Autonomous Collision Avoidance Using MPC with LQR-Based Weight Transformation.

Area of Science:

• Control Systems Engineering
• Robotics
• Automotive Engineering

Background:

• Model Predictive Control (MPC) is a powerful multi-objective control technique capable of managing system constraints.
• The performance of MPC is highly sensitive to the accurate prioritization of weights for each objective, necessitating effective tuning methods.
• Existing methods often struggle with precise weight tuning, impacting overall controller efficiency.

Purpose of the Study:

• To develop an analytical weight tuning technique for Model Predictive Control (MPC).
• To enhance MPC controller performance by aligning it with Linear Quadratic Regulator (LQR) controller benchmarks.
• To ensure system stability and optimal performance under both unconstrained and constrained operational conditions.

Main Methods:

• An analytical tuning technique is proposed by matching MPC performance with LQR controller performance.
• The methodology involves deriving the transformation of an LQR weighting matrix using a discrete algebraic Riccati equation (DARE).
• An MPC controller is designed based on the discrete-time linear quadratic tracking (LQT) problem, incorporating system constraints.

Main Results:

• The proposed method achieves optimal performance between unconstrained MPC and LQR controllers.
• It provides a sub-optimal solution when constraints are active during transient operations.
• The resulting MPC controller ensures asymptotic stability and effectively mimics discrete-time LQR behavior with appropriate weighting matrix selection.

Conclusions:

• The developed analytical tuning technique effectively optimizes MPC controller performance.
• The method ensures system stability and optimal control, even under active constraints.
• Validated through a vehicle collision avoidance system, the technique demonstrates potent collision-free path planning while respecting all system constraints.