面向NMPC运动规划系统的数值优化加速技术

doi:10.19562/j.chinasae.qcgc.2023.08.014

Abstract

Abstract:

Nonlinear Model Predictive Control （NMPC） is an effective method for the motion planning of automated vehicles， but its high demand of computation resources for numerical optimization limits its practical application. This paper improves the solving speed of the numerical optimization of NMPC motion planning system by reducing the dimension of optimization variables and simplifying the non-convex constraints for obstacle avoidance. Given the high nonlinearity of vehicle dynamics， Lagrange interpolation is adopted to discretize the state function of vehicle dynamics and the objective function to ensure the accuracy with less discretization points. Furthermore， an adaptive strategy is designed to adjust the order of Lagrange polynomials based on the numerical analysis of the distribution characteristics of the discretization error to further reduce the dimension of optimization variables. Moreover， a hybrid strategy is presented to construct the constraints for obstacle avoidance by combing the elliptic and linear time-varying ones together to realize good balance between the difficulty of numerical optimization and the conservatism of optimized results while ensuring the driving safety. The acceleration effect and performance of the proposed method are validated by simulation and experimental tests under various scenarios with multi-obstacles. The results show that compared with traditional methods the accuracy and efficiency of discretization of the proposed method is improved by 74% and 60%， respectively.

Key words: automatic driving, motion planning, model predictive control, Lagrange interpolation, obstacle avoidance constraints

Feng Gao,Defu Feng,Qiuxia Hu. Accelerating Technologies of Numerical Optimization for Motion Planning Designed by Nonlinear Model Predictive Control[J].Automotive Engineering, 2023, 45(8): 1438-1447.

Figures/Tables 22

参数	教值
$F T m i n v x$	$v x = [0 ? 5 ? 10 ? 15 ? 20 ? 25 ? 30] ? m / s$ $F T m i n = [5.2 ? 5 ? 4 ? 4 ? 3.8 ? 3 ? 2] ? k N$
$F T m a x v x$	$v x = [0 ? 5 ? 10 ? 15 ? 20 ? 25 ? 30] ? m / s$ $F T m a x = [4 ? 4 ? 4 ? 4 ? 3.7 ? 2.5 ? 2] ? k N$
$δ f v x$	$v x = [0 ? 5 ? 10 ? 15 ? 20 ? 25 ? 30] ? m / s$ $δ f = 32 ? 20 ? 7 ? 5 ? 3 ? 2 ? 2 ? (°)$
$? u m i n$	$5 ?? 000 ? N / s ?? 63 ?? (°) / s T$
$? u m a x$	$4 ?? 000 ? N / s ?? 63 ?? (°) / s T$

符号	单位	数值
$I z$	$k g ? m 2$	1 943
$m$	$k g$	1 460
$l f$	$m$	1.17
$l r$	$m$	1.77
$C y f$	$N / r a d$	54 600
$C y r$	$N / r a d$	54 600

References 27

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Accelerating Technologies of Numerical Optimization for Motion Planning Designed by Nonlinear Model Predictive Control

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