1. MMC
  2. All Volumes and Issues
  3. Volume 12, Number 2, 2025
  4. Motion planning of sensorless differential drive mobile robot using clothoid

Motion planning of sensorless differential drive mobile robot using clothoid

MMC.
2025;
Volume 12, Number 2
: pp. 693–708
https://doi.org/10.23939/mmc2025.02.693
Received: March 20, 2025
Revised: June 23, 2025
Accepted: June 26, 2025

Zakaria W. Z. E. W., Ramli A. L. A.,  Reif U.  Motion planning of sensorless differential drive mobile robot using clothoid.  Mathematical Modeling and Computing. Vol. 12, No. 2, pp. 693–708 (2025)

Authors:
  1. W. Z. E. W. Zakaria
  2. A. L. A. Ramli
  3. U. Reif
1
School of Industrial Technology, Universiti Sains Malaysia (USM)
2
School of Mathematical Sciences, Universiti Sains Malaysia (USM)
3
Technische Universität Darmstadt

Mobile robots have the ability to navigate safely and cost-effectively from one location to another.  In sensorless motion planning, the absence of sensor data poses challenges for continuous replanning to ensure that the robot follows the desired trajectory.  Our research addresses this gap by leveraging computational methods for curve generation within the domain of Computer-Aided Geometric Design (CAGD).  Specifically, we propose a clothoid-based, sensorless motion planning algorithm for differential drive mobile robots, assuming the known initial point, end point, and initial direction.  Differential drive mobile robots, commonly used in various vehicles and robotics applications, are valued for their reliability and ease of use.  These robots control movement through differential speed adjustments between the left and right wheels, with curvature determining the respective wheel speeds.  In this paper, we detail the process of generating the clothoid curve and connecting it across two or more points, ensuring that each consecutive clothoid follows the direction in which the previous clothoid ends.  We also present simulation results to assess the effectiveness of the proposed technique.  The curve formulation and computational approach are tailored to this specific problem, utilizing MATLAB's Remote API capabilities and CoppeliaSim's robot simulation software for implementation.

