Skip to main content
Log in

Jerk-bounded trajectory planning for rotary flexible joint manipulator: an experimental approach

  • Application of soft computing
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

The fundamental criteria for industrial manipulator applications are vibration free and smooth motion with minimum time. This paper investigates the trajectory tracking and vibration control of rotary flexible joint manipulator with parametric uncertainties. Firstly, the dynamic modeling via Euler Lagrange equation for a single link flexible joint manipulator is discussed. Secondly, for the execution of smooth motion between two points, bounded and continuous jerk trajectory is developed and implemented. In addition, the prospective strategy uses the concatenation of fifth-order polynomials to provide a smooth trajectory between two-way points. In the planned algorithm, user can independently define the position, velocity, acceleration and jerk values at both initial and final positions. The feature of user-defined parameters gives the versatility to the suggested algorithm for generating trajectories for diverse applications of robotic manipulators. Moreover, the planned scheme is easy to implement and computationally efficient. In the last, the performance of the presented scheme is examined by comparison with cubic splines and a linear segment with parabolic blends (LSPB) techniques. Generated trajectories were evaluated successfully by carrying multiple experiments on QUANSER’s flexible joint manipulator.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Data availability

Enquiries about data availability should be directed to the authors.

References

  • Ardeshiri T, Norrlöf M, Löfberg J (2011) Convex optimization approach for time-optimal path tracking of robots with speed-dependent constraints. IFAC Proc 1:14648–14653

    Article  Google Scholar 

  • Aribowo W, Terashima K (2014) Cubic spline trajectory planning and vibration suppression of semiconductor wafer transfer robot arm. Int J Autom Technol 2:265–274

    Article  Google Scholar 

  • Barre PJ, Bearee R, Borne P (2005) Influence of a jerk controlled movement law on the vibratory behaviour of high-dynamics systems. J Intell Robot Syst 3:275–293

    Article  Google Scholar 

  • Bilal H, Guo Y (2017) Experimental validation of fuzzy PID control of the flexible joint system in presence of uncertainties. In: Proc. IEEE 36th Chinese Control Conf, Dalian, China, July 2017, pp 4192–4197

  • Chen, Lin, et al. "Transformer-based Imitative Reinforcement Learning for Multi-Robot Path Planning." IEEE Transactions on Industrial Informatics (2023).

  • Demeulenaere B (2009) Caigny, de; optimal splines for rigid motion systems: benchmarking and extensions. J Mech Des 10:101005

    Article  Google Scholar 

  • Gasparetto A, Zanotto V (2010) Optimal trajectory planning for industrial robots. Adv Eng Softw 4:548–556

    Article  MATH  Google Scholar 

  • Guernane R, Nouara R (2011) Generating optimized paths for motion planning. Robot Auton Syst 10:789–800

    Article  Google Scholar 

  • Quanser Student Handout, Rotary Flexible Joint Module. http://www.quanser.com.

  • Huashan L, Lai X, Wu W (2013) Time-optimal and jerk-continuous trajectory planning for robot manipulators with kinematic constraints. Robot Comput Integr Manuf 2:309–317

    Google Scholar 

  • Kim JY, Dong-Hyeok K (2007) On-line minimum-time trajectory planning for industrial manipulators. In: IEEE International Conference “Control, Autom Syst”, Seoul, South Korea, pp 36–40

  • Krešimir P, Kovacic Z (2007) Trajectory planning algorithm based on the continuity of jerk. In: IEEE Mediterranean Conference “Control Autom”. Athens, Greece, pp 1–5.

  • Lee C, An D (2022) AI-based posture control algorithm for a 7-DOF robot manipulator. Machines 10(8):651

    Article  Google Scholar 

  • Li C, Zheng Z, Yuan J (2023) Trajectory tracking for repeated-impact-based detumbling using a multi-arm space robot. Aerosp Sci Technol. https://doi.org/10.1016/j.ast.2023.108144

    Article  Google Scholar 

  • Liu L, Chen C, Zhao X (2016) Smooth trajectory planning for a parallel manipulator with joint friction and jerk constraints. Int J Control Autom Syst 4:1022–1036

    Article  Google Scholar 

  • Liu Z et al (2023) Automatic joint motion planning of 9-DOF robot based on redundancy optimization for wheel hub polishing. Robot Comput-Integr Manuf 81:102500

    Article  Google Scholar 

  • Macfarlane S, Elizabeth AC (2001) Design of jerk bounded trajectories for online industrial robot applications. In: IEEE Int Conf “Robot Autom” Seoul, South Korea, pp 979–984.

