Input: Current robot state: ), Reference path: , Parameter: wheelbase (), lookahead range (), velocity limits , Thresholds: steering percentage thresholds [(corresponding to ), Constraint: Maximum steering angle
Output: Steering command (), linear velocity command ()
begin
	1. Compute dynamic lookahead distance (Velocity-based): Calculate normalized velocity ratio : Update lookahead distance :    2. PP Steering Calculation: Find goal point at distance from Transform to local coordinates : Calculate steering angle: Apply steering saturation: 3. Steering-Based Speed Control: Calculate steering intensity ratio : Compute velocity interpolation factor based on thresholds: Calculate adaptive velocity (Linear interpolation): 4. Return (
end

Stability and performance analysis (Lyapunov)

Lateral and heading errors are denoted ​ and ​ in a frenet frame attached to the reference path. The Lyapunov function is defined in Eq. (33):

33

Using the car-like kinematics (e.g., Eq. 11), the PP and PP-DSC relations together with the velocity constraints (e.g., Eqs. 21–26 and Eqs. 27–32), the time derivative along closed-loop trajectories admits the bound in Eq. (34):

34

For bounded curvature and sufficiently small errors, the mixed term is dominated, yielding the negative-definite inequality in Eq. (35):

35

which implies local asymptotic stability on straight or low-curvature segments. When curvature is nonzero but bounded, the steering-based speed envelope summarized in Eqs. (36),

36

which yields uniform ultimate boundedness of () under the same actuator limits.

To achieve this, the design parameters are selected by choosing ​ such that , setting based on terrain limits, and enforcing ​.

Implementation procedure

The proposed navigation system was implemented following a structured workflow, as illustrated in Fig. 9. The process begins with system initialization, sensor and communication checks, followed by localization using fused data from GNSS, IMU, and encoder sensors. A state estimation module integrates these inputs to support reliable path planning and path-following.

Fig. 9.

Flowchart of autonomous navigation process flow.

The system was tested in an open-sky environment under optimal GNSS conditions (Fig. 10a). All trials were conducted on a flat, unobstructed open field (≈ 64 × 20 m) under dry outdoor conditions, ensuring minimal GNSS obstruction and stable footing during runs. To evaluate the tracking performance, three trajectory types were tested: a linear path (19.59 m), a loop path (43.52 m), and a figure-eight path (42.71 m) (Fig. 10b). These paths were selected to reflect different motion dynamics ranging from straightforward movement to continuous and alternating turns allowing assessment of the system’s adaptability and tracking accuracy under varied navigation scenarios.

Fig. 10.

Field experimental setup and reference trajectories: (a) Aerial view of the test site under open-sky conditions; (b) Geometry and total path lengths () of the three test paths: Line (1), Loop (2), and Figure-eight (3).

Application framework for chemical process plant navigation

To evaluate the applicability of PP-DSC in industrial environments, this study extends the validation framework to AMR navigation within chemical process plants. The case study is based on an EFB biodiesel facility optimized using MINLP with Dow’s F&EI safety constraints⁶. In chemical plants, AMRs perform critical tasks including equipment inspection using thermal cameras and gas detectors, material transport between process units, safety monitoring in high-hazard areas, and emergency response operations. These applications require precise path tracking in confined spaces with varying hazard levels.

EFB biodiesel plant configuration and simulation model

To ensure a comprehensive evaluation, the study included testing in an open field environment to establish baseline performance, before extending the validation to an industrial setting. The reference facility is a 1000 t/d EFB biodiesel plant with a footprint of 92 × 65 m, comprising 57 equipment items across seven process sections (S1–S7) ranging from pretreatment to hydrocracking, as summarized in Table 4. The plant layout, along with designated hazard zones, is illustrated in Fig. 11.

Table 4.

Process section characteristics for EFB biodiesel plant.

Section	Function	Hazard	F&EI Radius* (m)	Path type
S1	Pretreatment	Low	0	Patrol
S2	Pyrolysis	High	8	Loop
S3	Combustion	High	6	Loop
S4	Separation	Medium	4	Figure-8
S5	Hydrotreating	High	7	Loop
S6	Distillation	Medium	5	Figure-8
S7	Hydrocracking	High	9	Loop

*Assumed values for simulation; original study uses F&EI constraints without explicit radii.

