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Closing Speed Computation using Stereo Camera and Applications in Unsignalized T-Intersection

Gautam Kumar, Ashwini Ratnoo

TL;DR

This work addresses safe ego-vehicle lane-exit maneuvers at unsignalized T-intersections under stereo-depth uncertainty. It introduces an adaptive depth-sampling strategy that bounds the closing speed by exploiting a quadratic depth-error model, and pairs it with a quadratic Bézier curve path whose convex hull enables deterministic conflict avoidance. A two-scenario conflict-resolution algorithm uses depth-bounds and speed bounds to decide when the ego vehicle can proceed or must wait, with validation based on realistic NGSIM traffic trajectories. The approach advances perception-uncertainty–aware planning with a practical, geometry-based trajectory and can be extended to other sensing modalities and traffic scenarios.

Abstract

This letter presents a conflict resolution strategy for an autonomous vehicle mounted with a stereo camera approaching an unsignalized T-intersection. A mathematical model for uncertainty in stereo camera depth measurements is considered and an analysis establishes the proposed adaptive depth sampling logic which guarantees an upper bound on the computed closing speed. Further, a collision avoidance logic is proposed that utilizes the closing speed bound and generates a safe trajectory plan based on the convex hull property of a quadratic Bézier curve-based reference path. Realistic validation studies are presented with neighboring vehicle trajectories generated using Next Generation Simulation (NGSIM) dataset.

Closing Speed Computation using Stereo Camera and Applications in Unsignalized T-Intersection

TL;DR

This work addresses safe ego-vehicle lane-exit maneuvers at unsignalized T-intersections under stereo-depth uncertainty. It introduces an adaptive depth-sampling strategy that bounds the closing speed by exploiting a quadratic depth-error model, and pairs it with a quadratic Bézier curve path whose convex hull enables deterministic conflict avoidance. A two-scenario conflict-resolution algorithm uses depth-bounds and speed bounds to decide when the ego vehicle can proceed or must wait, with validation based on realistic NGSIM traffic trajectories. The approach advances perception-uncertainty–aware planning with a practical, geometry-based trajectory and can be extended to other sensing modalities and traffic scenarios.

Abstract

This letter presents a conflict resolution strategy for an autonomous vehicle mounted with a stereo camera approaching an unsignalized T-intersection. A mathematical model for uncertainty in stereo camera depth measurements is considered and an analysis establishes the proposed adaptive depth sampling logic which guarantees an upper bound on the computed closing speed. Further, a collision avoidance logic is proposed that utilizes the closing speed bound and generates a safe trajectory plan based on the convex hull property of a quadratic Bézier curve-based reference path. Realistic validation studies are presented with neighboring vehicle trajectories generated using Next Generation Simulation (NGSIM) dataset.
Paper Structure (16 sections, 3 theorems, 34 equations, 7 figures, 1 algorithm)

This paper contains 16 sections, 3 theorems, 34 equations, 7 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. Our Contribution
  4. Problem Statement
  5. closing speed Computation with Uncertainty in Position
  6. Stereo Camera Position Uncertainty Model
  7. Upper Bound on the Computed Closing Speed
  8. Nominal closing speed
  9. Bounds on closing speed
  10. Proposed Conflict Resolution Approach
  11. Bézier Curve Path Planning
  12. Proposed Conflict Resolution Approach
  13. Simulation Studies
  14. Closing Speed Computation Results
  15. Conflict Resolution Validation
  16. ...and 1 more sections

Key Result

Proposition 1

For $x_m>\beta_3$, the roots of eq:error_model are real and the positive root is given by

Figures (7)

  • Figure 1: Lane exit scenario
  • Figure 2: Computation of closing speed and its bounds when sampling distance is (a) nominal (b) very small (c) large.
  • Figure 3: No conflict scenario: The neighboring vehicle has already crossed the intersection.
  • Figure 4: No conflict scenario: The neighboring vehicle is yet to reach the intersection when the ego vehicle reaches $P_f$. (Solid and faded boxes show vehicles' positions at $t_{P_i}$ and $t_{P_f}$, respectively.)
  • Figure 5: (a) Depth error variation with computed depth using $\beta_1 =0.002797,~\beta_2=-0.004249,~\beta_3=0.007311$. (b) Proposed sampling distance for abiding by a given relative deviation from the nominal closing speed. (c) Relative deviation from nominal closing speed considering fixed sampling distance $\Delta x$. (d) Nominal closing speed and its bounds considering $\epsilon=0.2$.
  • ...and 2 more figures

Theorems & Definitions (10)

  • Remark 1
  • Proposition 1
  • proof
  • Remark 2
  • Proposition 2
  • proof
  • Remark 3
  • Remark 4
  • Theorem 1
  • proof