  • Meng Q et al (2021) Motion planning and adaptive neural tracking control of an uncertain two-link rigid–flexible manipulator with vibration amplitude constraint. IEEE Trans Neural Netw Learn Syst 33.8:3814–3828

    MathSciNet  Google Scholar 

  • Nguyen KD, Ng TC, Chen IM (2008) On algorithms for planning s-curve motion profiles. Int J Adv Robot 1:99–106

    Google Scholar 

  • Pattacini U, Nori F, Natale L (2010) An experimental evaluation of a novel minimum-jerk cartesian controller for humanoid robots. In: IEEE/RSJ International Conf “Intell Robots Syst pp 1668–1674

  • Perumaal SS, Jawahar N (2013) Automated trajectory planner of an industrial robot for pick-and-place task. Int J Adv Robot Syst 2:100

    Article  Google Scholar 

  • Peza-Solis JF et al (2022) Trajectory tracking of a single flexible-link robot using a modal cascaded-type control. Appl Math Model 104:531–547

    Article  MathSciNet  MATH  Google Scholar 

  • Porawagama CD, Munasinghe, SR (2014) Reduced jerk joint space trajectory planning method using a 5–3–5 spline for robot manipulators. In: IEEE 7th International Conference “Information and Automation for Sustainability”, Colombo, Sri Lanka pp 1–6

  • Prakash A, Giri DK, Kumar SR (2022) Dynamic velocity error based trajectory tracking for space robotic manipulator. Aerosp Sci Technol 126:107650

    Article  Google Scholar 

  • Sencer B, Tajima S (2017) Frequency optimal feed motion planning in computer numerical controlled machine tools for vibration avoidance. J Manuf Sci Eng Trans 1:011006–011013

    Article  Google Scholar 

  • Shi M et al (2022) Research on vibration suppression and trajectory tracking control strategy of a flexible link manipulator. Appl Math Model 110:78–98

    Article  MathSciNet  MATH  Google Scholar 

  • Springer K, Gattringer H, Staufer P (2013) On time-optimal trajectory planning for a flexible link robot. Proc Inst Mech Eng, i: J Syst Control Eng 10:752–763

    Google Scholar 

  • Tortopidis I, Papadopoulos E (2007) On point-to-point motion planning for underactuated space manipulator systems. Robot Auton Syst 2:122–131

    Article  Google Scholar 

  • William S (2009) Command shaping for flexible systems—a review of the first 50 years. Int J Precis Eng Manuf 4:153–168

    Google Scholar 

  • Younsung C, Donghyung K, Soonwoong H (2017) Dual-arm robot motion planning for collision avoidance using B-spline curve. Int J Precis Eng Manuf 6:835–843

    Google Scholar 

  • Yu X, Dong M, Yin W (2022) Time-optimal trajectory planning of manipulator with simultaneously searching the optimal path. Comput Commun 181:446–453

    Article  Google Scholar 

  • Zhang K, Guo JX, Gao XS (2013) Cubic spline trajectory generation with axis jerk and tracking error constraints. Int J Precis Eng Manuf 7:1141–1146

    Article  Google Scholar 

  • Zhang Q, Li S, Guo JX (2016) Time-optimal path tracking for robots under dynamics constraints based on convex optimization. Robotica 34:2116–2139

    Article  Google Scholar 

  • Zhao MY, Gao XS, Zhang Q (2017) An efficient stochastic approach for robust time-optimal trajectory planning of robotic manipulators under limited actuation. Robotica 35:1–18

    Article  Google Scholar 

Download references

Funding

This work is supported by the National Natural Science Foundation of China under Grant No. 6213000091 and Sponsored by CAAI-Huawei MindSpore Open Fund.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hazrat Bilal.

Ethics declarations

Conflict of interest

The authors declare no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bilal, H., Yin, B., Kumar, A. et al. Jerk-bounded trajectory planning for rotary flexible joint manipulator: an experimental approach. Soft Comput 27, 4029–4039 (2023). https://doi.org/10.1007/s00500-023-07923-5

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-023-07923-5

Keywords

Navigation