# Optimizing Control-Friendly Trajectories with Self-Supervised Residual Learning

arXiv: https://arxiv.org/abs/2601.02738 · HTML: https://mlsanity.com/paper/2601.02738/

## Key facts

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

## Built on by (most cited first, 1 of 1)

- [FlowPilot: Real-Time World-Action Modeling for Agile UAV Navigation](https://mlsanity.com/paper/2608.00635/) (2026)

## Abstract (arXiv)

Real-world physics can only be analytically modeled with a certain level of precision for modern intricate robotic systems. As a result, tracking aggressive trajectories accurately could be challenging due to the existence of residual physics during controller synthesis. This paper presents a self-supervised residual learning and trajectory optimization framework to address the aforementioned challenges. At first, unknown dynamic effects on the closed-loop model are learned and treated as residuals of the nominal dynamics, jointly forming a hybrid model. We show that learning with analytic gradients can be achieved using only trajectory-level data while enjoying accurate long-horizon prediction with an arbitrary integration step size. Subsequently, a trajectory optimizer is developed to compute the optimal reference trajectory with the residual physics along it minimized. It ends up with trajectories that are friendly to the following control level. The agile flight of quadrotors illustrates that by utilizing the hybrid dynamics, the proposed optimizer outputs aggressive motions that can be precisely tracked.