Line-Search Filter Differential Dynamic Programming for Optimal Control with Nonlinear Equality Constraints
For roboticists and control engineers, FilterDDP provides a more robust and theoretically grounded algorithm for constrained optimal control, though it is an incremental improvement over existing DDP variants.
FilterDDP solves discrete-time optimal control problems with nonlinear equality constraints using a line-search filter method, achieving robust numerical performance and local quadratic convergence. It outperforms prior methods on three robotics contact-implicit trajectory optimization problems.
We present FilterDDP, a differential dynamic programming algorithm for solving discrete-time, optimal control problems (OCPs) with nonlinear equality constraints. Unlike prior methods based on merit functions or the augmented Lagrangian class of algorithms, FilterDDP uses a step filter in conjunction with a line search to handle equality constraints. We identify two important design choices for the step filter criteria which lead to robust numerical performance: 1) we use the Lagrangian instead of the cost in the step acceptance criterion and, 2) in the backward pass, we perturb the value function Hessian. Both choices are rigorously justified, for 2) in particular by a formal proof of local quadratic convergence. In addition to providing a primal-dual interior point extension for handling OCPs with both equality and inequality constraints, we validate FilterDDP on three contact implicit trajectory optimisation problems which arise in robotics.