# Fast Kinodynamic Planning on the Constraint Manifold with Deep Neural Networks

arXiv: https://arxiv.org/abs/2301.04330 · HTML: https://mlsanity.com/paper/2301.04330/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 88 references that are in the map.
- First posted on arXiv 11 Jan 2023.

## Builds on (most cited first, 23 of 23)

- [Responsive Safety in Reinforcement Learning by PID Lagrangian Methods](https://mlsanity.com/paper/2007.03964/) (2020)
- [Motion Planning Networks: Bridging the Gap Between Learning-based and Classical Motion Planners](https://mlsanity.com/paper/1907.06013/) (2019)
- [Continuous-Time Gaussian Process Motion Planning via Probabilistic Inference](https://mlsanity.com/paper/1707.07383/) (2017)
- [Batch Informed Trees (BIT*): Sampling-based Optimal Planning via the Heuristically Guided Search of Implicit Random Geometric Graphs](https://mlsanity.com/paper/1405.5848/) (2014)
- [Learning to Play Table Tennis From Scratch using Muscular Robots](https://mlsanity.com/paper/2006.05935/) (2020)
- [Perspectives on Sim2Real Transfer for Robotics: A Summary of the R:SS 2020 Workshop](https://mlsanity.com/paper/2012.03806/) (2020)
- [Batch Informed Trees (BIT*): Informed Asymptotically Optimal Anytime Search](https://mlsanity.com/paper/1707.01888/) (2017)
- [Asymptotically Optimal Sampling-based Kinodynamic Planning](https://mlsanity.com/paper/1407.2896/) (2014)
- [Learning Implicit Sampling Distributions for Motion Planning](https://mlsanity.com/paper/1806.01968/) (2018)
- [High Acceleration Reinforcement Learning for Real-World Juggling with Binary Rewards](https://mlsanity.com/paper/2010.13483/) (2020)
- [Constrained Motion Planning Networks X](https://mlsanity.com/paper/2010.08707/) (2020)
- [MPC-MPNet: Model-Predictive Motion Planning Networks for Fast, Near-Optimal Planning under Kinodynamic Constraints](https://mlsanity.com/paper/2101.06798/) (2021)
- [Efficient and Reactive Planning for High Speed Robot Air Hockey](https://mlsanity.com/paper/2107.06140/) (2021)
- [Learn and Link: Learning Critical Regions for Efficient Planning](https://mlsanity.com/paper/1903.03258/) (2019)
- [Trajectory Optimization on Manifolds: A Theoretically-Guaranteed Embedded Sequential Convex Programming Approach](https://mlsanity.com/paper/1905.07654/) (2019)
- [Learning from Experience for Rapid Generation of Local Car Maneuvers](https://mlsanity.com/paper/2012.03707/) (2020)
- [An analytical diabolo model for robotic learning and control](https://mlsanity.com/paper/2011.09068/) (2020)
- [State Supervised Steering Function for Sampling-based Kinodynamic Planning](https://mlsanity.com/paper/2206.07227/) (2022)
- [An Asymptotically-Optimal Sampling-Based Algorithm for Bi-directional Motion Planning](https://mlsanity.com/paper/1507.07602/) (2015)
- [RRT-CoLearn: towards kinodynamic planning without numerical trajectory optimization](https://mlsanity.com/paper/1710.10122/) (2017)
- [Batch and Incremental Kinodynamic Motion Planning using Dynamic Factor Graphs](https://mlsanity.com/paper/2005.12514/) (2020)
- [Speeding up deep neural network-based planning of local car maneuvers via efficient B-spline path construction](https://mlsanity.com/paper/2203.06963/) (2022)
- [Accelerating Kinodynamic RRT* Through Dimensionality Reduction](https://mlsanity.com/paper/2107.01259/) (2021)

## Built on by (most cited first, 9 of 9)

- [Motion Planning Diffusion: Learning and Adapting Robot Motion Planning with Diffusion Models](https://mlsanity.com/paper/2412.19948/) (2024)
- [Safe Reinforcement Learning on the Constraint Manifold: Theory and Applications](https://mlsanity.com/paper/2404.09080/) (2024)
- [Physics-informed Neural Motion Planning on Constraint Manifolds](https://mlsanity.com/paper/2403.05765/) (2024)
- [Learning Diverse Robot Striking Motions with Diffusion Models and Kinematically Constrained Gradient Guidance](https://mlsanity.com/paper/2409.15528/) (2024)
- [RAIL: Reachability-Aided Imitation Learning for Safe Policy Execution](https://mlsanity.com/paper/2409.19190/) (2024)
- [MaskPlanner: Learning-Based Object-Centric Motion Generation from 3D Point Clouds](https://mlsanity.com/paper/2502.18745/) (2025)
- [A Retrospective on the Robot Air Hockey Challenge: Benchmarking Robust, Reliable, and Safe Learning Techniques for Real-world Robotics](https://mlsanity.com/paper/2411.05718/) (2024)
- [ECO: Energy-Constrained Optimization with Reinforcement Learning for Humanoid Walking](https://mlsanity.com/paper/2602.06445/) (2026)
- [Toward Generalist Neural Motion Planners for Robotic Manipulators: Challenges and Opportunities](https://mlsanity.com/paper/2603.24318/) (2026)

## Abstract (arXiv)

Motion planning is a mature area of research in robotics with many well-established methods based on optimization or sampling the state space, suitable for solving kinematic motion planning. However, when dynamic motions under constraints are needed and computation time is limited, fast kinodynamic planning on the constraint manifold is indispensable. In recent years, learning-based solutions have become alternatives to classical approaches, but they still lack comprehensive handling of complex constraints, such as planning on a lower-dimensional manifold of the task space while considering the robot's dynamics. This paper introduces a novel learning-to-plan framework that exploits the concept of constraint manifold, including dynamics, and neural planning methods. Our approach generates plans satisfying an arbitrary set of constraints and computes them in a short constant time, namely the inference time of a neural network. This allows the robot to plan and replan reactively, making our approach suitable for dynamic environments. We validate our approach on two simulated tasks and in a demanding real-world scenario, where we use a Kuka LBR Iiwa 14 robotic arm to perform the hitting movement in robotic Air Hockey.