[Paper Review] Optimization-based Motion Planning in Virtual Driving Scenarios with Application to Communicating Autonomous Vehicles

Matthias Gerdts, Björn Martens|arXiv (Cornell University)|Jan 23, 2018

Robotic Path Planning Algorithms40 references4 citations

TL;DR

This paper presents an optimization-based motion planning framework for autonomous vehicles in virtual driving scenarios, using direct multiple shooting and model predictive control with sensitivity updates to efficiently compute optimal trajectories that minimize fuel use, maximize safety, and ensure collision avoidance. The key contribution is a distributed control algorithm for communicating autonomous vehicles that enables stable, real-time trajectory tracking under perturbations and measurement noise.

ABSTRACT

The paper addresses the problem of providing suitable reference trajectories in motion planning problems for autonomous vehicles. Among the various approaches to compute a reference trajectory, our aim is to find those trajectories which optimize a given performance criterion, for instance fuel consumption, comfort, safety, time, and obey constraints, e.g. collision avoidance, safety regions, control bounds. This task can be approached by geometric shortest path problems or by optimal control problems, which need to be solved efficiently. To this end we use direct discretization schemes and model-predictive control in combination with sensitivity updates to predict optimal solutions in the presence of perturbations. Applications arising in autonomous driving are presented. In particular, a distributed control algorithm for traffic scenarios with several autonomous vehicles that use car-to-car communication is introduced.

Motivation & Objective

• To develop a robust, real-time capable motion planning framework for autonomous vehicles in virtual driving simulations.
• To optimize vehicle trajectories based on performance criteria such as fuel efficiency, safety, comfort, and time while respecting dynamic and geometric constraints.
• To enable distributed control in multi-vehicle scenarios using car-to-car communication for improved coordination and safety.
• To ensure stability and tracking accuracy under model perturbations, measurement noise, and initial state offsets.
• To integrate sensitivity-based updates for efficient online re-optimization in response to environmental changes.

Proposed method

• Employs direct multiple shooting discretization of optimal control problems to enable efficient numerical solution of trajectory optimization.
• Uses model predictive control (MPC) with sensitivity updates to predict optimal solutions under perturbations, enhancing real-time adaptability.
• Applies a kinematic car model with state variables (x, y, ψ, v, δ) and control inputs (velocity v, steering angle δ) for trajectory computation.
• Implements a feedback controller based on inverse kinematics and proportional error feedback to track reference spline curves.
• Introduces a closed-loop control law with gains (k₁–k₆) that ensures local asymptotic stability via Hurwitz polynomial analysis.
• Models measurement noise and initial state offsets using white noise in position and velocity for robustness testing.

Experimental results

Research questions

• RQ1 How can optimal reference trajectories be computed efficiently for autonomous vehicles under multiple performance criteria and constraints?
• RQ2 What is the impact of perturbations and measurement noise on the stability and tracking performance of motion planning controllers?
• RQ3 How can car-to-car communication be leveraged in a distributed control framework to improve trajectory coordination and safety?
• RQ4 What role do sensitivity updates play in maintaining real-time performance during online re-optimization?
• RQ5 Under what conditions is the closed-loop system with feedback control asymptotically stable?

Key findings

• The feedback controller successfully tracks a reference spline trajectory under ideal conditions, with all simulations showing accurate path following.
• The system remains stable under white noise in position (±10 m) and velocity (±2 m/s), demonstrating robustness to realistic sensor errors.
• Even with an initial state offset of (10, 10) m from the reference trajectory, the controller achieves accurate tracking, confirming resilience to initialization errors.
• The linearized closed-loop system is locally asymptotically stable when the characteristic polynomial factors into Hurwitz polynomials (λ² + k₃λ + k₄)(λ + k₁).
• Sensitivity-based updates enable efficient online re-optimization, maintaining real-time performance in dynamic scenarios.
• The distributed control algorithm based on car-to-car communication enables coordinated motion planning in multi-vehicle environments with improved safety and efficiency.