# Newton methods for k-order Markov Constrained Motion Problems

arXiv: https://arxiv.org/abs/1407.0414 · HTML: https://mlsanity.com/paper/1407.0414/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2014.

## Built on by (most cited first, 6 of 6)

- [Learning Implicit Priors for Motion Optimization](https://mlsanity.com/paper/2204.05369/) (2022)
- [Model Predictive Control for Fluid Human-to-Robot Handovers](https://mlsanity.com/paper/2204.00134/) (2022)
- [The State of Robot Motion Generation](https://mlsanity.com/paper/2410.12172/) (2024)
- [Accelerating db-A* for Kinodynamic Motion Planning Using Diffusion](https://mlsanity.com/paper/2503.05539/) (2025)
- [A Taxonomy of Self-Handover](https://mlsanity.com/paper/2504.04939/) (2025)
- [MO-SeGMan: Rearrangement Planning Framework for Multi Objective Sequential and Guided Manipulation in Constrained Environments](https://mlsanity.com/paper/2511.01476/) (2025)

## Abstract (arXiv)

This is a documentation of a framework for robot motion optimization that aims to draw on classical constrained optimization methods. With one exception the underlying algorithms are classical ones: Gauss-Newton (with adaptive step size and damping), Augmented Lagrangian, log-barrier, etc. The exception is a novel any-time version of the Augmented Lagrangian. The contribution of this framework is to frame motion optimization problems in a way that makes the application of these methods efficient, especially by defining a very general class of robot motion problems while at the same time introducing abstractions that directly reflect the API of the source code.