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Kino-PAX: Highly Parallel Kinodynamic Sampling-based Planner

Nicolas Perrault, Qi Heng Ho, Morteza Lahijanian

TL;DR

Kino-PAX addresses the challenge of real-time kinodynamic motion planning in high-dimensional spaces by introducing a highly parallel SBMP designed for GPU architectures. It decomposes the iterative tree-growth process into three parallel subroutines and organizes sampling with a region-based decomposition, using three disjoint sets ($V_U$, $V_O$, $V_E$) and a region partition $\mathcal{R}$ to guide exploration. The paper proves probabilistic completeness, analyzes scalability with hardware improvements, and demonstrates millisecond-scale planning times (up to $<8$ ms for 6D and $<25$ ms for 12D) on GPUs, including embedded devices, with substantial speedups over CPU baselines. Key contributions include the Kino-PAX algorithm, hyperparameter and decomposition guidance, probabilistic-completeness analysis, and extensive benchmarks across multiple dynamical systems. These results indicate a significant practical impact for real-time, high-dimensional kinodynamic planning on modern parallel hardware.

Abstract

Sampling-based motion planners (SBMPs) are effective for planning with complex kinodynamic constraints in high-dimensional spaces, but they still struggle to achieve real-time performance, which is mainly due to their serial computation design. We present Kinodynamic Parallel Accelerated eXpansion (Kino-PAX), a novel highly parallel kinodynamic SBMP designed for parallel devices such as GPUs. Kino-PAX grows a tree of trajectory segments directly in parallel. Our key insight is how to decompose the iterative tree growth process into three massively parallel subroutines. Kino-PAX is designed to align with the parallel device execution hierarchies, through ensuring that threads are largely independent, share equal workloads, and take advantage of low-latency resources while minimizing high-latency data transfers and process synchronization. This design results in a very efficient GPU implementation. We prove that Kino-PAX is probabilistically complete and analyze its scalability with compute hardware improvements. Empirical evaluations demonstrate solutions in the order of 10 ms on a desktop GPU and in the order of 100 ms on an embedded GPU, representing up to 1000 times improvement compared to coarse-grained CPU parallelization of state-of-the-art sequential algorithms over a range of complex environments and systems.

Kino-PAX: Highly Parallel Kinodynamic Sampling-based Planner

TL;DR

Kino-PAX addresses the challenge of real-time kinodynamic motion planning in high-dimensional spaces by introducing a highly parallel SBMP designed for GPU architectures. It decomposes the iterative tree-growth process into three parallel subroutines and organizes sampling with a region-based decomposition, using three disjoint sets (, , ) and a region partition to guide exploration. The paper proves probabilistic completeness, analyzes scalability with hardware improvements, and demonstrates millisecond-scale planning times (up to ms for 6D and ms for 12D) on GPUs, including embedded devices, with substantial speedups over CPU baselines. Key contributions include the Kino-PAX algorithm, hyperparameter and decomposition guidance, probabilistic-completeness analysis, and extensive benchmarks across multiple dynamical systems. These results indicate a significant practical impact for real-time, high-dimensional kinodynamic planning on modern parallel hardware.

Abstract

Sampling-based motion planners (SBMPs) are effective for planning with complex kinodynamic constraints in high-dimensional spaces, but they still struggle to achieve real-time performance, which is mainly due to their serial computation design. We present Kinodynamic Parallel Accelerated eXpansion (Kino-PAX), a novel highly parallel kinodynamic SBMP designed for parallel devices such as GPUs. Kino-PAX grows a tree of trajectory segments directly in parallel. Our key insight is how to decompose the iterative tree growth process into three massively parallel subroutines. Kino-PAX is designed to align with the parallel device execution hierarchies, through ensuring that threads are largely independent, share equal workloads, and take advantage of low-latency resources while minimizing high-latency data transfers and process synchronization. This design results in a very efficient GPU implementation. We prove that Kino-PAX is probabilistically complete and analyze its scalability with compute hardware improvements. Empirical evaluations demonstrate solutions in the order of 10 ms on a desktop GPU and in the order of 100 ms on an embedded GPU, representing up to 1000 times improvement compared to coarse-grained CPU parallelization of state-of-the-art sequential algorithms over a range of complex environments and systems.
Paper Structure (19 sections, 2 theorems, 9 equations, 3 figures, 1 table, 4 algorithms)

This paper contains 19 sections, 2 theorems, 9 equations, 3 figures, 1 table, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Formulation
  4. Kino-PAX
  5. Core Algorithm
  6. Initialization
  7. Node Extension
  8. Node Selection
  9. Tuning and Performance Discussion
  10. Tuning Parameter
  11. Decomposition Tuning
  12. Efficient Application to Highly Parallel Devices
  13. Analysis
  14. Probabilistic Completeness
  15. Scalability
  16. ...and 4 more sections

Key Result

Lemma 1

Let $x \in \mathcal{T}$ be a node in the tree. The probability that $x$ is selected for extension is lower bounded by $\epsilon \in (0,1)$.

Figures (3)

  • Figure 1: Illustration of the Kino-PAX expansion process: (a) The current sets $V_E$ and $V_{O}$, where the numbers in each grid cell represent the value of $P_{accept}(\mathcal{R}_i)$. (b) Expansion of $V_E$ with branching factor $\lambda = 2$. (c) Acceptance of promising samples and update of $P_{\text{accept}}(\mathcal{R}_i)$. (d) Updated $V_E$, ready for the next iteration. (e) Expansion of $V_E$, producing a valid trajectory to $X_{\text{goal}}$.
  • Figure 2: Environments used throughout the experiments with the solution trajectory produced by Kino-PAX. Initial position and goal region are shown by blue and green spheres, respectively. Environments (a) and (c) are taken from ichter2017group.
  • Figure 3: Results of varying the expected tree size $t_e$ for the 12D nonlinear quadcopter system in environment \ref{['fig:trees']}. (a) Number of Failures vs. $t_e$. (b) Mean runtime and variance of Kino-PAX vs. $t_e$.

Theorems & Definitions (6)

  • Remark 1
  • Definition 1: Probabilistic Completeness
  • Lemma 1
  • proof
  • Theorem 1
  • proof : Proof Sketch