differential drive
clothoid
robot simulation
motion planning
mobile robot
  1. Sun H., Zhang W., Yu R., Zhang Y.  Motion planning for mobile robots – Focusing on deep reinforcement learning: A systematic review.  IEEE Access.  9, 69061–69081 (2021).
  2. Xiao X., Liu B., Warnell G., Stone P.  Motion planning and control for mobile robot navigation using machine learning: a survey.  Autonomous Robots.  46 (5),  569–597 (2022).
  3. Liu C., Zhai L., Zhang X.  Research on local real-time obstacle avoidance path planning of unmanned vehicle based on improved artificial potential field method.  2022 6th CAA International Conference on Vehicular Control and Intelligence (CVCI).  1–6 (2022).
  4. Janoš J., Von'asek V., Pěnička R.  Multi-goal path planning using multiple random trees.  IEEE Robotics and Automation Letters.  6 (2), 4201–4208 (2021).
  5. Arslan Ö., Tiemessen A.  Adaptive Bézier degree reduction and splitting for computationally efficient motion planning.  IEEE Transactions on Robotics.  38 (6), 3655–3674 (2022).
  6. Zhang M., Sutcliffe M., Nicholson P. I., Yang Q.  Efficient Autonomous Path Planning for Ultrasonic Non-Destructive Testing: A Graph Theory and K-Dimensional Tree Optimisation Approach.  Machines.  11 (12), 1059 (2023).
  7. Hang P., Lv C., Xing Y., Huang C., Hu Z.  Human-like decision making for autonomous driving: A noncooperative game theoretic approach.  IEEE Transactions on Intelligent Transportation Systems.  22 (4), 2076–2087 (2020).
  8. Khatib O.  Real-time obstacle avoidance for manipulators and mobile robots.  The International Journal of Robotics Research.  5 (1), 90–98 (1986).
  9. Zhu K., Zhang T.  Deep reinforcement learning based mobile robot navigation: A review.  Tsinghua Science and Technology.  26 (5), 674–691 (2021).
  10. Lumelsky V. J., Stepanov A. A.  Path-planning strategies for a point mobile automaton moving amidst unknown obstacles of arbitrary shape.  Algorithmica.  2 (1), 403–430 (1987).
  11. Singh R., Ren J., Lin X.  A review of deep reinforcement learning algorithms for mobile robot path planning.  Vehicles.  5 (4), 1423–1451 (2023).
  12. Hewawasam H. S., Ibrahim M. Y., Appuhamillage G. K.  Past, present and future of path-planning algorithms for mobile robot navigation in dynamic environments.  IEEE Open Journal of the Industrial Electronics Society.  3, 353–365 (2022).
  13. Wijayathunga L., Rassau A., Chai D.  Challenges and solutions for autonomous ground robot scene understanding and navigation in unstructured outdoor environments: A review.  Applied Sciences.  13 (17), 9877 (2023).
  14. Wang B., Liu Z., Li Q., Prorok A.  Mobile robot path planning in dynamic environments through globally guided reinforcement learning.  IEEE Robotics and Automation Letters.  5 (4), 6932–6939 (2020).
  15. Alshorman A. M., Alshorman O., Irfan M., Glowacz A., Muhammad F., Caesarendra W.  Fuzzy-based fault-tolerant control for omnidirectional mobile robot.  Machines.  8 (3), 55 (2020).
  16. Cimurs R., Suh I. H., Lee J. H.  Information-based heuristics for learned goal-driven exploration and mapping.  2021 18th International Conference on Ubiquitous Robots (UR).  571–578 (2021).
  17. Li C., Guo S., Guo J.  Study on obstacle avoidance strategy using multiple ultrasonic sensors for spherical underwater robots.  IEEE Sensors Journal.  22 (24), 24458–24470 (2022).
  18. Ngwenya T., Ayomoh M., Yadavalli S.  Virtual obstacles for sensors incapacitation in robot navigation: A systematic review of 2D path planning.  Sensors.  22 (18), 6943 (2022).
  19. Costanzo M.  Control of robotic object pivoting based on tactile sensing.  Mechatronics.  76, 102545 (2021).
  20. Khalil A., Mukhopadhyay S., Rehman H.  Comparative Performance Analysis of PI Controller and MRAC for a Differential Drive Robot.  2022 5th International Conference on Communications, Signal Processing, and their Applications (ICCSPA).  1–6 (2022).
  21. Xia S., Zhao M., Adhivarahan C., Hou K., Chen Y., Nie J., Wu E., Dantu K., Jiang X.  Anemoi: A Low-cost Sensorless Indoor Drone System for Automatic Mapping of 3D Airflow Fields.  ACM MobiCom '23: Proceedings of the 29th Annual International Conference on Mobile Computing and Networking.  77, 1–16 (2023).
  22. Li Y., Li Y., Zhu M., Xu Z., Mu D.  A nonlinear momentum observer for sensorless robot collision detection under model uncertainties.  Mechatronics.  78, 102603 (2021).
  23. Yuan H., Goh K., Andras P., Luo W., Wang C., Gao Y.  Steering angle sensorless control for four-wheel steering vehicle via sliding mode control method.  Transactions of the Institute of Measurement and Control.  46 (3), 453–462 (2024).
  24. Zhou C., Huang B., Fränti P.  A review of motion planning algorithms for intelligent robots.  Journal of Intelligent Manufacturing.  33 (2), 387–424 (2022).
  25. Merrell B., Droge G.  Clothoid-based moving formation control using virtual structures.  2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).  11567–11572 (2020).
  26. Silva J. A. R., Grassi V.  Clothoid-based global path planning for autonomous vehicles in urban scenarios.  2018 IEEE International Conference on Robotics and Automation (ICRA).  4312–4318 (2018).
  27. Bertolazzi E., Frego M.  Interpolating clothoid splines with curvature continuity.  Mathematical Methods in the Applied Sciences.  41 (4), 1723–1737 (2018).
  28. Bertolazzi E., Frego M.  $G^1$ fitting with clothoids.  Mathematical Methods in the Applied Sciences.  38 (5), 881–897 (2015).
  29. Binninger A., Sorkine-Hornung O.  Smooth interpolating curves with local control and monotone alternating curvature.  Computer Graphics Forum.  41 (5), 25–38 (2022).
  30. Horváth E., Pozna C. R.  Clothoid-based trajectory following approach for self-driving vehicles.  2021 IEEE 19th World Symposium on Applied Machine Intelligence and Informatics (SAMI).  000251–000254 (2021).
  31. Sinha S.  Automatic generation of obstacle-free trajectories for AGVs.  Dissertation (2022).
  32. Kala R., Warwick K.  Dynamic distributed lanes: motion planning for multiple autonomous vehicles.  Applied Intelligence.  41, 260–281 (2014).
  33. Girbés V., Vanegas G., Armesto L.  Clothoid-based three-dimensional curve for attitude planning.  Journal of Guidance, Control, and Dynamics.  42 (8), 1886–1898 (2019).
  34. Broman E., Rossing I.  A system for procedural camera movements for navigation in astrographics.  Dissertation (2020).
  35. IA Technology.  Pioneer3-DX.  https://www.generationrobots.com/media/Pioneer3DX-P3DX-RevA.pdf (2011).
  36. Scaglia G. J. E., Serrano M. E., Godoy S. A., Rossomando F.  Linear algebra-based controller for trajectory tracking in mobile robots with additive uncertainties estimation.  IMA Journal of Mathematical Control and Information.  37 (2), 607–624 (2020).
  37. Weisstein E.  Cornu spiral.  https://mathworld.wolfram.com/CornuSpiral.html  (2023).
  38. Meek D. S., Walton D. J.  An arc spline approximation to a clothoid.  Journal of Computational and Applied Mathematics.  170 (1), 59–77 (2004).
  39. Wan Zakaria W. Z. E., Ramli A., Misro M. Y., Wahab M. N. A.  Motion Planning of Differential Drive Mobile Robot Using Circular Arc.  Engineering Letters.  32 (1), 160–167 (2024).
  40. Há V. T., Thuong T. T.. Thanh N. T., Vinh V. Q.  Research on Some Control Algorithms to Compensate for the Negative Effects of Model Uncertainty Parameters, External Interference, and Wheeled Slip for Mobile Robot.  Actuators.  13 (1), 31 (2024).
  41. Gao X., Yan L., Gerada C.  Modeling and analysis in trajectory tracking control for wheeled mobile robots with wheel skidding and slipping: Disturbance rejection perspective.  Actuators.  10 (9), 222 (2021).
  42. Othman N. A., Reif U., Ramli A., Misro M. Y.  Manoeuvring speed estimation of a lane-change system using geometric Hermite interpolation.  Ain Shams Engineering Journal.  12 (4), 4015–4021 (2021).
  43. Zakaria W. Z. E. W., Ramli A., Ali J. M.  Bezier curves interpolation with endpoint constraints on road map.  AIP Conference Proceedings.  2184 (1), 060060 (2019).
  44. Wahrburg A., Guida S., Enayati N., Zanchettin A. M., Rocco P.  Extending dynamic movement primitives towards high-performance robot motion.  2020 IEEE 16th International Workshop on Advanced Motion Control (AMC).  52–58 (2020).