Fig. 11.

EFB plant layout (92 × 65 m) with F&EI-based hazard zones and AMR trajectories.

While the actual infrastructure involves a multi-floor arrangement (varying from 1 to 3 floors), this study employs a two-dimensional (2D) kinematic model operating strictly in the X-Y plane. Each process section is simulated independently based on its ground-floor layout. This planar approach is appropriate as wheeled AMR navigation is confined to flat floor surfaces—excluding vertical transport mechanisms—thereby allowing for a consistent and direct comparison of algorithm performance across the facility’s diverse path geometries.

Safety-aware navigation and simulation

The PP-DSC algorithm was extended with a safety factor S_f for F&EI-based velocity modulation: where when inside the hazard zone, otherwise 1.0. A minimum factor of 0.3 prevents complete stoppage. Kinematic simulation was implemented in Python 3.10 using the exact PP-DSC equations: PP steering (Eq. 21), dynamic lookahead (Eq. 29), and velocity adaptation (Eqs. 31–32). The bicycle model used = 0.02 s with parameters: wheelbase 1.04 m, maximum steering 25°, lookahead 1.0–4.0 m, and velocity 0.5–3.0 m/s. The simulation adopted a wheelbase of 1.04 m to represent industrial-grade AMR platforms typically used in chemical plants, which are larger than the field experimental robot (0.6135 m).

Experiment setup

Field experiments were conducted to evaluate the GNSS-RTK-based navigation system’s path-tracking accuracy and positioning capability under real-world conditions. The experimental setup consisted of a mobile robot equipped with GNSS, IMU, and onboard computer (Fig. 12a), and a GNSS-RTK base station mounted on a tripod for high-precision differential correction (Fig. 12b). Tests were performed in an open field with minimal signal obstruction. Three trajectory types were evaluated: linear, loop, and figure-eight paths, at speeds ranging from 1 to 5 m/s. Routes were defined using UTM coordinates for precise Cartesian control. In all experimental trials, the robot was initialized at the starting point of the reference trajectory. The robot was manually positioned to align with the path tangent, ensuring minimal initial lateral error and heading deviation. This setup was chosen to evaluate tracking stability and control performance starting from an ideal state³⁰ .

Fig. 12.

Experimental platform and GNSS-RTK base station setup. (a) Mobile robot platform equipped with GNSS, IMU, and onboard computer. (b) GNSS-RTK base station on tripod for high-precision localization.

Two algorithms were compared: standard PP as baseline and the enhanced PP-DSC with dynamic lookahead and steering-aware velocity modulation. Performance was evaluated based on trajectory adherence and positioning precision using GNSS-RTK localization. Experimental conditions are summarized in Table 5, and all tests were conducted under real-time outdoor conditions to validate the system’s practical applicability.

Table 5.

Experimental condition summary.

Parameter	Value
Evaluation metrics	Path tracking accuracy, positioning capability
Coordinate system	UTM (Universal Transverse Mercator)
Control format	Cartesian (x, y)
Test scenarios	line path, loop path, and figure-eight path
Speed range	1–5 m/s
Positioning method	GNSS-RTK
Environment	Real-world conditions (actual routes)

Results and discussion

Performance comparison of path tracking algorithms

To quantitatively evaluate the effectiveness of the proposed PP-DSC algorithm, a comparative analysis was conducted against the standard PP algorithm across three reference trajectories: straight, loop, and figure-eight. To ensure statistical reliability, each experimental scenario was repeated for 5 independent trials, and the values reported represent the average performance. The tracking accuracy was quantified based on lateral deviation from the reference path using four standard metrics: Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Maximum Error (Max error), and Standard Deviation (SD).

