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Safe Autonomous Lane Changing: Planning with Dynamic Risk Fields and Time-Varying Convex Space Generation

Zhen Tian, Zhihao Lin

TL;DR

The paper tackles safe autonomous lane changing in dynamic traffic by integrating a Dynamic Risk Field (DRF) with a time-varying convex feasible space, and solves the resulting finite-horizon nonlinear optimal control problem via a constrained iLQR. The DRF captures static and velocity-dependent collision risk, while the convex space guarantees kinematic feasibility and collision avoidance, with a growth tensor guiding real-time expansion. The approach demonstrates superior safety and efficiency in simulations against multiple baselines, achieving shorter lane-change distances and times with zero collisions, and shows robust adaptability in dual-lane roundabouts. This framework provides a real-time, risk-aware trajectory generation method suitable for complex, interactive traffic environments.

Abstract

This paper presents a novel trajectory planning pipeline for complex driving scenarios like autonomous lane changing, by integrating risk-aware planning with guaranteed collision avoidance into a unified optimization framework. We first construct a dynamic risk fields (DRF) that captures both the static and dynamic collision risks from surrounding vehicles. Then, we develop a rigorous strategy for generating time-varying convex feasible spaces that ensure kinematic feasibility and safety requirements. The trajectory planning problem is formulated as a finite-horizon optimal control problem and solved using a constrained iterative Linear Quadratic Regulator (iLQR) algorithm that jointly optimizes trajectory smoothness, control effort, and risk exposure while maintaining strict feasibility. Extensive simulations demonstrate that our method outperforms traditional approaches in terms of safety and efficiency, achieving collision-free trajectories with shorter lane-changing distances (28.59 m) and times (2.84 s) while maintaining smooth and comfortable acceleration patterns. In dense roundabout environments the planner further demonstrates robust adaptability, producing larger safety margins, lower jerk, and superior curvature smoothness compared with APF, MPC, and RRT based baselines. These results confirm that the integrated DRF with convex feasible space and constrained iLQR solver provides a balanced solution for safe, efficient, and comfortable trajectory generation in dynamic and interactive traffic scenarios.

Safe Autonomous Lane Changing: Planning with Dynamic Risk Fields and Time-Varying Convex Space Generation

TL;DR

The paper tackles safe autonomous lane changing in dynamic traffic by integrating a Dynamic Risk Field (DRF) with a time-varying convex feasible space, and solves the resulting finite-horizon nonlinear optimal control problem via a constrained iLQR. The DRF captures static and velocity-dependent collision risk, while the convex space guarantees kinematic feasibility and collision avoidance, with a growth tensor guiding real-time expansion. The approach demonstrates superior safety and efficiency in simulations against multiple baselines, achieving shorter lane-change distances and times with zero collisions, and shows robust adaptability in dual-lane roundabouts. This framework provides a real-time, risk-aware trajectory generation method suitable for complex, interactive traffic environments.

Abstract

This paper presents a novel trajectory planning pipeline for complex driving scenarios like autonomous lane changing, by integrating risk-aware planning with guaranteed collision avoidance into a unified optimization framework. We first construct a dynamic risk fields (DRF) that captures both the static and dynamic collision risks from surrounding vehicles. Then, we develop a rigorous strategy for generating time-varying convex feasible spaces that ensure kinematic feasibility and safety requirements. The trajectory planning problem is formulated as a finite-horizon optimal control problem and solved using a constrained iterative Linear Quadratic Regulator (iLQR) algorithm that jointly optimizes trajectory smoothness, control effort, and risk exposure while maintaining strict feasibility. Extensive simulations demonstrate that our method outperforms traditional approaches in terms of safety and efficiency, achieving collision-free trajectories with shorter lane-changing distances (28.59 m) and times (2.84 s) while maintaining smooth and comfortable acceleration patterns. In dense roundabout environments the planner further demonstrates robust adaptability, producing larger safety margins, lower jerk, and superior curvature smoothness compared with APF, MPC, and RRT based baselines. These results confirm that the integrated DRF with convex feasible space and constrained iLQR solver provides a balanced solution for safe, efficient, and comfortable trajectory generation in dynamic and interactive traffic scenarios.

Paper Structure

This paper contains 13 sections, 4 theorems, 23 equations, 9 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Dynamic Risk Field and Convex Space
  3. Risk Field Modeling
  4. Dynamic Convex Space Generation
  5. Optimization-based Planning Framework
  6. Optimization Problem Formulation
  7. iLQR-based Solution
  8. Stability Analysis
  9. EXPERIMENTAL EVALUATION
  10. Evolution of Dynamic Risk Field
  11. Evolution of Convex Feasible Space
  12. Safety-Aware Motion Behaviour
  13. CONCLUSION

Key Result

Proposition 1

There is a state-dependent growth tensor $\mathcal{G}(\mathbf{s},t) \in \mathbb{R}^{2 \times 2}$ such that the evolution of the convex set $\mathcal{C}(\mathbf{s},t)$ is described by where $\mathbf{n}(\mathbf{p})$ denotes the outward normal vector at position $\mathbf{p}$ on the boundary $\partial\mathcal{C}(\mathbf{s},t)$. The growth tensor $\mathcal{G}(\mathbf{s},t)$ admits the following decomp

Figures (9)

  • Figure 1: Overall architecture of the proposed trajectory planning framework. The Scenarios and Environment module provides the perceived environment states, including surrounding-vehicle motion and road configuration. The host vehicle integrates three key components: (i) a Vehicle Model that captures kinematic evolution, (ii) a DRF that evaluates spatial and velocity-dependent collision risk, (iii) a Convex Feasible Space that guarantees safety and kinematic limits, and (iv) a Cost Function balancing safety, comfort, efficiency, and risk. A Constrained iLQR Solver optimizes the risk-aware trajectory within the feasible space. Surrounding HDVs provide observed motion, forming a closed Environment Interaction Loop. The output is a Planned Trajectory ensuring safe and smooth navigation.
  • Figure 2: Illustration of the dynamic risk field.
  • Figure 3: Evolution of the dynamic convex feasible space $\mathcal{C}(\mathbf{s},t)$ over time. The rectangles represent the growing feasible regions that satisfy both kinematic constraints and safety requirements, while the green curve represents a trajectory.
  • Figure 4: Convergence analysis of proposed method.
  • Figure 5: Comparison of different lane changing trajectory planning methods. (a) Visualization of dynamic convex feasible space as red rectangles and DRF at $t = 1.5~\mathrm{s}$. The green line shows the planned trajectory, green dots represent the trajectory before optimization. (b) Comparison of lane changing using different trajectory planning methods. (c) Comparison of longitudinal velocities. (d) Comparison of lateral velocities. (e) Comparison of longitudinal accelerations.
  • ...and 4 more figures

Theorems & Definitions (5)

  • Definition 1: Dynamic Convex Feasible Space
  • Proposition 1: Growth Tensor Representation
  • Lemma 1: Kinematic Feasibility Conditions
  • Theorem 1: Dynamic Separating Hyperplane Safety
  • Theorem 2: Existence and Evolution of Feasible Spaces