# Sequence-of-Constraints MPC: Reactive Timing-Optimal Control of Sequential Manipulation

arXiv: https://arxiv.org/abs/2203.05390 · HTML: https://mlsanity.com/paper/2203.05390/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Mar 2022.

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

- [VoxPoser: Composable 3D Value Maps for Robotic Manipulation with Language Models](https://mlsanity.com/paper/2307.05973/) (2023)
- [ReKep: Spatio-Temporal Reasoning of Relational Keypoint Constraints for Robotic Manipulation](https://mlsanity.com/paper/2409.01652/) (2024)
- [Language to Rewards for Robotic Skill Synthesis](https://mlsanity.com/paper/2306.08647/) (2023)
- [Task and Motion Planning for Execution in the Real](https://mlsanity.com/paper/2406.03641/) (2024)
- [Diffusion-Informed Probabilistic Contact Search for Multi-Finger Manipulation](https://mlsanity.com/paper/2410.00841/) (2024)
- [Hierarchical Contact-Rich Trajectory Optimization for Multi-Modal Manipulation using Tight Convex Relaxations](https://mlsanity.com/paper/2503.07963/) (2025)

## Abstract (arXiv)

Task and Motion Planning has made great progress in solving hard sequential manipulation problems. However, a gap between such planning formulations and control methods for reactive execution remains. In this paper we propose a model predictive control approach dedicated to robustly execute a single sequence of constraints, which corresponds to a discrete decision sequence of a TAMP plan. We decompose the overall control problem into three sub-problems (solving for sequential waypoints, their timing, and a short receding horizon path) that each is a non-linear program solved online in each MPC cycle. The resulting control strategy can account for long-term interdependencies of constraints and reactively plan for a timing-optimal transition through all constraints. We additionally propose phase backtracking when running constraints of the current phase cannot be fulfilled, leading to a fluent re-initiation behavior that is robust to perturbations and interferences by an experimenter.