Trajectory planning is a fundamental problem in robotics. It facilitates a wide range of applications in navigation and motion planning, control, and multi-agent coordination. Trajectory planning is a difficult problem due to its computational complexity and real-world environment complexity with uncertainty, non-linearity, and real-time requirements. The multi-agent trajectory planning problem adds another dimension of difficulty due to inter-agent interaction. Existing solutions are either search-based or optimization-based approaches with simplified assumptions of environment, limited planning speed, and limited scalability in the number of agents. In this work, we make the first attempt to reformulate single agent and multi-agent trajectory planning problem as query problems over an implicit neural representation of trajectories. We formulate such implicit representation as Neural Trajectory Models (NTM) which can be queried to generate nearly optimal trajectory in complex environments. We conduct experiments in simulation environments and demonstrate that NTM can solve single-agent and multi-agent trajectory planning problems. In the experiments, NTMs achieve (1) sub-millisecond panning time using GPUs, (2) almost avoiding all environment collision, (3) almost avoiding all inter-agent collision, and (4) generating almost shortest paths. We also demonstrate that the same NTM framework can also be used for trajectories correction and multi-trajectory conflict resolution refining low quality and conflicting multi-agent trajectories into nearly optimal solutions efficiently. (Open source code will be available at https://github.com/laser2099/neural-trajectory-model)

翻译：轨迹规划是机器人学中的基础问题，它支撑着导航与运动规划、控制以及多智能体协调等广泛应用场景。该问题因计算复杂性、真实环境的非线性与不确定性以及实时性要求而极具挑战性，而多智能体轨迹规划更因智能体间的相互作用增加了额外的维度难度。现有解决方案要么基于搜索方法，要么基于优化方法，但都存在环境假设简化、规划速度有限以及智能体数量可扩展性不足等问题。本研究首次尝试将单智能体与多智能体轨迹规划问题重构为对轨迹隐式神经表征的查询问题。我们将这种隐式表征构建为神经轨迹模型（NTM），通过查询该模型可在复杂环境中生成近乎最优的轨迹。仿真实验表明，NTM能够有效解决单智能体与多智能体轨迹规划问题。实验结果显示，NTM实现了：（1）在GPU上的亚毫秒级规划速度；（2）几乎完全避免所有环境碰撞；（3）几乎完全避免所有智能体间碰撞；（4）生成近乎最短的路径。我们还证实，同一NTM框架还可用于轨迹校正与多轨迹冲突消解，能够将低质量或存在冲突的多智能体轨迹高效优化为近似最优解。（开源代码将发布于 https://github.com/laser2099/neural-trajectory-model）