[Paper Review] Gain Scheduling LPV Control Scheme for the Autonomous Guidance Problem using a Dynamic Modelling Approach

Eugenio Alcalá, Vicenç Puig+2 more|arXiv (Cornell University)|Dec 1, 2017

Vehicle Dynamics and Control Systems7 references3 citations

TL;DR

This paper proposes a gain-scheduling LPV control scheme for autonomous vehicle guidance by decoupling longitudinal and lateral control using kinematic and dynamic vehicle models. A cascade design ensures the dynamic controller (inner loop) operates faster than the kinematic controller (outer loop), solving two smaller LMI-LQR problems for improved stability and performance, achieving less than 0.5 km/h velocity error and sub-meter lateral error in a simulated urban scenario.

ABSTRACT

This work proposes a solution for the longitudinal and lateral control problem of urban autonomous vehicles using a gain scheduling LPV control approach. Using the kinematic and dynamic vehicle models, a linear parameter varying (LPV) representation is adopted and a cascade control methodology is proposed for controlling both vehicle behaviours. In particular, for the control design, the use of both models separately lead to solve two LPV LMI-LQR problems. Furthermore, to achieve the desired levels of performance, an approach based on cascade design of the the kinematic and dynamic controllers has been proposed. This cascade control scheme is based on the idea that the dynamic closed loop behaviour is designed to be faster than the kinematic closed loop one. The obtained gain scheduling LPV control approach, jointly with a trajectory generation module, has presented suitable results in a simulated city driving scenario.

Motivation & Objective

• Address the complex autonomous guidance problem in urban environments where traffic, infrastructure, and safety constraints increase control difficulty.
• Overcome limitations of single-model control by separating kinematic and dynamic vehicle behaviors for more accurate and stable control.
• Improve performance and robustness in mixed longitudinal and lateral control by ensuring the inner dynamic loop is faster than the outer kinematic loop.
• Develop a scalable, modular control solution using Linear Matrix Inequality (LMI)-based LQR design for LPV systems to handle varying vehicle operating conditions.
• Validate the approach in a realistic urban driving simulation to demonstrate feasibility and performance under complex, dynamic scenarios.

Proposed method

• Formulate a linear parameter-varying (LPV) representation of the vehicle using separate kinematic and dynamic models to capture different time-scale behaviors.
• Design two independent LMI-LQR controllers—one for the kinematic outer loop (position and heading control) and one for the dynamic inner loop (velocity and yaw rate control)—to simplify the design process.
• Implement a cascade control architecture where the dynamic controller is designed to be faster than the kinematic controller, ensuring stability and performance through hierarchical control.
• Use decay rate constraints (η = 3 for dynamic loop, β = 0.5 for kinematic loop) to shape the closed-loop pole placement and ensure desired transient response.
• Integrate the control scheme with a trajectory generation module to produce smooth reference signals for the controllers in a simulated city environment.
• Validate the control performance using simulation results across velocity, position, and control input trajectories under realistic urban driving conditions.

Experimental results

Research questions

• RQ1 How can a single control framework effectively manage both longitudinal and lateral vehicle dynamics in urban autonomous driving scenarios?
• RQ2 Can a cascade LPV control structure with separate kinematic and dynamic models improve performance and stability compared to a monolithic controller?
• RQ3 What is the impact of enforcing a faster inner-loop dynamic response on the overall system performance and robustness?
• RQ4 To what extent can LMI-LQR techniques applied to LPV models ensure stability and performance across varying vehicle speeds and turning rates?
• RQ5 How do the resulting control actions and tracking errors behave in a complex, real-world-like urban driving scenario?

Key findings

• The kinematic-dynamic cascade LPV control scheme achieved a maximum linear velocity error of 0.5 km/h, demonstrating effective tracking of the reference speed despite path curvature.
• The angular velocity response showed improved performance due to integral action, though some overshoot occurred due to abrupt changes in the reference signal at curve exits.
• Longitudinal position error remained below 0.4 m during normal driving, indicating good path tracking under steady-state conditions.
• Lateral position error was kept within a few decimeters, increasing slightly at higher speeds and angular velocities, but remained acceptable for urban navigation.
• The steering control action exhibited smooth behavior, while braking force signals were abrupt when approaching curves, due to the absence of dedicated brake control and high coupling between longitudinal and lateral dynamics.
• Closed-loop pole placement confirmed that both controllers met their respective decay rate constraints (η = 3, β = 0.5), validating the hierarchical design and ensuring stable, fast inner-loop dynamics.