Table 6 reveals a distinct performance gap across all tested geometries, with PP-DSC delivering significantly tighter control than fixed-lookahead baselines. On straight paths, PP-DSC achieved exceptional stability with RMSE of 0.05 m compared to 0.22 m for standard PP (4 m lookahead), representing a 77% error reduction and effectively eliminating steady-state oscillations. This precision extended to loop paths, where standard PP struggled with significant lateral drift (Max error: 1.59 m), while PP-DSC maintained tight curve adherence with RMSE of 0.09 m—an improvement of over 84%. On the complex figure-eight path, PP-DSC adapted smoothly to alternating curvature, maintaining consistent RMSE of 0.10 m compared to 0.32–0.34 m for standard methods. Overall, the data confirms that PP-DSC offers a substantial upgrade in tracking precision, particularly in geometrically complex environments.

Table 6.

Performance comparison of PP and PP-DSC algorithms on various path types.

Path	Algorithm	Lookahead (m)	Mean (m)	RMSE (m)	MAE (m)	Max error (m)	SD (m)
Line	PP	1	0.11	0.12	0.11	0.30	0.06
	PP	4	0.19	0.22	0.19	0.31	0.09
	PP-DSC	Dynamic	0.05	0.05	0.05	0.09	0.02
Loop	PP	1	0.28	0.44	0.28	1.31	0.33
	PP	4	0.40	0.58	0.40	1.59	0.43
	PP-DSC	Dynamic	0.07	0.09	0.07	0.30	0.06
Figure-eight	PP	1	0.27	0.34	0.27	0.93	0.21
	PP	4	0.25	0.32	0.25	0.89	0.20
	PP-DSC	Dynamic	0.08	0.10	0.08	0.26	0.06

Speed adaptation analysis

The ability to regulate velocity according to path geometry is essential for improving tracking accuracy and motion stability. Unlike standard PP, which uses fixed lookahead and does not adapt speed in real time, PP-DSC dynamically adjusts velocity based on steering percentage—the ratio of current steering angle to maximum steering angle (Eq. 30). The velocity is modified within predefined bounds (Eqs. 31–32), allowing deceleration during sharp turns and acceleration on straight paths.

Figure 13 presents time histories of steering angle and velocity for each trajectory. On straight paths (Fig. 13a), standard PP exhibited high velocity variance (SD = 2.41 m/s for 4 m lookahead), while PP-DSC maintained stable average velocity of 4.39 m/s with minimal SD of 0.20 m/s. For circular paths (Fig. 13b), PP-DSC demonstrated significant speed reduction in turns (2.50 m/s drop) compared to standard PP (0.10 m/s drop), prioritizing tracking accuracy over raw speed. Similarly, on figure-eight paths (Fig. 13c), PP-DSC showed consistent adaptive behavior with speed drop of 2.50 m/s during directional changes. Table 7 confirms this adaptive behavior quantitatively.

Fig. 13.

Velocity and steering angle time histories of PP-DSC on different path types: (a) line (normal speed test to demonstrate stability); (b) loop; (c) figure-eight.

Table 7.

Comparison of speed performance and smoothness for PP and PP-DSC algorithms.

Path	Algorithm	Lookahead	Avg speed (m/s)	Max speed (m/s)	Min speed (m/s)	SD (m/s)	Speed drop in turns (m/s)
Line	PP	1.00	3.11	4.87	0.50	2.32	0.30
	PP	4.00	2.41	4.82	0.50	2.41	0.10
	PP-DSC	Dynamic	4.39	4.62	4.16	0.20	0.10
Loop	PP	1.00	2.51	3.00	0.50	0.98	0.30
	PP	4.00	2.60	3.00	0.50	1.02	0.10
	PP-DSC	Dynamic	2.10	3.00	0.50	1.16	2.50
Figure-eight	PP	1.00	2.13	2.78	0.50	1.15	0.30
	PP	4.00	2.64	2.75	0.50	0.54	0.10
	PP-DSC	Dynamic	0.99	3.00	0.50	1.03	2.50

Unlike standard PP, which maintained relatively static speed profiles regardless of path geometry, PP-DSC demonstrated a strategic trade-off: achieving higher speeds on straight paths (4.39 m/s vs. 2.41 m/s) while automatically throttling down on curves to minimize lateral deviation. This geometry-aware speed regulation aligns with findings by Macenski et al.²⁹.

