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Application of Polynomial Transition Curves for Trajectory Planning on the Headlands

Author

Listed:
  • Marek Boryga

    (Department of Mechanical Engineering and Automation, Faculty of Production Engineering, University of Life Sciences in Lublin, Lublin 20-612, Poland)

  • Paweł Kołodziej

    (Department of Mechanical Engineering and Automation, Faculty of Production Engineering, University of Life Sciences in Lublin, Lublin 20-612, Poland)

  • Krzysztof Gołacki

    (Department of Mechanical Engineering and Automation, Faculty of Production Engineering, University of Life Sciences in Lublin, Lublin 20-612, Poland)

Abstract

This paper presents a method of polynomial transition curve application for making agricultural aggregate movement paths during headland turn drives as well as within the field. Four types of agricultural aggregate paths in five different variant designs are discussed. Each path is composed of only two curves, making the so-called transition bi-curve. The curvature described by the linear function as well as the third, fifth, seventh, and ninth degree polynomials was designated. Moreover, a trajectory planning algorithm in which the movement proceeds along two transition curves composing the so-called bi-curve was proposed. The simulation was carried out applying the MATLAB program in which the 4th order Runge–Kutta method was used. The results were presented by means of figures showing the proposed paths and kinematic quantity courses in the displacement function. The obtained trajectories were compared regarding the size and kinematic quantities. The trajectories, whose curvature is described by the 3° polynomial, were found to possess the smallest absolute values of maximal acceleration and jerk and to lack jerk discontinuity. The proposed solutions can be applied for planning trajectory of not only agriculture machines and aggregates but also autonomous vehicles or mobile robots.

Suggested Citation

  • Marek Boryga & Paweł Kołodziej & Krzysztof Gołacki, 2020. "Application of Polynomial Transition Curves for Trajectory Planning on the Headlands," Agriculture, MDPI, vol. 10(5), pages 1-16, May.
    • Handle: RePEc:gam:jagris:v:10:y:2020:i:5:p:144-:d:352888
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    References listed on IDEAS

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    1. Volodymyr Bulgakov & Simone Pascuzzi & Volodymyr Nadykto & Semjons Ivanovs, 2018. "A Mathematical Model of the Plane-Parallel Movement of an Asymmetric Machine-and-Tractor Aggregate," Agriculture, MDPI, vol. 8(10), pages 1-15, October.
    2. Volodymyr Bulgakov & Simone Pascuzzi & Hristo Beloev & Semjons Ivanovs, 2019. "Theoretical Investigations of the Headland Turning Agility of a Trailed Asymmetric Implement-and-Tractor Aggregate," Agriculture, MDPI, vol. 9(10), pages 1-11, October.
    3. Šarauskis, Egidijus & Vaitauskienė, Kristina & Romaneckas, Kęstutis & Jasinskas, Algirdas & Butkus, Vidmantas & Kriaučiūnienė, Zita, 2017. "Fuel consumption and CO2 emission analysis in different strip tillage scenarios," Energy, Elsevier, vol. 118(C), pages 957-968.
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