Abstract

This article introduces physics-informed neural networks (PINNs) to the field of motion planning by utilizing a PINN framework as the steering function in the kinodynamic rapidly-exploring random tree (RRT*) algorithm. The goal of this paper is to show that PINN-based methods can be used successfully for aerospace motion planning applications. We test the RRT* algorithm coupled with PINN steering, what we call PINN-RRT*, by solving spacecraft energy-optimal motion planning problems governed by the Hill–Clohessy–Wiltshire (HCW) equations of motion and nonlinear equations of relative motion (NERM), where a deputy satellite must rendezvous with a chief satellite while avoiding spherical keep-out-zones and complying with an approach corridor. The particular PINN framework we employ approximates the solution of nonlinear two-point boundary value problems (TPBVPs), which must be solved to form connections between waypoints in the RRT* tree, via the Theory of Functional Connections (TFC). TFC enables the PINN to analytically satisfy the boundary conditions (BCs) of the TPBVP. Thus, the admissible solution search space of each nonlinear TPBVP is reduced to just the trajectories that already satisfy the BCs. Using our proposed approach, each energy-optimal TPBVP solution during the run-time of the PINN-RRT* algorithm was computed in centiseconds and with an average error on the order of machine epsilon for both the HCW and NERM dynamics.

中文翻译：

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使用物理信息神经网络快速探索随机树以解决约束能量最优交会问题

摘要

本文利用 PINN 框架作为运动动力学快速探索随机树 (RRT*) 算法中的转向函数，将物理信息神经网络 (PINN) 引入运动规划领域。本文的目的是证明基于 PINN 的方法可以成功用于航空航天运动规划应用。我们通过解决由 Hill–Clohessy–Wiltshire (HCW) 运动方程和非线性相对运动方程 (NERM) 控制的航天器能量最优运动规划问题，测试与 PINN 转向相结合的 RRT* 算法，我们称之为 PINN-RRT* ），副卫星必须与主卫星会合，同时避开球形禁区并遵守进场走廊。我们采用的特定 PINN 框架近似解决非线性两点边值问题 (TPBVP)，必须通过功能连接理论 (TFC) 解决该问题才能在 RRT* 树中的航路点之间形成连接。 TFC 使 PINN 能够在分析上满足 TPBVP 的边界条件 (BC)。因此，每个非线性 TPBVP 的允许解搜索空间被减少到已经满足 BC 的轨迹。使用我们提出的方法，PINN-RRT* 算法运行时的每个能量最优 TPBVP 解决方案均以厘秒为单位计算，对于 HCW 和 NERM 动力学，平均误差约为机器 epsilon 量级。