Localization accuracy

Localization accuracy is a key metric for evaluating the effectiveness of path-tracking algorithms, particularly in systems that rely on GNSS-RTK combined with real-time motion control. In this study, accuracy was assessed by comparing the robot’s actual position to the reference trajectory, with positional deviation at each time step used to compute standard error metrics.

Figure 14 illustrates the path tracking comparison between PP and PP-DSC algorithms across all tested trajectories. On straight paths (Fig. 14a), PP with 4 m lookahead exhibited noticeable oscillations and steady-state error with mean deviation of 0.19 m, while PP-DSC maintained tight adherence to the reference line with mean deviation of only 0.05 m—a 74% improvement. For loop paths (Fig. 14b), PP demonstrated pronounced overshooting behavior in curved sections (mean deviation: 0.52 m, max error: 1.59 m), leading to significant lateral drift during sustained turns. In contrast, PP-DSC significantly improved tracking fidelity in this segment (mean deviation: 0.07 m, max error: 0.30 m), representing an 87% reduction in mean error. Similarly, on figure-eight paths (Fig. 14c), which involve alternating left and right curves with variable curvature, PP showed inconsistent tracking with frequent overshoot and undershoot (mean deviation: 0.25 m). PP-DSC maintained highly consistent performance throughout the complex geometry (mean deviation: 0.08 m), successfully negotiating directional transitions without the erratic deviations seen in the fixed-lookahead approach.

Fig. 14.

Path tracking comparison with zoomed-in segments: (a) line; (b) loop; (c) figure-eight.

Table 8 summarizes the quantitative comparison by segment type. The PP algorithm exhibited substantially greater deviation during curves compared to straight sections, highlighting its limitation in handling continuous curvature. Conversely, PP-DSC maintained low and stable error metrics across both straight and curved path segments, demonstrating its adaptability to varying geometric conditions. PP-DSC differs from existing adaptive lookahead methods²⁹ by co-adapting both lookahead distance and forward speed through a single steering-normalized signal, which explains the observed robustness on curved segments. These results validate the effectiveness of the dynamic steering-based control strategy for improving localization accuracy, particularly in environments with frequent directional changes and complex path geometries.

Table 8.

Quantitative error comparison between PP and PP-DSC.

Path	Algorithm	Lookahead	Segment type	Mean deviation (m)	Max deviation (m)	SD (m)
Line	PP	1	Straight	0.11	0.30	0.06
		4	Straight	0.19	0.31	0.09
	PP-DSC	Dynamic	Straight	0.05	0.09	0.02
Loop	PP	1	Straight	0.23	1.31	0.42
		1	Curve	0.33	1.31	0.40
		4	Straight	0.28	0.50	0.27
		4	Curve	0.52	1.59	0.32
	PP-DSC	Dynamic	Straight	0.05	0.22	0.05
		Dynamic	Curve	0.07	0.30	0.07
Figure-eight	PP	1	Straight	0.25	0.93	0.20
		1	Curve	0.25	0.89	0.24
		4	Straight	0.22	0.89	0.21
		4	Curve	0.25	0.89	0.24
	PP-DSC	Dynamic	Straight	0.07	0.24	0.06
		Dynamic	Curve	0.08	0.26	0.07

Simulation results in chemical plant environment

The PP-DSC algorithm with safety integration was validated through kinematic simulation across all seven sections of the EFB biodiesel plant. Three algorithm configurations were compared: Standard PP with fixed lookahead distance of 4.0 m and constant velocity of 2.5 m/s, PP-DSC with dynamic lookahead and velocity adaptation, and PP-DSC+Safety with additional F&EI-based velocity modulation in designated hazard zones. The simulation results provide critical insights for deploying AMRs in chemical process environments where safety constraints and confined spaces present challenges distinct from open-field environments.

Trajectory analysis for EFB process applications

Figure 15 presents trajectory comparisons between standard PP and PP-DSC+Safety in three representative process sections, each corresponding to distinct chemical process operations with different hazard profiles and AMR task requirements.

Fig. 15.

Trajectory comparison across process sections: (a) S2 Pyrolysis reactor inspection, (b) S4 Separation unit sample transport, (c) S7 Hydrocracker inspection.

