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Integration of Trailer and Tractor Mobile Robot Considering Towing Dynamics Cover

Integration of Trailer and Tractor Mobile Robot Considering Towing Dynamics

By: Ünal Dana and  Levent Çetin  
Open Access
|Mar 2026

Figures & Tables

Figure 1.

2D illustration of (a) omniwheel mobile robot and (b) trailer

Figure 2.

Forces (a), torques (b) on trailer

Figure 3.

Forces (a), torques (b) on omniwheel mobile robot

Figure 4.

Mobile robot integrated trailer representation

Figure 5.

Cubic Bézier curve

Figure 6.

Pure pursuit algorithm

Figure 7.

Pure pursuit algorithm example for (a) low, (b) high lookahead distance

Figure 8.

Dynamic tracking control

Figure 9.

Input voltage and output velocity against time

Figure 10.

Curve fitting of the transfer function

Figure 11.

Tested motor transfer function and PID parameters

Figure 12.

PID controlled motor transfer function

Figure 13.

Simulation block diagram of trailer control

Figure 14.

Trailer control simulation in MATLAB Simulink

Figure 15.

Subsystem of path generation and path tracking algorithm

Figure 16.

Dynamic tracking control subsystem

Figure 17.

Subsystem of the trailer mechanical Simscape model

Figure 18.

Stopping algorithm of the trailer

Figure 19.

Simulation start, the trailer is at the beginning of the path (a) isometric view, (b) front view, (c) top view, (d) bottom view

Figure 20.

Simulation Block Diagram of the tractor robot

Figure 21.

Subsystem of dynamic tracking control of trailer towed by omniwheel mobile robot

Figure 22.

Simulation start, the mobile robot and trailer are at the beginning of the path (a) isometric view, (b) left view, (c) top view, (d) bottom view

Figure 23.

Bézier Curve path analysis with tuned parameters

Figure 24.

Linear velocity of the towed trailer

Figure 25.

Angular velocity of towed trailer

Figure 26.

Square path analysis (D=0.75 m)

Figure 27.

Linear velocity of towed trailer on square path

Figure 28.

Angular velocity of towed trailer on square path

Figure 29.

Square path analysis (D=1.25 m)

Figure 30.

Linear velocity of towed trailer on square path

Figure 31.

Angular velocity of towed trailer on square path

Figure 32.

Circular path analysis

Figure 33.

Linear velocity of towed trailer on circular path

Figure 34.

Angular velocity of towed trailer on circular path

Figure 35.

Archimedean spiral path analysis

Figure 36.

Linear velocity of towed trailer on Archimedean spiral path

Figure 37.

Simulated vs desired angular velocity of towed trailer on Archimedean spiral path

Figure 38.

Simulation block diagram including PID control

Figure 39.

Simulating the selected motors

Figure 40.

Bézier curve path analysis with implementation of PID controlled dc motors

Figure 41.

Linear velocity of towed trailer on Bézier curve path with implementation of PID controlled dc motors

Figure 42.

Angular velocity of towed trailer on Bézier curve path with implementation of PID controlled dc motors

Tuned PID Parameters

PIDN
Motor 10.2310.3580.00715796.2
Motor 20.1580.4930.0115750.9
Motor 30.1660.5350.0126962.8

Performance Comparison of Non-Tuned, Tuned, and Motor Integrated PID Tuned Controllers

MetricNon-TunedTunedMotor Integrated PID Tuned
Steady State Linear Velocity Error (Vess,%)13.296.264.32
Linear Velocity Overshoot (%)8.6817.4817.17
Steady State Time (Tss, s)N/AN/A61.9
Maximum Angular Velocity Error (ϕ˙emax ,rad/s)\left( {{{\dot \phi }_{{\rm{emax }}}},{\rm{rad}}/{\rm{s}}} \right)0.1040.0920.117
Average Angular Velocity Error (ϕ˙eavg ,rad/s)\left( {{{\dot \phi }_{{\rm{eavg }}}},{\rm{rad}}/{\rm{s}}} \right)0.0100.0060.008
Execution Time (s)74.772068.757367.2488
Tracking Error (Max, m)0.07770.07550.0756
Tracking Error (RMS, m)0.04250.04080.0404
Tracked Path Length (m)6.6206.6206.630
Planned Path Length (m)6.6276.6276.627
DOI: https://doi.org/10.14313/jamris-2026-003 | Journal eISSN: 2080-2145 | Journal ISSN: 1897-8649
Language: English
Page range: 24 - 40
Submitted on: Feb 28, 2025
|
Accepted on: Apr 25, 2025
|
Published on: Mar 31, 2026
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2026 Ünal Dana, Levent Çetin, published by Łukasiewicz Research Network – Industrial Research Institute for Automation and Measurements PIAP
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.