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Steady-State Drifting Equilibrium Analysis of Single-Track Two-Wheeled Robots for Controller Design

Feilong Jing, Yang Deng, Boyi Wang, Xudong Zheng, Yifan Sun, Zhang Chen, Bin Liang

TL;DR

This work extends drifting concepts to single-track two-wheeled robots by deriving a Newton-Euler-based model that accommodates large sideslip and wheel-ground constraints. It introduces ADESA, an analytical drifting-equilibrium solver, alongside a numerical method, to rapidly compute equilibria and reveal drift mechanisms, including counter-steering. Building on these equilibria, the authors design an MPC-based drifting controller and a transition controller that leverages ADESA for fast warm-starts, validated in MuJoCo simulations across varying conditions. The results demonstrate accurate equilibrium prediction, robust drifting control, and feasible equilibrium transitions, highlighting practical potential for enhanced maneuverability and safety in STTW platforms.

Abstract

Drifting is an advanced driving technique where the wheeled robot's tire-ground interaction breaks the common non-holonomic pure rolling constraint. This allows high-maneuverability tasks like quick cornering, and steady-state drifting control enhances motion stability under lateral slip conditions. While drifting has been successfully achieved in four-wheeled robot systems, its application to single-track two-wheeled (STTW) robots, such as unmanned motorcycles or bicycles, has not been thoroughly studied. To bridge this gap, this paper extends the drifting equilibrium theory to STTW robots and reveals the mechanism behind the steady-state drifting maneuver. Notably, the counter-steering drifting technique used by skilled motorcyclists is explained through this theory. In addition, an analytical algorithm based on intrinsic geometry and kinematics relationships is proposed, reducing the computation time by four orders of magnitude while maintaining less than 6% error compared to numerical methods. Based on equilibrium analysis, a model predictive controller (MPC) is designed to achieve steady-state drifting and equilibrium points transition, with its effectiveness and robustness validated through simulations.

Steady-State Drifting Equilibrium Analysis of Single-Track Two-Wheeled Robots for Controller Design

TL;DR

This work extends drifting concepts to single-track two-wheeled robots by deriving a Newton-Euler-based model that accommodates large sideslip and wheel-ground constraints. It introduces ADESA, an analytical drifting-equilibrium solver, alongside a numerical method, to rapidly compute equilibria and reveal drift mechanisms, including counter-steering. Building on these equilibria, the authors design an MPC-based drifting controller and a transition controller that leverages ADESA for fast warm-starts, validated in MuJoCo simulations across varying conditions. The results demonstrate accurate equilibrium prediction, robust drifting control, and feasible equilibrium transitions, highlighting practical potential for enhanced maneuverability and safety in STTW platforms.

Abstract

Drifting is an advanced driving technique where the wheeled robot's tire-ground interaction breaks the common non-holonomic pure rolling constraint. This allows high-maneuverability tasks like quick cornering, and steady-state drifting control enhances motion stability under lateral slip conditions. While drifting has been successfully achieved in four-wheeled robot systems, its application to single-track two-wheeled (STTW) robots, such as unmanned motorcycles or bicycles, has not been thoroughly studied. To bridge this gap, this paper extends the drifting equilibrium theory to STTW robots and reveals the mechanism behind the steady-state drifting maneuver. Notably, the counter-steering drifting technique used by skilled motorcyclists is explained through this theory. In addition, an analytical algorithm based on intrinsic geometry and kinematics relationships is proposed, reducing the computation time by four orders of magnitude while maintaining less than 6% error compared to numerical methods. Based on equilibrium analysis, a model predictive controller (MPC) is designed to achieve steady-state drifting and equilibrium points transition, with its effectiveness and robustness validated through simulations.

Paper Structure

This paper contains 17 sections, 23 equations, 9 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Drifting Model
  3. Nomenclature
  4. Geometry and kinematics relationships
  5. Drifting dynamics
  6. Drifting Equilibrium
  7. Numerical Method
  8. Analytical Method
  9. Equilibrium Analysis
  10. Drifting Controller
  11. Steady-state Drifting Control
  12. Drifting Equilibrium Transition Control
  13. Simulation Results
  14. Comparison of Drifting Equilibrium
  15. Drifting Equilibrium Transition Control
  16. ...and 2 more sections

Figures (9)

  • Figure 1: Drifting maneuver of skilled motorcyclists and STTW robots. The top picture shows that motorcyclists use the counter-steering drifting technique motorcyclist, and the bottom is snapshots of the STTW robot drifting in MuJoCo simulation.
  • Figure 2: Schematic of the drifting STTW robot
  • Figure 3: Top view of the drifting STTW robot
  • Figure 4: Simplified drifting model of the STTW robot
  • Figure 5: Steady-state drifting equilibrium under different yaw rates and steering angles. 'CS' stands for 'Counter-Steering', and 'PS' stands for 'Positive-Steering'.
  • ...and 4 more figures