Figure 15a Pyrolysis section (S2): This high-hazard section houses thermal decomposition reactors operating at 450–500 °C, where AMR inspection tasks involve monitoring reactor vessel integrity, detecting thermal anomalies, and checking for bio-oil leakage. The loop trajectory circumnavigates the pyrolysis reactor with an assumed F&EI exclusion radius of 8 m. Standard PP (red line) achieved RMSE of 0.040 m with maximum error of 0.076 m, while PP-DSC+Safety (green line) achieved RMSE of 0.080 m with maximum error of 0.251 m. The dashed circle indicates the F&EI hazard zone boundary where the AMR must reduce velocity to minimize ignition risk from potential flammable vapor releases. From a chemical engineering perspective, the superior tracking accuracy of Standard PP in this section is advantageous for close-proximity inspection of reactor flanges, pressure relief valves, and instrumentation connections where precise positioning is critical for thermal imaging and gas detection.

Figure 15b Separation section (S4): This floor section performs phase separation via quenching operations, requiring AMRs to transport quality control samples between the separation vessels and the plant laboratory. The figure-8 trajectory represents a typical sample collection route connecting two separation units. Both algorithms showed elevated tracking errors due to the complex path geometry with sharp directional reversals: Standard PP achieved RMSE of 0.701 m while PP-DSC+Safety reached 0.940 m, representing 34% performance degradation. The significantly higher error for PP-DSC+Safety is attributed to the “path jumping” phenomenon at the figure-8 intersection point. When the dynamic lookahead distance reduces to approximately 1–2 m during curve navigation, the algorithm searches for the nearest waypoint within this shortened radius. At the path intersection, waypoints from both loops fall within the search radius, causing the algorithm to incorrectly select waypoints on the opposite loop and deviate from the intended trajectory. In contrast, Standard PP with its fixed 4 m lookahead maintains visibility beyond the intersection point, consistently tracking waypoints on the correct loop. In chemical process operations, such tracking errors could cause the AMR to deviate from designated safe corridors between process equipment, potentially entering restricted maintenance zones or obstructing operator access paths. The medium hazard level (F&EI radius 4 m) around separation vessels reflects risks from volatile organic compounds (VOCs) released during liquid-vapor separation. Sample transport missions in this section require careful path planning to avoid interference with operators performing manual sampling or equipment adjustments. This finding suggests that self-intersecting paths should be avoided in industrial AMR route design, or alternative path-tracking algorithms with loop-aware waypoint selection should be considered for such geometries.

Figure 15c Hydrocracking section (S7): This section contains the highest-risk equipment in the plant, with hydrogen compressors and hydrocracking reactors creating the largest assumed F&EI exclusion zone (radius 9 m). The AMR inspection mission involves monitoring hydrogen leak detection sensors, checking compressor vibration levels, and verifying catalyst bed temperature profiles. Standard PP achieved RMSE of 0.045 m compared to 0.075 m for PP-DSC+Safety. The tight tracking accuracy of Standard PP is particularly valuable in this section, as hydrogen releases pose severe explosion risks and the AMR must maintain precise distances from potential ignition sources. The consistent path following also ensures reproducible sensor positioning for trend analysis of equipment condition over multiple inspection cycles, which is essential for predictive maintenance programs in hydroprocessing units.

Velocity and safety factor analysis

Figure 16 presents detailed behavioral analysis of AMR navigation in the pyrolysis section (S2), demonstrating how the safety-aware algorithm responds to F&EI constraints in a high-hazard chemical process environment.

Fig. 16.

Pyrolysis section (S2) detailed analysis: (a) velocity profiles, (b) safety factor variation, (c) dynamic lookahead distance, (d) cross-track error distribution.

Figure 16a Velocity profiles: The velocity comparison reveals fundamental differences in how each algorithm approaches navigation near hazardous chemical equipment. Standard PP (red line) maintains constant velocity at 2.5 m/s throughout the inspection trajectory, regardless of proximity to the pyrolysis reactor operating at 450–500 °C. This behavior, while providing consistent tracking, does not account for the elevated risk when the AMR passes within the F&EI exclusion zone. PP-DSC (blue line) adapts velocity based on path curvature, starting at approximately 0.5 m/s during initialization, accelerating to 3.0 m/s on straight segments, then stabilizing around 2.0–2.3 m/s during steady-state operation. PP-DSC+Safety (green line) shows similar dynamic behavior but with consistently lower velocities due to safety modulation, stabilizing at approximately 1.9–2.0 m/s. From a process safety perspective, these reduced velocities compared to Standard PP provide longer response time for emergency stops if the onboard gas detector identifies elevated concentrations of pyrolysis vapors or combustible gases.

