# Constant-time Motion Planning with Anytime Refinement for Manipulation

arXiv: https://arxiv.org/abs/2311.00837 · HTML: https://mlsanity.com/paper/2311.00837/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 32 references that are in the map.
- First posted on arXiv 1 Nov 2023.

## Builds on (most cited first, 11 of 11)

- [Integrated Task and Motion Planning](https://mlsanity.com/paper/2010.01083/) (2020)
- [Motion Planning around Obstacles with Convex Optimization](https://mlsanity.com/paper/2205.04422/) (2022)
- [Long-Horizon Multi-Robot Rearrangement Planning for Construction Assembly](https://mlsanity.com/paper/2106.02489/) (2021)
- [Shortest Paths in Graphs of Convex Sets](https://mlsanity.com/paper/2101.11565/) (2021)
- [Experience-Based Planning with Sparse Roadmap Spanners](https://mlsanity.com/paper/1410.1950/) (2014)
- [Provably Constant-time Planning and Replanning for Real-time Grasping Objects off a Conveyor Belt](https://mlsanity.com/paper/2101.07148/) (2021)
- [Certified Polyhedral Decompositions of Collision-Free Configuration Space](https://mlsanity.com/paper/2302.12219/) (2023)
- [Non-Euclidean Motion Planning with Graphs of Geodesically-Convex Sets](https://mlsanity.com/paper/2305.06341/) (2023)
- [Robust Task and Motion Planning for Long-Horizon Architectural Construction Planning](https://mlsanity.com/paper/2003.07754/) (2020)
- [Alternative Paths Planner (APP) for Provably Fixed-time Manipulation Planning in Semi-structured Environments](https://mlsanity.com/paper/2012.14970/) (2020)
- [Growing Convex Collision-Free Regions in Configuration Space using Nonlinear Programming](https://mlsanity.com/paper/2303.14737/) (2023)

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

- [RaySt3R: Predicting Novel Depth Maps for Zero-Shot Object Completion](https://mlsanity.com/paper/2506.05285/) (2025)
- [Accelerating Search-Based Planning for Multi-Robot Manipulation by Leveraging Online-Generated Experiences](https://mlsanity.com/paper/2404.00143/) (2024)
- [Constant-Time Planning for Chaining Collision-free Motion to Manipulation Behaviors](https://mlsanity.com/paper/2512.00939/) (2025)
- [Multi Graph Search for High-Dimensional Robot Motion Planning](https://mlsanity.com/paper/2602.12096/) (2026)

## Abstract (arXiv)

Robotic manipulators are essential for future autonomous systems, yet limited trust in their autonomy has confined them to rigid, task-specific systems. The intricate configuration space of manipulators, coupled with the challenges of obstacle avoidance and constraint satisfaction, often makes motion planning the bottleneck for achieving reliable and adaptable autonomy. Recently, a class of constant-time motion planners (CTMP) was introduced. These planners employ a preprocessing phase to compute data structures that enable online planning provably guarantee the ability to generate motion plans, potentially sub-optimal, within a user defined time bound. This framework has been demonstrated to be effective in a number of time-critical tasks. However, robotic systems often have more time allotted for planning than the online portion of CTMP requires, time that can be used to improve the solution. To this end, we propose an anytime refinement approach that works in combination with CTMP algorithms. Our proposed framework, as it operates as a constant time algorithm, rapidly generates an initial solution within a user-defined time threshold. Furthermore, functioning as an anytime algorithm, it iteratively refines the solution's quality within the allocated time budget. This enables our approach to strike a balance between guaranteed fast plan generation and the pursuit of optimization over time. We support our approach by elucidating its analytical properties, showing the convergence of the anytime component towards optimal solutions. Additionally, we provide empirical validation through simulation and real-world demonstrations on a 6 degree-of-freedom robot manipulator, applied to an assembly domain.