Research On Key Technologies Of Autonomous Driving Motion Planning Based On Nonlinear Model Predictive Control

Autonomous vehicle is of great importance in improving the intelligent level of transportation,and also the crucial content of building China’s strength in transportation.However,the vehicle itself is a multi-degree of freedom strong coupling nonlinear system,and the feasible region of its motion planning also presents the characteristics of high-dimensional and non-convex.On the one hand,the commonly used vehicle models are only suitable for specific working conditions,which is difficult to meet the needs of high-level autonomous driving;on the other hand,with the improvement of intelligent level,the optimization dimension of motion planning in complex scenario increases rapidly,which leads to the lack of real-time solution.These problems have become the bottleneck which restricts the motion planning based on nonlinear model predictive control(NMPC)to be practical.Based on NMPC motion planning,the following research is carried out in four aspects: the establishment and simplification of vehicle dynamics prediction model,the numerical discretization method with high precision and low dimension,the hierarchical distributed parallel optimization solution and the experimental verification.Vehicle dynamical model is the basis of NMPC motion planning.However,the current vehicle models such as kinematics model and single-track dynamics can only be used in low-speed or high-speed small angle conditions.Therefore,based on the statistical analysis of the range of vehicle normal travel conditions,this paper establishes a longitudinal and lateral coupling vehicle dynamical model suitable for high-speed,low-speed and large steering conditions.In order to balance the complexity and accuracy of the model,the coupling characteristics between longitudinal and lateral dynamics are further studied through the analysis of amplitude frequency characteristics,and the weak part of dynamical coupling is reasonably simplified to obtain a single coupling dynamic model,which reduces the computational complexity of the model on the premise of ensuring the accuracy of the model.Finally,the simulation results of NMPC motion planning based on different models show that the proposed single coupling dynamical model improves the performance of kinematic model based NMPC motion planning in high-speed and tire cornering condition,and improves the performance of single-track model based NMPC motion planning in low-speed and large steering conditions.The dimension of optimization variables and the number of non-convex constraints directly affect the real-time solution of the discretized NMPC motion planning.The local interpolation characteristics of the current multiple shooting discretization method determines that it needs to use dense shooting points to ensure the discretization accuracy,which leads to the high dimension of the discretized optimization problem.In this paper,based on the continuous and strong nonlinear characteristics of vehicle dynamics,the global interpolation characteristic of Lagrange orthogonal polynomial interpolation discretization method is applied to reduce the discrete points while ensuring the accuracy.Due to the different nonlinear degree of vehicle dynamics under different conditions,an adaptive variable order discretization method based on the numerical study of the distribution characteristics of discretization error is proposed,which further reduces the discretization dimension.In the multi obstacle scenario,the elliptic obstacle avoidance constraint makes the optimization problem non-convex,while the linear obstacle avoidance constraint leads to unduly conservative planning results.To solve this problem,in this paper,starting from the influence degree of obstacles on subject vehicle,the elliptic obstacle avoidance constraint is adopted for the obstacle with the greatest influence,and the linear time-varying safety corridor constraint obtained by discretization and convexification of the elliptic obstacle avoidance constraint for other obstacles.Then,a hybrid obstacle avoidance constraint method is proposed to achieve the balance between non-convexity and conservatism of obstacle avoidance constraint.The optimization variable reduction and obstacle avoidance constraint convexification method can reduce the consumption of computational resources for motion planning,but the current mainstream vehicle processor are still difficult to meet the requirements.In order to make use of the multi-core and parallel computing ability of the current vehicle high-performance processor,this paper further improves the real-time performance of NMPC motion planning through parallel optimization at the solution level.Aiming at the problem that the coupling of optimization variables cannot be divided into blocks for parallel optimization in NMPC motion planning,the global variable is introduced to transform the original coupling optimization problem into a decomposable one.Furthermore,based on the theoretical analysis of the characteristics of the parallel optimization process of NMPC motion planning,the consistency constraint relaxation method is used to complete the parallel solution transformation of NMPC motion planning satisfying the necessary conditions of convergence.On this basis,a hierarchical parallel optimization algorithm for NMPC motion planning is proposed The algorithm uses the inner layer alternating direction multiplier method(ADMM)to realize parallel optimization to improve the real-time performance,and the outer layer augmented Lagrange method to accelerate the convergence of relaxation variables to ensure the feasibility of the solution.Theoretical analysis based on iterative descent method of Lyapunov function shows that the algorithm has global convergence.In order to verify the effectiveness of the proposed NMPC motion planning method,a real vehicle experimental platform and a vehicle in the loop experimental platform are developed based on the integration of software and hardware such as d SPACE rapid prototype controller and Pre Scan.The safety and comfort of the NMPC motion planning method proposed in this paper is compared with the traditional method through the vehicle in the loop experiment in high-speed and multi obstacle scenario.The effectiveness of the proposed NMPC motion planning method is verified by real vehicle experiments in six typical scenarios,such as curves with varying slope and curvature,sidewalk,intersection,traffic congestion,confluence and lane reduction.The experimental results show that the NMPC motion planning method proposed in this paper has good motion planning performance in different speed ranges,changing road curvatures and multi-obstacle complex scenarios,and has high real-time performance with the maximum single step running time less than 50 ms,which meets the requirements of vehicle application.