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A Feedback Linearized Model Predictive Control Strategy for Input-Constrained Self-Driving Cars

Cristian Tiriolo, Walter Lucia

TL;DR

This work tackles trajectory tracking for self-driving cars under longitudinal and steering velocity constraints by integrating input-output feedback linearization with a dual-mode Model Predictive Control framework. It derives a linearized two-state output model with state-dependent, time-varying input constraints and proposes a worst-case circular inner approximation to enable tractable MPC while guaranteeing recursive feasibility and uniformly ultimately bounded tracking error within a robust invariant region. The paper converts the resulting optimization into a convex QCQP via polyhedral inner approximations, yielding a real-time solvable problem and providing theoretical guarantees on feasibility and stability. Experimental validation on a Quanser QCar demonstrates improved tracking performance and lower computation times compared with nonlinear MPC and backstepping, with public code availability enhancing reproducibility and adoption.

Abstract

This paper proposes a novel real-time affordable solution to the trajectory tracking control problem for self-driving cars subject to longitudinal and steering angular velocity constraints. To this end, we develop a dual-mode Model Predictive Control (MPC) solution starting from an input-output feedback linearized description of the vehicle kinematics. First, we derive the state-dependent input constraints acting on the linearized model and characterize their worst-case time-invariant inner approximation. Then, a dual-mode MPC is derived to be real-time affordable and ensuring, by design, constraints fulfillment, recursive feasibility, and uniformly ultimate boundedness of the tracking error in an ad-hoc built robust control invariant region. The approach's effectiveness and performance are experimentally validated via laboratory experiments on a Quanser Qcar. The obtained results show that the proposed solution is computationally affordable and with tracking capabilities that outperform two alternative control schemes.

A Feedback Linearized Model Predictive Control Strategy for Input-Constrained Self-Driving Cars

TL;DR

This work tackles trajectory tracking for self-driving cars under longitudinal and steering velocity constraints by integrating input-output feedback linearization with a dual-mode Model Predictive Control framework. It derives a linearized two-state output model with state-dependent, time-varying input constraints and proposes a worst-case circular inner approximation to enable tractable MPC while guaranteeing recursive feasibility and uniformly ultimately bounded tracking error within a robust invariant region. The paper converts the resulting optimization into a convex QCQP via polyhedral inner approximations, yielding a real-time solvable problem and providing theoretical guarantees on feasibility and stability. Experimental validation on a Quanser QCar demonstrates improved tracking performance and lower computation times compared with nonlinear MPC and backstepping, with public code availability enhancing reproducibility and adoption.

Abstract

This paper proposes a novel real-time affordable solution to the trajectory tracking control problem for self-driving cars subject to longitudinal and steering angular velocity constraints. To this end, we develop a dual-mode Model Predictive Control (MPC) solution starting from an input-output feedback linearized description of the vehicle kinematics. First, we derive the state-dependent input constraints acting on the linearized model and characterize their worst-case time-invariant inner approximation. Then, a dual-mode MPC is derived to be real-time affordable and ensuring, by design, constraints fulfillment, recursive feasibility, and uniformly ultimate boundedness of the tracking error in an ad-hoc built robust control invariant region. The approach's effectiveness and performance are experimentally validated via laboratory experiments on a Quanser Qcar. The obtained results show that the proposed solution is computationally affordable and with tracking capabilities that outperform two alternative control schemes.
Paper Structure (21 sections, 5 theorems, 60 equations, 7 figures, 3 tables, 1 algorithm)

This paper contains 21 sections, 5 theorems, 60 equations, 7 figures, 3 tables, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. Paper's Contribution and Organization
  3. Preliminaries and Problem Formulation
  4. Car-like vehicle modeling
  5. Problem's statement
  6. Proposed Solution
  7. Nonlinear MPC
  8. Input-Output Feedback Linearization
  9. Tracking Error Model and Input Constraint Characterization
  10. Robust Invariant Control Design
  11. Feedback Linearized Model Predictive Control
  12. Experimental Results
  13. Experimental Setup
  14. Configuration of the proposed controller
  15. Car's state estimation
  16. ...and 6 more sections

Key Result

Lemma 1

If the reference trajectory $q_r(t)$ complies with Assumption ass:ref-trajectory, $v_r(t)$ and $\omega_r(t)$ satisfies eq:ref-traj-variable-inputs and $0< v_r(t)\leq V>0, \forall t$ and $\forall |\varphi_r(t)|\leq \frac{\pi}{2},\, \forall t,$ then the tracking-error zero dynamics $\dot{\tilde{\eta}}

Figures (7)

  • Figure 1: Car-like vehicle
  • Figure 2: Time-varying input constraint set and its worst-case approximation
  • Figure 3: Possible side length configurations for $\mathcal{U}(\eta)$
  • Figure 4: Proposed experimental setup
  • Figure 5: Experimental results: Trajectory
  • ...and 2 more figures

Theorems & Definitions (18)

  • Definition 1
  • Definition 2
  • Definition 3
  • Remark 1
  • Remark 2
  • proof
  • Remark 3
  • Lemma 1
  • Lemma 2
  • proof
  • ...and 8 more