# Constrained Differential Dynamic Programming Revisited

arXiv: https://arxiv.org/abs/2005.00985 · HTML: https://mlsanity.com/paper/2005.00985/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 May 2020.

## Built on by (most cited first, 3 of 3)

- [A Differential Dynamic Programming Framework for Inverse Reinforcement Learning](https://mlsanity.com/paper/2407.19902/) (2024)
- [DiffCoord: Differentiable Coordination for Distributed Multi-Agent Trajectory Optimization](https://mlsanity.com/paper/2509.01630/) (2025)
- [Self-Reflective Terrain-Aware Robot Adaptation for Consistent Off-Road Ground Navigation](https://mlsanity.com/paper/2111.06742/) (2021)

## Abstract (arXiv)

Differential Dynamic Programming (DDP) has become a well established method for unconstrained trajectory optimization. Despite its several applications in robotics and controls however, a widely successful constrained version of the algorithm has yet to be developed. This paper builds upon penalty methods and active-set approaches, towards designing a Dynamic Programming-based methodology for constrained optimal control. Regarding the former, our derivation employs a constrained version of Bellman's principle of optimality, by introducing a set of auxiliary slack variables in the backward pass. In parallel, we show how Augmented Lagrangian methods can be naturally incorporated within DDP, by utilizing a particular set of penalty-Lagrangian functions that preserve second-order differentiability. We demonstrate experimentally that our extensions (individually and combinations thereof) enhance significantly the convergence properties of the algorithm, and outperform previous approaches on a large number of simulated scenarios.