# SyDeBO: Symbolic-Decision-Embedded Bilevel Optimization for Long-Horizon Manipulation in Dynamic Environments

arXiv: https://arxiv.org/abs/2010.11078 · HTML: https://mlsanity.com/paper/2010.11078/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Oct 2020.

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

- [A Survey of Optimization-based Task and Motion Planning: From Classical To Learning Approaches](https://mlsanity.com/paper/2404.02817/) (2024)
- [Adversarially Regularized Policy Learning Guided by Trajectory Optimization](https://mlsanity.com/paper/2109.07627/) (2021)
- [Impedance Primitive-augmented Hierarchical Reinforcement Learning for Sequential Tasks](https://mlsanity.com/paper/2508.19607/) (2025)
- [Hierarchical Contact-Rich Trajectory Optimization for Multi-Modal Manipulation using Tight Convex Relaxations](https://mlsanity.com/paper/2503.07963/) (2025)

## Abstract (arXiv)

This study proposes a Task and Motion Planning (TAMP) method with symbolic decisions embedded in a bilevel optimization. This TAMP method exploits the discrete structure of sequential manipulation for long-horizon and versatile tasks in dynamically changing environments. At the symbolic planning level, we propose a scalable decision-making method for long-horizon manipulation tasks using the Planning Domain Definition Language (PDDL) with causal graph decomposition. At the motion planning level, we devise a trajectory optimization (TO) approach based on the Alternating Direction Method of Multipliers (ADMM), suitable for solving constrained, large-scale nonlinear optimization in a distributed manner. Distinct from conventional geometric motion planners, our approach generates highly dynamic manipulation motions by incorporating the full robot and object dynamics. Furthermore, in lieu of a hierarchical planning approach, we solve a holistically integrated bilevel optimization problem involving costs from both the low-level TO and the high-level search. Simulation and experimental results demonstrate dynamic manipulation for long-horizon object sorting tasks in clutter and on a moving conveyor belt.