The accurate prediction of smooth steering inputs is crucial for automotive applications because control actions with jitter might cause the vehicle system to become unstable. To address this problem in automobile lane-keeping control without the use of additional smoothing algorithms, we developed a novel soft-constrained iterative linear quadratic regulator (soft-CILQR) algorithm by integrating CILQR algorithm and a model predictive control (MPC) constraint relaxation method. We incorporated slack variables into the state and control barrier functions of the soft-CILQR solver to soften the constraints in the optimization process such that control input stabilization can be achieved in a computationally simple manner. Two types of automotive lane-keeping experiments (numerical simulations and experiments involving challenging vision-based maneuvers) were conducted with a linear system dynamics model to test the performance of the proposed soft-CILQR algorithm, and its performance was compared with that of the CILQR algorithm. In the numerical simulations, the soft-CILQR and CILQR solvers managed to drive the system toward the reference state asymptotically; however, the soft-CILQR solver obtained smooth steering input trajectories more easily than did the CILQR solver under conditions involving additive disturbances. The results of the vision-based experiments in which an ego vehicle drove in perturbed TORCS environments with various road friction settings were consistent with those of the numerical tests. The proposed soft-CILQR algorithm achieved an average runtime of 2.55 ms and is thus applicable for real-time autonomous driving scenarios.

翻译：平滑转向输入的精确预测对汽车应用至关重要，因为存在抖振的控制动作可能导致车辆系统失稳。为解决汽车车道保持控制中无需额外平滑算法的问题，我们通过融合CILQR算法与模型预测控制约束松弛方法，提出了一种新型软约束迭代线性二次调节器算法。我们在soft-CILQR求解器的状态与控制屏障函数中引入松弛变量，以软化优化过程中的约束条件，从而能以计算简便的方式实现控制输入稳定。采用线性系统动力学模型进行了两类汽车车道保持实验（数值仿真与具有挑战性的基于视觉的机动实验），以测试所提soft-CILQR算法的性能，并与CILQR算法进行对比。数值仿真结果表明，soft-CILQR与CILQR求解器均能渐近驱动系统至参考状态；但在存在加性扰动的条件下，soft-CILQR求解器能更易获得平滑的转向输入轨迹。在TORCS扰动环境中通过不同路面摩擦系数设置的基于视觉实验所得结果与数值测试结论一致。所提soft-CILQR算法平均运行时间为2.55毫秒，适用于实时自动驾驶场景。