Obstacle Avoidance of Autonomous Vehicles: An LPVMPC with Scheduling Trust Region

TL;DR

This work tackles safe reference tracking and obstacle avoidance for autonomous driving by embedding a nonlinear vehicle model into a linear parameter-varying (LPV) form and solving the MPC problem as a quadratic program. A scheduling trust region is introduced via soft constraints on state and input deviations from predicted values, bounding scheduling-parameter prediction errors to retain feasibility. The authors develop both NMPC and LPVMPC frameworks, with the LPVMPC featuring adaptive linear obstacle handling and a QP-based solve, and they demonstrate that the LPVMPC with scheduling trust region achieves comparable tracking performance to NMPC while offering dramatically faster computation and greater feasibility than standard LPVMPC. The results indicate real-time applicability for obstacle-rich driving scenarios, with potential for extending to dynamic obstacles and recursive feasibility in future work.

Abstract

Reference tracking and obstacle avoidance rank among the foremost challenging aspects of autonomous driving. This paper proposes control designs for solving reference tracking problems in autonomous driving tasks while considering static obstacles. We suggest a model predictive control (MPC) strategy that evades the computational burden of nonlinear nonconvex optimization methods after embedding the nonlinear model equivalently to a linear parameter-varying (LPV) formulation using the so-called scheduling parameter. This allows optimal and fast solutions of the underlying convex optimization scheme as a quadratic program (QP) at the expense of losing some performance due to the uncertainty of the future scheduling trajectory over the MPC horizon. Also, to ensure that the modeling error due to the application of the scheduling parameter predictions does not become significant, we propose the concept of scheduling trust region by enforcing further soft constraints on the states and inputs. A consequence of using the new constraints in the MPC is that we construct a region in which the scheduling parameter updates in two consecutive time instants are trusted for computing the system matrices, and therefore, the feasibility of the MPC optimization problem is retained. We test the method in different scenarios and compare the results to standard LPVMPC as well as nonlinear MPC (NMPC) schemes.

Figures (9)

• Figure 1: Vehicle dynamics representation nezami2023design
• Figure 2: Linear obstacle avoidance constraint
• Figure 3: Comparison of the feasibility of the proposed LPVMPC with the trusts region in this paper to a standard LPVMPC for 10 obstacle avoidance scenarios.
• Figure 4: Open-loop trajectories of Standard LPVMPC at consecutive simulation time steps
• Figure 5: Open-loop trajectories of LPVMPC with trust region at consecutive simulation time steps

Theorems & Definitions (1)

• Definition 3.1: Scheduling trust region