  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.
