[Paper Review] A Framework for Collision-Tolerant Optimal Trajectory Planning of Autonomous Vehicles

Mark Mote, Juan-Pablo Afman+1 more|arXiv (Cornell University)|Nov 22, 2016

Robotic Path Planning Algorithms4 citations

TL;DR

This paper proposes a mixed integer programming (MIP)-based framework for optimal trajectory planning in autonomous vehicles that intentionally incorporates controlled collisions to improve performance. By modeling collisions with a damage function and optimizing under constraints on impact velocity, the method achieves a 13.59% reduction in travel time compared to collision-free planning, demonstrating that collision tolerance can enhance efficiency in constrained environments.

ABSTRACT

Collision-tolerant trajectory planning is the consideration that collisions, if they are planned appropriately, enable more effective path planning for robots capable of handling them. A mixed integer programming (MIP) optimization formulation demonstrates the computational practicality of optimizing trajectories that comprise planned collisions. A damage quantification function is proposed, and the influence of damage functions constraints on the trajectory are studied in simulation. Using a simple example, an increase in performance is achieved under this schema as compared to collision-free optimal trajectories.

Motivation & Objective

• To address the limitation of traditional collision-free trajectory planning, which restricts vehicle performance in constrained environments.
• To explore whether planned collisions can improve trajectory efficiency by enabling shorter, more direct paths.
• To develop a computationally practical optimization framework that integrates collision dynamics and damage constraints.
• To evaluate the performance gain of collision-tolerant planning over collision-free alternatives in a 1D simulation.
• To investigate how damage functions influence trajectory design and system robustness under controlled impact conditions.

Proposed method

• Formulates the trajectory planning problem as a mixed-integer programming (MIP) optimization to handle discrete collision events and continuous dynamics.
• Models collisions using a perfectly plastic (inelastic) impact model with a simplified 1D kinematic representation of the vehicle and wall.
• Introduces a damage function to quantify collision severity, using maximum impact velocity as a key constraint to limit structural stress.
• Incorporates vehicle dynamics constraints, including maximum acceleration (6 m/s²), maximum velocity (15 m/s), and kinematic bounds.
• Solves the MIP problem using the Gurobi solver in MATLAB, enabling the computation of optimal trajectories with or without collision events.
• Extends the framework to include damage constraints in the optimization, penalizing high-velocity impacts while still allowing beneficial collisions.

Experimental results

Research questions

• RQ1 Can intentional collisions improve trajectory performance compared to collision-free optimal planning in autonomous vehicles?
• RQ2 How does the inclusion of a damage function—specifically a maximum impact velocity constraint—affect trajectory optimization and system safety?
• RQ3 What is the performance trade-off between collision-tolerant trajectories with damage constraints and those without?
• RQ4 How does the final destination influence the decision to pursue a collision trajectory, and when is collision avoidance preferred?
• RQ5 To what extent can the MIP framework be extended to handle elastic collisions, multiple obstacles, and higher-dimensional systems?

Key findings

• The collision-tolerant trajectory planner reduced travel time by 13.59% (from 2.55 s to 2.245 s) compared to the collision-free optimal planner in a 1D scenario with a wall.
• When a damage constraint (maximum impact velocity) was introduced, the trajectory time increased slightly to 2.39 s, representing a 6.27% improvement over the collision-free baseline.
• The collision-tolerant approach outperformed the collision-free planner even with damage constraints, indicating that controlled impacts can enhance performance while maintaining safety.
• For final positions slightly offset from the wall (Δx = 10 cm), the planner avoided collisions when they no longer contributed to cost minimization, showing adaptive decision-making.
• The MIP framework successfully handled both collision and non-collision trajectories, demonstrating computational feasibility and flexibility for integration with damage models.
• The results suggest that incorporating damage functions into the optimization can enable robust, high-performance planning even in off-nominal scenarios, with potential for extension to multi-agent and multi-obstacle systems.