智能汽车的运动控制直接决定了自动驾驶的行驶性能，模型预测控制（MPC, Model Predictive Control）是解决该问题的重要方法。然而，由于行驶性能需求多样、约束数目繁多，MPC算法难以满足在线优化的实时性要求，限制了在自动驾驶领域的应用。当前自动驾驶控制器正向多核异构体系发展，这使得并行求解MPC问题成为可能。面向这一发展趋势，本文对比分析了时域分解与约束分解两类并行MPC算法设计机制，分别提出了跨节点共识及共识约束压缩加速收敛策略，同时将Anderson方法应用于迭代过程加速，最后结合智能汽车轨迹跟踪控制问题，对并行加速算法的控制以及收敛性能进行验证。这为高实时智能汽车轨迹跟踪控制奠定了基础。首先，将MPC问题分解为适用于并行计算的子问题。基于算子分裂技术，通过引入全局（共识）变量，对MPC问题存在的耦合变量进行解耦。时域分解机制，将原问题分解为若干个仅考虑单步的子优化问题；约束分解机制，将原问题分解为可以求出解析解的等式约束二次规划子问题，以及若干个只考虑单步不等式约束的子问题。针对分解后的子问题之间的共识优化问题，利用交替方向乘子法（ADMM, Alternating Direction Method of Multipliers），以并行方式迭代计算最优解。其次，针对两类并行MPC算法，分别提出了两种加速收敛策略。针对时域分解机制，提出了跨节点共识策略，以提高优化过程中子问题之间的信息传递效率；针对约束分解机制，提出了共识约束压缩策略，考虑只有控制变量约束问题，降低了共识约束数目及在线计算复杂度；由于两类机制都只依赖于梯度信息迭代优化，在梯度基础上加入了过去迭代点中包含的信息，实现了迭代过程的Anderson加速。最后，结合智能汽车轨迹跟踪的数值实验，验证了两类并行MPC算法的控制性能和收敛速度。针对双移线工况的轨迹跟踪控制问题，分析了两类并行MPC算法与集中式MPC算法的控制效果及精度；针对算法的收敛性能，选择目前应用广泛的可变惩罚参数法和Nesterov方法作为基准，系统的分析了所提出四类加速策略的迭代收敛速度。验证表明，时域分解机制下，跨节点共识及Anderson加速策略相比于标准算法，能够分别减少67.1%和61.3%的迭代步数；约束分解机制下，Anderson加速及共识约束压缩策略相比于标准算法，能够分别减少87.2%和86.7%的迭代步数。
The motion control of intelligent vehicles directly determines the driving performance of autonomous driving, and Model Predictive Control (MPC) is an important method to solve this problem. However, due to the diverse driving performance requirements and a large number of constraints, MPC algorithms are difficult to meet the real-time requirements for online optimization, limiting the application in the field of autonomous driving. The current development of autonomous driving controllers towards multi-core heterogeneous systems has made it possible to solve MPC problems in parallel. For this development trend, this paper compares and analyzes the design mechanisms of two types of parallel MPC algorithms: time-splitting and constraint-splitting, proposes cross-node consensus and consensus constraint compression acceleration strategies, respectively, and applies Anderson's method to iterative process acceleration. This research lays a foundation for high real-time intelligent vehicle trajectory tracking control.First, the MPC problem is decomposed into sub-problems applicable to parallel computing. Based on the operator splitting technique, the coupling variables present in the MPC problem are decoupled by introducing global (consensus) variables. The time-splitting mechanism decomposes the original problem into several sub-optimization problems considering only a single step; the constraint-splitting mechanism decomposes the original problem into equationally constrained quadratic programming sub-problems, which can be derived an analytic solution, and several sub-problems considering only single-step inequality constraints. For the consensus optimization problem between the decomposed sub-problems, the optimal solution is computed iteratively in a parallel way using the Alternating Direction Method of Multipliers (ADMM).Second, two accelerated convergence strategies are proposed for each of the two types of parallel MPC algorithms. For the time-splitting mechanism, a cross-node consensus strategy is proposed to improve the efficiency of information transfer between sub-problems during the optimization process; for the constraint-splitting mechanism, a consensus constraint compression strategy is proposed to reduce the number of consensus constraints and online computational complexity by considering only the control variable constraint. For both types of mechanisms that rely only on gradient information for iterative optimization, the Anderson acceleration method is utilized to add the information collected in the past iteration on top of the gradient.Second, two accelerated convergence strategies are proposed for each of the two types of parallel MPC algorithms. For the time-splitting mechanism, a cross-node consensus strategy is proposed to improve the efficiency of information transfer between sub-problems during the optimization process; for the constraint-splitting mechanism, a consensus constraint compression strategy is proposed to reduce the number of consensus constraints and online computational complexity by considering only the control variable constraint. Since both types of mechanisms rely only on gradient information for iterative optimization, adding the information contained in past iteration points on top of the gradient information, the Anderson acceleration of the iterative process is achieved.Finally, the control performance and convergence speed of the two types of parallel MPC algorithms are verified by combining the numerical experiments of the intelligent vehicle trajectory tracking problem. In order to compare the convergence performance of the algorithms, the iterative convergence speed of the proposed four types of acceleration strategies is systematically analyzed by choosing the widely used variable penalty parameter method and the Nesterov method as benchmarks. The verification shows that the cross-node consensus and Anderson acceleration strategies can reduce the number of iteration steps by 67.1% and 61.3%, respectively, compared with the standard algorithm under the time-splitting mechanism; the Anderson acceleration and consensus constraint compression strategies can reduce the number of iteration steps by 87.2% and 86.7%, respectively, compared with the standard algorithm under the constraint-splitting mechanism.