Figure 16b Safety factor variation: The safety factor (S_f) plot demonstrates how the F&EI-based velocity modulation responds to the AMR’s position relative to the hazard center. The dashed line at S_f = 1.0 represents operation outside the hazard zone. The red shaded region indicates when the AMR operates within the F&EI zone with reduced velocity. As shown in the figure, the safety factor ranges from approximately 0.84–0.87 throughout most of the 20-second inspection cycle, with a minimum of approximately 0.84 at closest approach to the reactor center. This indicates that the loop trajectory maintains the AMR within the hazard zone for nearly the entire inspection mission, as the path circumnavigates the pyrolysis reactor at distances closer than the 8 m F&EI radius. For chemical plant operations, this safety margin ensures continuous velocity modulation during reactor inspection, providing operators in the control room with confidence that the AMR maintains reduced speed throughout the high-risk proximity zone.

Figure 16c Dynamic lookahead distance: The lookahead distance comparison illustrates why Standard PP outperforms PP-DSC in this confined loop path scenario. Standard PP maintains a fixed 4.0 m lookahead (red line), providing consistent anticipation of the curved trajectory around the reactor. PP-DSC and PP-DSC+Safety dynamically adjust lookahead between 3.0 and 4.0 m based on steering demands, reducing lookahead during high-curvature segments where the path bends around equipment corners. In chemical plant environments with tight turning radii (5–12 m in this study), the shortened lookahead can cause the algorithm to focus too narrowly on immediate path segments, losing awareness of upcoming directional changes. This contrasts with agricultural applications where gradual curves over 100–200 m paths benefit from the dynamic adaptation. The implication for chemical process navigation is that lookahead parameters optimized for open-field operations require recalibration for industrial facilities where equipment spacing constraints create fundamentally different path geometries.

Figure 16d Error distribution: The histogram comparison of cross-track errors provides statistical insight into tracking reliability for chemical process inspection tasks. Standard PP exhibits a narrow, symmetric distribution centered at µ = 0.037 m, indicating consistent positioning throughout the inspection cycle. PP-DSC shows a broader distribution (µ = 0.054 m), while PP-DSC+Safety produces slightly higher mean error (µ = 0.057 m) due to velocity reduction in hazard zones. For chemical engineering applications requiring repeatable sensor positioning—such as thermal imaging of reactor vessels, ultrasonic thickness measurements of piping, or fixed-point gas concentration monitoring—the tighter error distribution of Standard PP ensures more consistent data quality across multiple inspection cycles. This repeatability is essential for trending equipment condition over time, as maintenance engineers rely on consistent measurement positions to detect gradual degradation such as corrosion progression, insulation deterioration, or developing thermal anomalies.

Performance comparison across process sections

Table 9 summarizes simulation results across all seven process sections, with performance analyzed in the context of chemical engineering operations and AMR task requirements. The data reveals that Standard PP outperformed PP-DSC+Safety in five of seven sections (S1–S4, S7), with RMSE increases ranging from + 27% in S1 pretreatment to + 100% in S2 pyrolysis. Sections S5 (hydrotreating) and S6 (distillation) showed PP-DSC+Safety advantages, with RMSE reductions of 17% and 11% respectively, demonstrating that the algorithm performs well in moderate-curvature paths where its design assumptions from agricultural applications remain valid.

Table 9.

Tracking accuracy comparison with chemical process context.

