Ultrafast Sampling-based Kinodynamic Planning via Differential Flatness

2026-03-16

AI Summary

This work addresses the computational inefficiency of motion planning for high-degree-of-freedom robots operating under dynamic constraints in complex environments. The authors propose a high-speed trajectory planning method grounded in differential flatness, which maps the dynamics into a flat output space to enable analytical, time-parameterized trajectory generation. By integrating SIMD-based parallel acceleration with a sampling-based planning framework, the approach achieves, for the first time, a general-purpose, highly accurate, and ultra-fast trajectory planner for differentially flat systems—including robotic arms, ground vehicles, and aerial robots. Experiments demonstrate that the method generates dynamically feasible trajectories in microseconds to milliseconds in both simulated and real-world cluttered dynamic environments, substantially improving planning efficiency while rigorously preserving dynamic feasibility and tracking accuracy.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

Motion planning under dynamics constraints, i.e., kinodynamic planning, enables safe robot operation by generating dynamically feasible trajectories that the robot can accurately track. For high-\dof robots such as manipulators, sampling-based motion planners are commonly used, especially for complex tasks in cluttered environments. However, enforcing constraints on robot dynamics in such planners requires solving either challenging two-point boundary value problems (BVPs) or propagating robot dynamics over time, both of which are computational bottlenecks that drastically increase planning times. Meanwhile, recent efforts have shown that sampling-based motion planners can generate plans in microseconds using parallelization, but are limited to geometric paths. This paper develops AkinoPDF, a fast parallelized sampling-based kinodynamic motion planning technique for a broad class of differentially flat robot systems, including manipulators, ground and aerial vehicles, and more. Differential flatness allows us to transform the motion planning problem from the original state space to a flat output space, where an analytical time-parameterized solution of the BVP and dynamics integration can be obtained. A trajectory in the flat output space is then converted back to a closed-form dynamically feasible trajectory in the original state space, enabling fast validation via ``single instruction, multiple data" parallelism. Our method is fast, exact, and compatible with any sampling-based motion planner. We extensively verify the effectiveness of our approach in both simulated benchmarks and real experiments with cluttered and dynamic environments, requiring mere microseconds to milliseconds of planning time.

Problem

• kinodynamic planning
• differential flatness
• motion planning
• dynamics constraints
• sampling-based planning

Innovation

• differential flatness
• kinodynamic planning
• sampling-based planning
• parallel motion planning
• closed-form trajectory