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的应用。由于计算复杂性高、真实环境存在不确定性、非线性和实时性要求等挑战，轨迹规划是一个难题。多智能体轨迹规划因智能体间的相互交互而增添了额外难度。现有解决方案要么是基于搜索或基于优化的方法，它们对环境做出了简化假设，规划速度有限且难以扩展到大规模智能体。在本工作中，我们首次尝试将单智能体和多智能体轨迹规划问题重构成对轨迹隐式神经表征的查询问题。我们将这种隐式表征形式化为神经轨迹模型（NTM），通过查询该模型可在复杂环境中生成近乎最优的轨迹。我们在仿真环境中进行了实验，表明NTM能够解决单智能体和多智能体轨迹规划问题。实验结果显示，NTM可实现（1）利用GPU达到亚毫秒级的规划时间，（2）几乎避免所有环境碰撞，（3）几乎避免所有智能体间碰撞，以及（4）生成近乎最短路径。我们还证明了相同的NTM框架也可用于轨迹修正和多轨迹冲突消解，能高效地将低质量、冲突的多智能体轨迹优化为近乎最优的解决方案。（开源代码详见https://github.com/laser2099/neural-trajectory-model）