Neural Trajectory Model: Implicit Neural Trajectory Representation for Trajectories Generation

TL;DR

This work tackles the challenge of trajectory planning in robotics, including multi-agent coordination, by reframing planning as queries over an implicit neural trajectory representation. The authors introduce the Neural Trajectory Model (NTM), which uses a differentiable $SDF$-based environment and a transformer-based architecture to generate multiple time-parameterized trajectories from start-goal pairs, with training guided by ground-truth trajectories and multiple safety/performance losses. Key contributions include (1) a novel implicit neural trajectory representation; (2) fast, near-optimal planning with sub-millisecond inference on GPUs; (3) support for trajectory refinement and multi-agent de-confliction via a trajectory optimizer and coordination workflows; and (4) demonstration of scalability to larger numbers of agents and potential for large-scale coordination. The results indicate significant speedups and safety improvements over traditional search-based methods, with practical implications for real-time planning and multi-agent systems in complex environments. Future work points to dynamic environments, real-world motion dynamics, and broader large-scale coordination scenarios.

Abstract

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)

Figures (5)

• Figure 1: Neural Trajectory Model
• Figure 2: Neural Trajectory Model Training
• Figure 3: Eight-agent trajectory planning in Ice Forest Env
• Figure 4: Eight-agent trajectory planning in Building Forest Env
• Figure 5: Large-scale trajectory planning in Building Forest Env