# Probabilistic Framework for Constrained Manipulations and Task and Motion Planning under Uncertainty

arXiv: https://arxiv.org/abs/2003.04259 · HTML: https://mlsanity.com/paper/2003.04259/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Mar 2020.

## Built on by (most cited first, 5 of 5)

- [ReKep: Spatio-Temporal Reasoning of Relational Keypoint Constraints for Robotic Manipulation](https://mlsanity.com/paper/2409.01652/) (2024)
- [Sequential Manipulation Planning on Scene Graph](https://mlsanity.com/paper/2207.04364/) (2022)
- [Active Learning of Abstract Plan Feasibility](https://mlsanity.com/paper/2107.00683/) (2021)
- [Constrained Stein Variational Trajectory Optimization](https://mlsanity.com/paper/2308.12110/) (2023)
- [STAMP: Differentiable Task and Motion Planning via Stein Variational Gradient Descent](https://mlsanity.com/paper/2310.01775/) (2023)

## Abstract (arXiv)

Logic-Geometric Programming (LGP) is a powerful motion and manipulation planning framework, which represents hierarchical structure using logic rules that describe discrete aspects of problems, e.g., touch, grasp, hit, or push, and solves the resulting smooth trajectory optimization. The expressive power of logic allows LGP for handling complex, large-scale sequential manipulation and tool-use planning problems. In this paper, we extend the LGP formulation to stochastic domains. Based on the control-inference duality, we interpret LGP in a stochastic domain as fitting a mixture of Gaussians to the posterior path distribution, where each logic profile defines a single Gaussian path distribution. The proposed framework enables a robot to prioritize various interaction modes and to acquire interesting behaviors such as contact exploitation for uncertainty reduction, eventually providing a composite control scheme that is reactive to disturbance. The supplementary video can be found at https://youtu.be/CEaJdVlSZyo