Working Paper Article Version 1 This version is not peer-reviewed

Autonomous Collision Avoidance using MPC with LQR-based Weight Transformation

Version 1 : Received: 4 April 2021 / Approved: 7 April 2021 / Online: 7 April 2021 (16:58:36 CEST)
(This article belongs to the Research Topic EUSAR 2020—Preprints)

How to cite: taherian, S.; Halder, K.; Dixit, S.; Fallah, S. Autonomous Collision Avoidance using MPC with LQR-based Weight Transformation. Preprints 2021, 2021040213 taherian, S.; Halder, K.; Dixit, S.; Fallah, S. Autonomous Collision Avoidance using MPC with LQR-based Weight Transformation. Preprints 2021, 2021040213

Abstract

Model predictive control (MPC) is a multi-objective control technique that can handle 2 system constraints. However, the performance of an MPC controller highly relies on a proper 3 prioritization weight for each objective, which highlights the need for a precise weight tuning 4 technique. In this paper, we propose an analytical tuning technique by matching the MPC 5 controller performance with the performance of a linear quadratic regulator (LQR) controller. The 6 proposedmethodology derives the transformation of LQRweightingmatrixwith a fixedweighting 7 factor using discrete algebraic Riccati equation (DARE) and designs MPC controller using the 8 idea of discrete time linear quadratic tracking problem (LQT) in the presence of constraints. 9 The proposed methodology ensures the optimal performance between unconstrained MPC and 10 LQR controller and provides a sub-optimal solution while the constraints are active during 11 transient operations. The resultingMPC behaves as the discrete time LQR by selecting appropriate 12 weighting matrix in the MPC control problem and ensures the asymptotic stability of the system. 13 In this paper, the effectiveness of the proposed technique is investigated in the application of 14 a novel vehicle collision avoidance system which is designed in the form of linear inequality 15 constraints within MPC. The simulation results confirm the potency of the proposed MPC control 16 technique in performing a safe, feasible and collision free path while respecting the inputs, states 17 and collision avoidance constraints.

Subject Areas

Trajectory planning; MPC; LQR; LQT; inverse optimal control; collision avoidance

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