Section	Process operation	AMR task	PP RMSE (m)	PP-DSC+Safety RMSE (m)	Δ Error (%)
S1	Pretreatment	Area patrol	0.319	0.406	+ 27%
S2	Pyrolysis	Reactor inspection	0.040	0.080	+ 100%
S3	Combustion	Combustor inspection	0.040	0.078	+ 95%
S4	Separation	Sample transport	0.701	0.940	+ 34%
S5	Hydrotreating	Compressor inspection	0.395	0.326	−17%
S6	Distillation	Product transport	0.467	0.416	−11%
S7	Hydrocracking	Hydrocracker inspection	0.045	0.075	+ 67%

Figure 17a visualizes the RMSE comparison across all sections with an orange dashed line indicating the 0.15 m target threshold for acceptable tracking accuracy. Sections S2, S3, and S7 achieved sub-threshold performance with Standard PP, while other sections exceeded this target regardless of algorithm selection. The bar chart clearly shows that S4 separation section exhibited the highest errors (0.70–0.94 m) due to the path jumping phenomenon at figure-8 intersections, while S2 pyrolysis and S7 hydrocracking achieved the lowest errors (0.04–0.08 m) with simple loop paths.

Fig. 17.

Performance summary: (a) RMSE comparison by section with 0.15 m target threshold, (b) overall algorithm performance.

Figure 17b presents overall algorithm performance metrics. Standard PP achieved mean RMSE of 0.287 m and mean maximum error of 0.710 m. PP-DSC showed mean RMSE of 0.330 m and mean maximum error of 0.817 m. Notably, PP-DSC+Safety exhibited mean RMSE of 0.332 m but achieved lower mean maximum error of 0.806 m compared to PP-DSC, indicating that safety-aware velocity modulation effectively reduces extreme tracking deviations despite marginally higher average errors. This characteristic is particularly valuable for chemical plant operations where preventing extreme deviations from safe corridors is more critical than minimizing average tracking error.

The results reveal geometry-dependent performance patterns that provide evidence-based algorithm selection criteria. In high-hazard sections with thermal reactors (S2, S3) and hydrogen-handling equipment (S7), Standard PP achieved sub-0.05 m RMSE using loop paths with radii of 5–9 m around individual equipment items, where the fixed 4.0 m lookahead provides optimal trajectory anticipation. Conversely, PP-DSC+Safety demonstrated superior performance in sections S5 and S6, where larger equipment footprints create moderate-curvature paths that align with the algorithm’s design characteristics. In these sections, PP-DSC+Safety achieved RMSE reductions of 17% and 11% respectively compared to Standard PP, demonstrating that the algorithm excels in moderate-curvature paths. Furthermore, the integrated F&EI-based safety factor ensures automatic velocity reduction in hazard zones, maintaining compliance with Process Safety Management (PSM) requirements while adding less than 1% tracking overhead compared to PP-DSC without safety modulation.

Implications for chemical process operations

Table 10 summarizes overall algorithm performance. Standard PP achieved the best average RMSE (0.287 m), while PP-DSC and PP-DSC+Safety showed 14.9% and 15.6% higher RMSE respectively. Notably, PP-DSC+Safety exhibited lower maximum error (0.806 m) than PP-DSC (0.817 m), indicating that safety modulation helps constrain extreme deviations despite marginally higher mean error.

Table 10.

Overall performance summary.

Metric	Standard PP	PP-DSC	PP-DSC+Safety
Average RMSE (m)	0.287	0.330	0.332
Average Max Error (m)	0.710	0.817	0.806
RMSE increase vs. Standard PP	–	+ 14.9%	+ 15.6%
Best for	Small loops (S2,S3,S7)	Medium loops (S5,S6)	Medium loops (S5,S6)

The F&EI-based safety factor adds less than 1% tracking overhead while providing automatic velocity reduction in hazard zones, addressing PSM and Layer of Protection Analysis (LOPA) requirements. As demonstrated in S2 pyrolysis section, the safety factor maintained at 0.84–0.87 throughout the inspection cycle confirms that velocity modulation is essential for compliant operations.

