The accurate prediction of smooth steering inputs is crucial for autonomous vehicle 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 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 so that stabilizing control inputs can be calculated in a relatively simple manner. Two types of automotive lane-keeping experiments were conducted with a linear system dynamics model to test the performance of the proposed soft-CILQR algorithm and to compare its performance with that of the CILQR algorithm: numerical simulations and experiments involving challenging vision-based maneuvers. 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. In the experiments with visual inputs, the soft-CILQR controller outperformed the CILQR controller in terms of tracking accuracy and steering smoothness during the driving of an ego vehicle on TORCS.

翻译：精确预测平滑转向输入对于自动驾驶车辆应用至关重要，因为带有抖动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这一问题，我们通过将CILQR算法与模型预测控制（MPC）约束松弛方法相结合，提出了一种软约束迭代线性二次型调节器（soft-CILQR）算法。我们在soft-CILQR求解器的状态和控制障碍函数中引入松弛变量，以软化优化过程中的约束，从而能以相对简单的方式计算稳定的控制输入。我们利用线性系统动力学模型进行了两类汽车车道保持实验，以测试所提soft-CILQR算法的性能，并将其与CILQR算法的性能进行对比：数值仿真实验和基于视觉的具有挑战性的机动操作实验。在数值仿真中，soft-CILQR和CILQR求解器均能将系统渐近地驱向参考状态；然而，在存在加性干扰的条件下，soft-CILQR求解器比CILQR求解器更容易获得平滑的转向输入轨迹。在视觉输入实验中，当在TORCS平台上驾驶自车时，soft-CILQR控制器在跟踪精度和转向平滑度方面均优于CILQR控制器。