# Crocoddyl: An Efficient and Versatile Framework for Multi-Contact Optimal Control

arXiv: https://arxiv.org/abs/1909.04947 · HTML: https://mlsanity.com/paper/1909.04947/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Sep 2019.

## Built on by (most cited first, 30 of 34)

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- [Revisiting Implicit Differentiation for Learning Problems in Optimal Control](https://mlsanity.com/paper/2310.14468/) (2023)
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- [Multi-Agent Chance-Constrained Stochastic Shortest Path with Application to Risk-Aware Intelligent Intersection](https://mlsanity.com/paper/2210.01766/) (2022)
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- [Tracking Control for a Spherical Pendulum via Curriculum Reinforcement Learning](https://mlsanity.com/paper/2309.14096/) (2023)
- [Constrained Reinforcement Learning for Unstable Point-Feet Bipedal Locomotion Applied to the Bolt Robot](https://mlsanity.com/paper/2508.02194/) (2025)
- [Warm-Starting Collision-Free Model Predictive Control With Object-Centric Diffusion](https://mlsanity.com/paper/2601.02873/) (2026)
- [ODYN: An All-Shifted Non-Interior-Point Method for Quadratic Programming in Robotics and AI](https://mlsanity.com/paper/2602.16005/) (2026)
- [First do not fall: learning to exploit a wall with a damaged humanoid robot](https://mlsanity.com/paper/2203.00316/) (2022)
- [Probabilistic Control and Majorization of Optimal Control](https://mlsanity.com/paper/2205.03279/) (2022)
- [Learning Human Reaching Optimality Principles from Minimal Observation Inverse Reinforcement Learning](https://mlsanity.com/paper/2510.00329/) (2025)
- [Bayesian Optimization for Automatic Tuning of Torque-Level Nonlinear Model Predictive Control](https://mlsanity.com/paper/2512.03772/) (2025)

## Abstract (arXiv)

We introduce Crocoddyl (Contact RObot COntrol by Differential DYnamic Library), an open-source framework tailored for efficient multi-contact optimal control. Crocoddyl efficiently computes the state trajectory and the control policy for a given predefined sequence of contacts. Its efficiency is due to the use of sparse analytical derivatives, exploitation of the problem structure, and data sharing. It employs differential geometry to properly describe the state of any geometrical system, e.g. floating-base systems. Additionally, we propose a novel optimal control algorithm called Feasibility-driven Differential Dynamic Programming (FDDP). Our method does not add extra decision variables which often increases the computation time per iteration due to factorization. FDDP shows a greater globalization strategy compared to classical Differential Dynamic Programming (DDP) algorithms. Concretely, we propose two modifications to the classical DDP algorithm. First, the backward pass accepts infeasible state-control trajectories. Second, the rollout keeps the gaps open during the early "exploratory" iterations (as expected in multiple-shooting methods with only equality constraints). We showcase the performance of our framework using different tasks. With our method, we can compute highly-dynamic maneuvers (e.g. jumping, front-flip) within few milliseconds.