Trajectory optimization has been used extensively in robotic systems. In particular, iterative Linear Quadratic Regulator (iLQR) has performed well as an off-line planner and online nonlinear model predictive control solver, with a lower computational cost. However, standard iLQR cannot handle any constraints or perform reasonable initialization of a state trajectory. In this paper, we propose a hybrid constrained iLQR variant with a multiple-shooting framework to incorporate general inequality constraints and infeasible states initialization. The main technical contributions are twofold: 1) In addition to inheriting the simplicity of the initialization in multiple-shooting settings, a two-stage framework is developed to deal with state and/or control constraints robustly without loss of the linear feedback term of iLQR. Such a hybrid strategy offers fast convergence of constraint satisfaction. 2) An improved globalization strategy is proposed to exploit the coupled effects between line-searching and regularization, which is able to enhance the numerical robustness of the constrained iLQR approaches. Our approach is tested on various constrained trajectory optimization problems and outperforms the commonly-used collocation and shooting methods.

翻译：轨迹优化在机器人系统中得到了广泛应用。其中，迭代线性二次型调节器（iLQR）因其计算成本较低，在离线规划与在线非线性模型预测控制求解中表现优异。然而，标准iLQR无法处理任何约束条件，也无法对状态轨迹进行合理初始化。本文提出一种基于多段打靶框架的混合约束iLQR变体，以纳入一般不等式约束和不可行状态初始化。主要技术贡献包含两点：1）在保留多段打靶设置中初始化简便性的基础上，开发了两阶段框架以鲁棒处理状态和/或控制约束，同时不损失iLQR的线性反馈项。这种混合策略能够实现约束满足的快速收敛。2）提出改进的全局化策略，充分利用线搜索与正则化之间的耦合效应，增强约束iLQR方法的数值鲁棒性。所提方法在各类约束轨迹优化问题中进行了测试，性能优于常用的配点法和打靶法。