# State Supervised Steering Function for Sampling-based Kinodynamic Planning

arXiv: https://arxiv.org/abs/2206.07227 · HTML: https://mlsanity.com/paper/2206.07227/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2022.

## Built on by (most cited first, 3 of 3)

- [High-Speed Accurate Robot Control using Learned Forward Kinodynamics and Non-linear Least Squares Optimization](https://mlsanity.com/paper/2206.08487/) (2022)
- [Fast Kinodynamic Planning on the Constraint Manifold with Deep Neural Networks](https://mlsanity.com/paper/2301.04330/) (2023)
- [Differentiable Motion Manifold Primitives for Reactive Motion Generation under Kinodynamic Constraints](https://mlsanity.com/paper/2410.12193/) (2024)

## Abstract (arXiv)

Sampling-based motion planners such as RRT* and BIT*, when applied to kinodynamic motion planning, rely on steering functions to generate time-optimal solutions connecting sampled states. Implementing exact steering functions requires either analytical solutions to the time-optimal control problem, or nonlinear programming (NLP) solvers to solve the boundary value problem given the system's kinodynamic equations. Unfortunately, analytical solutions are unavailable for many real-world domains, and NLP solvers are prohibitively computationally expensive, hence fast and optimal kinodynamic motion planning remains an open problem. We provide a solution to this problem by introducing State Supervised Steering Function (S3F), a novel approach to learn time-optimal steering functions. S3F is able to produce near-optimal solutions to the steering function orders of magnitude faster than its NLP counterpart. Experiments conducted on three challenging robot domains show that RRT* using S3F significantly outperforms state-of-the-art planning approaches on both solution cost and runtime. We further provide a proof of probabilistic completeness of RRT* modified to use S3F.