Plant operators should select algorithms based on mission requirements: Standard PP with fixed 4.0 m lookahead is recommended for reactor inspection in S2, S3, and S7 where sub-0.10 m positioning accuracy is required, while PP-DSC+Safety is recommended for material transport in S5 and S6 where moderate-curvature paths align with algorithm design characteristics. The PP-DSC parameters optimized for open-field conditions do not transfer effectively to chemical plant environments, as the 5–9 m path radii typical of equipment spacing create fundamentally different curvature profiles than gentle curves in open areas. These findings are consistent with earlier results where PP-DSC with fixed lookahead achieved RMSE values of 0.009 m on straight paths and 0.021 m on S-curves at 1.0–3.0 m/s³⁰, confirming that the steering-based velocity modulation principle scales effectively to higher speeds and larger operational areas when combined with adaptive lookahead adjustment.

Conclusions

This study developed PP-DSC, an enhanced Pure Pursuit algorithm deployed on a steering-type AMR platform. Field experiments demonstrated significant improvement over Standard PP, with the enhanced performance attributed to PP-DSC’s ability to automatically reduce velocity before entering curves while extending lookahead on straight segments, resulting in smoother transitions and more stable trajectory tracking.

Cross-domain evaluation in a simulated EFB biodiesel plant (57 equipment items across seven process sections) revealed geometry-dependent performance characteristics. Standard PP outperformed Safety-integrated PP-DSC in overall metrics due to path jumping at figure-8 intersections, where shortened dynamic lookahead caused the algorithm to select waypoints on the wrong loop. However, Safety-integrated PP-DSC achieved better performance in moderate-curvature sections (S5 hydrotreating and S6 distillation) where path geometries aligned with its design characteristics.

The F&EI-based safety integration demonstrated practical viability, maintaining safety factor at 0.84–0.87 throughout inspection cycles while ensuring automatic velocity reduction in hazard zones for PSM compliance. These findings establish evidence-based algorithm selection criteria for chemical plant AMR deployment: Standard PP for tight-radius inspection paths around individual equipment, Safety-integrated PP-DSC for moderate-curvature transport routes requiring hazard zone velocity compliance.

Limitations and future work

For open-field applications, future research will incorporate machine learning techniques for complex terrain adaptation, extend the control framework to handle 3D dynamics on slopes and varying friction on wet surfaces, and conduct long-endurance multi-cycle testing to evaluate robustness against error accumulation.

For industrial chemical plant applications, hybrid algorithms switching between fixed lookahead for sharp corners and dynamic adaptation for open corridors could combine the strengths of both approaches. Physical validation in pilot-scale or decommissioned facilities would verify simulation predictions under real-world conditions. Integration with plant digital twin systems could enable path optimization based on real-time process conditions, while adaptive parameter tuning based on local path curvature detection could maintain PP-DSC advantages across diverse environments.

Regarding limitations, the proposed equations are platform-agnostic but validated on a single steering-type robot only. MEMS-based IMU thermal drift was negligible in short-duration tests but requires active temperature compensation for long-term applications. The current implementation is limited to single-floor operation; multi-floor navigation requiring elevator integration or ramp traversal has not been addressed. Generalization across different geometries, slopes, and wet surfaces requires empirical verification through multi-robot simulation followed by hardware trials.

Author contributions

Conceptualization, N.P. and S.S.; Data curation, N.P.; Formal analysis, N.P., N.J., A.P., P.K., and S.S.; Funding acquisition, P.K. and S.S.; Investigation, N.P., N.J. and S.S.; Resources, N.P., P.K., and S.S.; Software, N.P. and S.S.; Supervision, S.S.; Validation, N.P. and S.S.; Writing—original draft preparation, N.P. and S.S.; Writing—review and editing, N.P., N.J., A.P., P.K., and S.S.; All authors have read and agreed to the published version of the manuscript.

Funding

This research was supported by Gensurv Co., Ltd., Thailand, through the provision of equipment. This work was partially supported by the National Research Council of Thailand (NRCT) contract no. N84A680679. The authors also acknowledge Khon Kaen University for granting access to research facilities.

Data availability

Data will be made available on request.

Declarations

Competing interests

The authors declare no competing interests.

Declaration of generative AI in scientific writing

During the preparation of this work, the authors used Claude Opus 4.5 to improve the readability and language of the manuscript. After using this tool/service, the authors carefully reviewed and edited the content as necessary and certified that the technology was used under full human oversight. The authors take full responsibility for the content of the published article.