NTFIELDS: NEURAL TIME FIELDS FOR PHYSICS-INFORMED ROBOT MOTION PLANNING

Abstract

Neural Motion Planners (NMPs) have emerged as a promising tool for solving robot navigation tasks in complex environments. However, these methods often require expert data for learning, which limits their application to scenarios where data generation is time-consuming. Recent developments have also led to physicsinformed deep neural models capable of representing complex dynamical Partial Differential Equations (PDEs). Inspired by these developments, we propose Neural Time Fields (NTFields) for robot motion planning in cluttered scenarios. Our framework represents a wave propagation model generating continuous arrival time to find path solutions informed by a nonlinear first-order PDE called the Eikonal equation. We evaluate our method in various cluttered 3D environments, including the Gibson dataset, and demonstrate its ability to solve motion planning problems for 4-DOF and 6-DOF robot manipulators where the traditional grid-based Eikonal planners often face the curse of dimensionality. Furthermore, the results show that our method exhibits high success rates and significantly lower computational times than the state-of-the-art methods, including NMPs that require training data from classical planners. Our code is released:

1. INTRODUCTION

Motion Planning (MP) is one of the core components of an autonomous robot system that aims to interact physically with its surrounding environments. MP algorithms find path solutions from the robot's start state to the goal state while respecting all constraints, such as collision avoidance. The quest for fast, scalable MP methods has led from traditional approaches such as RRT* (LaValle et al., 2001 ), Informed-RRT* (Gammell et al., 2014 ), and FMT* (Janson et al., 2015) to NMPs that exhibit promising performance in high-dimensional spaces. However, a significant bottleneck in state-of-the-art NMPs is their need for expert trajectories from traditional MP methods, limiting their application to high-dimensional scenarios where large-scale data generation is time-consuming. Recent developments have provided us with ways to have physics-informed deep learning models (Raissi et al., 2019; Li et al., 2020; Smith et al., 2020) that can directly solve complex PDEs such as Navier-Stokes, Burgers, and Schrodinger equations. Inspired by these neural PDE solvers and to overcome the expert data needs of NMPs, this paper introduces NTFields for robot motion planning in cluttered environments. Our NTFields are generated by a physics-informed neural model driven by a first-order, non-linear PDE called the Eikonal equation, whose solution represents the shortest arrival time from a source to a destination location under a pre-defined speed model, and leads to the continuous shortest-path between two locations (Sethian, 1996; Clawson et al., 2014) . Our model generates a continuous time field between the robot's given start and goal configurations while respecting collision-avoidance constraints, leading to a path solution in sub-seconds. Our method's salient features and contributions are summarized as follows: 1) A novel physicsinformed PDE solving the Eikonal equation formulation for robot motion planning under collisionavoidance constraints in high-dimensional spaces. 2) A novel neural architecture design that encapsulates various properties of our PDE, resulting in a scalable, fast NMP method. 3) A novel bidirectional algorithm that quickly finds path solutions by iteratively following the gradient of neural time fields, marching towards each other from the start and goal configurations. 4) Unlike prior, 1

availability

https://github.com/ruiqini

