HM-DDP: A Hybrid Multiple-shooting Differential Dynamic Programming Method for Constrained Trajectory Optimization

Trajectory optimization has been used extensively in robotic systems. In particular, Differential Dynamic Programming (DDP) has performed well as an off-line planner or an online nonlinear model predictive control solver, with a lower computational cost compared with other general-purpose nonlinear programming solvers. However, standard DDP cannot handle any constraints or perform reasonable initialization of a state trajectory. In this paper, we propose a hybrid constrained DDP variant with a multiple-shooting framework. The main technical contributions are twofold: 1) In addition to inheriting the simplicity of the initialization in multiple shooting, a two-stage framework is developed to deal with state and control inequality constraints robustly without loss of the linear feedback term of DDP. Such a hybrid strategy offers a 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 DDP-like approaches. Our approach is tested on three constrained trajectory optimization problems with nonlinear inequality constraints and outperforms the commonly-used collocation and shooting methods in terms of runtime and constraint satisfaction.