# Trajectory Optimization on Manifolds: A Theoretically-Guaranteed Embedded Sequential Convex Programming Approach

arXiv: https://arxiv.org/abs/1905.07654 · HTML: https://mlsanity.com/paper/1905.07654/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 May 2019.

## Built on by (most cited first, 4 of 4)

- [Fast Kinodynamic Planning on the Constraint Manifold with Deep Neural Networks](https://mlsanity.com/paper/2301.04330/) (2023)
- [Physics-informed Neural Motion Planning on Constraint Manifolds](https://mlsanity.com/paper/2403.05765/) (2024)
- [Deep Learning Warm Starts for Trajectory Optimization on the International Space Station](https://mlsanity.com/paper/2505.05588/) (2025)
- [A Structured Prediction Approach for Robot Imitation Learning](https://mlsanity.com/paper/2309.14829/) (2023)

## Abstract (arXiv)

Sequential Convex Programming (SCP) has recently gained popularity as a tool for trajectory optimization due to its sound theoretical properties and practical performance. Yet, most SCP-based methods for trajectory optimization are restricted to Euclidean settings, which precludes their application to problem instances where one must reason about manifold-type constraints (that is, constraints, such as loop closure, which restrict the motion of a system to a subset of the ambient space). The aim of this paper is to fill this gap by extending SCP-based trajectory optimization methods to a manifold setting. The key insight is to leverage geometric embeddings to lift a manifold-constrained trajectory optimization problem into an equivalent problem defined over a space enjoying a Euclidean structure. This insight allows one to extend existing SCP methods to a manifold setting in a fairly natural way. In particular, we present a SCP algorithm for manifold problems with refined theoretical guarantees that resemble those derived for the Euclidean setting, and demonstrate its practical performance via numerical experiments.