基于hp自适应伪谱法的自主泊车路径规划

Path Planning of Autonomous Parking Based on hp-adaptive Pseudospectral Method

针对自主泊车路径规划最优控制问题求解收敛速率慢的问题,提出基于hp自适应高斯伪谱法的自主泊车路径规划方法。首先建立车辆运动学模型,并考虑自主泊车过程中避障约束和边界约束,再以泊车时间最短为性能目标函数,将自主泊车路径规划问题转化为最优控制问题。采用高斯伪谱法对最优控制问题进行离散化处理并采用序列二次规划进行求解,在求解过程中通过动态调整网格区间个数和多项式阶数实现提高求解收敛速率。根据实际场景选取4种工况并进行路径规划仿真,并将3种伪谱法进行对比分析,仿真结果表明hp自适应高斯伪谱法能够提升自主泊车路径规划最优控制问题求解收敛速率,同时该算法可以实现在狭窄泊车位内的泊车路径规划,通过实车试验验证提出的方法获得的自主泊车路径的有效性。

Aiming at the problem that the convergence rate is slow when solving the optimal control problem of autonomous parking path planning,a method of autonomous parking path planning based on hp-adaptive Gauss pseudospectral method is proposed.First,the vehicle kinematical model is established,then the collision avoidance constraints and the boundary constraints in autonomous parking processes are further considered,finally the problem of autonomous parking path planning is converted into the optimal control problem which takes the shortest parking time as the cost function.The optimal control problem is discretized by Gauss pseudospectral method,and solved by sequential quadratic programming,in which the number of mesh intervals and degree of the polynomial are adjusted dynamically improving the convergence rate.According to the actual scenario,four autonomous parking conditions are designed and path planning is simulated,and three pseudospectral methods are compared and analyzed.The simulation results show that the convergence rate of the optimal control problem of autonomous parking path planning is improved by the hp-adaptive Gauss pseudospectral method,and the proposed mothed can obtain the parking path in a narrow parking lot,the effectiveness of the proposed method for autonomous parking path planning is verified by real vehicle tests.