Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Efficient MPC for Emergency Evasive Maneuvers, Part I: Hybridization of the Nonlinear Problem

Leila Gharavi, Bart De Schutter, Simone Baldi

TL;DR

This paper introduces a hybridization approach for efficient approximation of nonlinear vehicle dynamics and non-convex constraints and offers guidelines for implementation of the presented hybridization framework in other applications.

Abstract

Despite the extensive application of nonlinear Model Predictive Control (MPC) in automated driving, balancing its computational efficiency with respect to the control performance and constraint satisfaction remains a challenge in emergency scenarios: in such situations, sub-optimal but computationally fast responses are more valuable than optimal responses obtained after long computations. In this paper, we introduce a hybridization approach for efficient approximation of nonlinear vehicle dynamics and non-convex constraints using a hybrid systems modeling framework. Hybridization allows to reformulate the nonlinear MPC problem during emergency evasive maneuvers as a hybrid MPC problem. In this regard, Max-Min-Plus-Scaling (MMPS) hybrid modeling is used to approximate the nonlinear vehicle dynamics. Meanwhile, different formulations for constraint approximation are presented, and various grid-generation methods are compared to solve these approximation problems. Among these, two novel grid types are introduced to structurally include the influence of the system dynamics on the grid point distributions in the state domain. Overall, the work presents and compares three hybrid models and four hybrid constraints for efficient MPC synthesis and offers guidelines for implementation of the presented hybridization framework in other applications.

Efficient MPC for Emergency Evasive Maneuvers, Part I: Hybridization of the Nonlinear Problem

TL;DR

This paper introduces a hybridization approach for efficient approximation of nonlinear vehicle dynamics and non-convex constraints and offers guidelines for implementation of the presented hybridization framework in other applications.

Abstract

Despite the extensive application of nonlinear Model Predictive Control (MPC) in automated driving, balancing its computational efficiency with respect to the control performance and constraint satisfaction remains a challenge in emergency scenarios: in such situations, sub-optimal but computationally fast responses are more valuable than optimal responses obtained after long computations. In this paper, we introduce a hybridization approach for efficient approximation of nonlinear vehicle dynamics and non-convex constraints using a hybrid systems modeling framework. Hybridization allows to reformulate the nonlinear MPC problem during emergency evasive maneuvers as a hybrid MPC problem. In this regard, Max-Min-Plus-Scaling (MMPS) hybrid modeling is used to approximate the nonlinear vehicle dynamics. Meanwhile, different formulations for constraint approximation are presented, and various grid-generation methods are compared to solve these approximation problems. Among these, two novel grid types are introduced to structurally include the influence of the system dynamics on the grid point distributions in the state domain. Overall, the work presents and compares three hybrid models and four hybrid constraints for efficient MPC synthesis and offers guidelines for implementation of the presented hybridization framework in other applications.
Paper Structure (18 sections, 33 equations, 7 figures, 5 tables, 2 algorithms)

This paper contains 18 sections, 33 equations, 7 figures, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Model Approximation
  4. Constraint Approximation
  5. Relation to the State-of-the-Art
  6. Grid Generation
  7. Approximation Problem Formulation
  8. Model Approximation
  9. Constraint Approximation
  10. Model and Constraint Hybridization for Vehicle Control
  11. Nonlinear System Descriptions
  12. Grid Definition and Coverage
  13. Model Approximation Results
  14. Constraint Approximation and Validation
  15. Conclusions and Outlook
  16. ...and 3 more sections

Figures (7)

  • Figure 1: A schematic view of different implementations of the proposed grid-generation approaches for model and constraint approximation.
  • Figure 2: Illustration of MMPS and ellipsoidal approximation of the nonlinear constraints.
  • Figure 3: Configuration of the single-track vehicle model.
  • Figure 4: Location of training and validation grid points in the $v_y-v_x$ domain for different grid-generation approaches in model approximation
  • Figure 5: Location of the training and validation combined grid points in the $v_y-v_x$ domain for constraint approximation
  • ...and 2 more figures

Theorems & Definitions (5)

  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Remark 5