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Post-Collision Trajectory Restoration for a Single-track Ackermann Vehicle using Heuristic Steering and Tractive Force Functions

Samsaptak Ghosh, M. Felix Orlando, Sohom Chakrabarty

Abstract

Post-collision trajectory restoration is a safety-critical capability for autonomous vehicles, as impact-induced lateral motion and yaw transients can rapidly drive the vehicle away from the intended path. This paper proposes a structured heuristic recovery control law that jointly commands steering and tractive force for a generalized single-track Ackermann vehicle model. The formulation explicitly accounts for time-varying longitudinal velocity in the lateral-yaw dynamics and retains nonlinear steering-coupled interaction terms that are commonly simplified in the literature. Unlike approaches that assume constant longitudinal speed, the proposed design targets the transient post-impact regime where speed variations and nonlinear coupling significantly influence recovery. The method is evaluated in simulation on the proposed generalized single-track model and a standard 3DOF single-track reference model in MATLAB, demonstrating consistent post-collision restoration behaviour across representative initial post-impact conditions.

Post-Collision Trajectory Restoration for a Single-track Ackermann Vehicle using Heuristic Steering and Tractive Force Functions

Abstract

Post-collision trajectory restoration is a safety-critical capability for autonomous vehicles, as impact-induced lateral motion and yaw transients can rapidly drive the vehicle away from the intended path. This paper proposes a structured heuristic recovery control law that jointly commands steering and tractive force for a generalized single-track Ackermann vehicle model. The formulation explicitly accounts for time-varying longitudinal velocity in the lateral-yaw dynamics and retains nonlinear steering-coupled interaction terms that are commonly simplified in the literature. Unlike approaches that assume constant longitudinal speed, the proposed design targets the transient post-impact regime where speed variations and nonlinear coupling significantly influence recovery. The method is evaluated in simulation on the proposed generalized single-track model and a standard 3DOF single-track reference model in MATLAB, demonstrating consistent post-collision restoration behaviour across representative initial post-impact conditions.
Paper Structure (11 sections, 21 equations, 6 figures, 2 tables)

This paper contains 11 sections, 21 equations, 6 figures, 2 tables.

Table of Contents

  1. Vehicle Model
  2. Force and Steering Control function
  3. Steering Function
  4. Tractive Force Function
  5. Simulation Results
  6. Case 1 (Lateral Collision at the C.G. of the vehicle):
  7. Case 2 (Lateral Collision not at the C.G. of the vehicle):
  8. Discussion
  9. Reproducibility and Implementation Notes
  10. Limitations and Future Work
  11. CONCLUSIONS

Figures (6)

  • Figure 1: Schematic diagram of the proposed generalized vehicle model showing the force components and velocity.
  • Figure 2: Case 1 and Case 2 collision scenario: (a) Steering angle ($\delta_s$), (b) Tractive force ($F_{xt}$)
  • Figure 3: Case 1 collision scenario: (a) Longitudinal velocity ($v_x$), (b) Lateral velocity ($v_y$), (c) Angular velocity ($w_z$), (d) Orientation angle ($\psi_o$)
  • Figure 4: Post-collision trajectory restoration for Case 1 collision scenario
  • Figure 5: Case 2 collision scenario: (a) Longitudinal velocity ($v_x$), (b) Lateral velocity ($v_y$), (c) Angular velocity ($w_z$), (d) Orientation angle ($\psi_o$)
  • ...and 1 more figures