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A four-bodies motorcycle dynamic model for observer design

Tychique Nzalalemba Kabwangala, Ziad Alkhoury, Jawwad Ahmed, Mihaly Petreczky, Laurentiu Hetel, Lotfi Belkoura

Abstract

Motivated by the need to predict dangerous scenarios, this article introduces a non-linear dynamic model for motorcycles consisting of four rigid bodies. Using Jourdain's principle, the model incorporates both longitudinal and lateral dynamics, targeting a balance between numerical complexity and accuracy of representation. The paper further employs the model to design a Luenberger observer based on linear quadratic regulator theory, for estimating physical states based on sensor measurements. In turn, the state estimates are useful for predicting dangerous scenarios (lowside, highside, fall). The relevance of the approach is demonstrated through simulations of various rectilinear trajectories and a lane-changing scenario using BikeSim simulator.

A four-bodies motorcycle dynamic model for observer design

Abstract

Motivated by the need to predict dangerous scenarios, this article introduces a non-linear dynamic model for motorcycles consisting of four rigid bodies. Using Jourdain's principle, the model incorporates both longitudinal and lateral dynamics, targeting a balance between numerical complexity and accuracy of representation. The paper further employs the model to design a Luenberger observer based on linear quadratic regulator theory, for estimating physical states based on sensor measurements. In turn, the state estimates are useful for predicting dangerous scenarios (lowside, highside, fall). The relevance of the approach is demonstrated through simulations of various rectilinear trajectories and a lane-changing scenario using BikeSim simulator.

Paper Structure

This paper contains 16 sections, 20 equations, 8 figures, 3 tables.

Table of Contents

  1. Introduction
  2. PTW description and objectives
  3. Tire dynamics.
  4. Vertical tire forces.
  5. Longitudinal and lateral tire forces.
  6. Objectives.
  7. Dynamic model derivation
  8. Modeling assumptions.
  9. Preliminaries on Jourdain's principle.
  10. Explicit equations using Jourdain's principle.
  11. Non-linear dynamic model derivation.
  12. OBSERVER DESIGN
  13. RESULTS AND DISCUSSION
  14. Rectilinear trajectories.
  15. Overtaking scenario.
  16. ...and 1 more sections

Figures (8)

  • Figure 1: PTW model description
  • Figure 2: Motorcycle and tire forces description
  • Figure 3: Overtaking scenario at 100 kph
  • Figure 4: Observer dynamics for rectilinear trajectories at 100 km/h. Red lines: curves from BikeSim. Blue dashed lines: observer results.
  • Figure 5: Observer designed for 80 kph, tested at 100 and 50 kph. Red lines: curves from BikeSim. Blue dashed lines: observer results.
  • ...and 3 more figures