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An Online Spatial-Temporal Graph Trajectory Planner for Autonomous Vehicles

Jilan Samiuddin, Benoit Boulet, Di Wu

TL;DR

This work tackles online trajectory planning for autonomous vehicles by modeling the planner as a sequence of spatial-temporal graphs that include the ego, surrounding actors, and virtual road-aligned nodes. A Graph Attention Network encoder–decoder processes these heterogeneous graphs to output the ego’s next pose, with softmax-based weighting over virtual nodes to capture preferred future positions, all while enforcing constraints via a simple behavioral layer and obstacle/velocity potential functions. The approach supports driving behaviors such as lane-keeping, lane-changing, car-following, and speed-keeping, and demonstrates robust feasibility across challenging tasks (driving through traffic, merging, exiting) with competitive safety and efficiency relative to two baselines. The method offers interpretability through attention maps and has potential for extension to more diverse tasks and cooperative multi-agent scenarios.

Abstract

The autonomous driving industry is expected to grow by over 20 times in the coming decade and, thus, motivate researchers to delve into it. The primary focus of their research is to ensure safety, comfort, and efficiency. An autonomous vehicle has several modules responsible for one or more of the aforementioned items. Among these modules, the trajectory planner plays a pivotal role in the safety of the vehicle and the comfort of its passengers. The module is also responsible for respecting kinematic constraints and any applicable road constraints. In this paper, a novel online spatial-temporal graph trajectory planner is introduced to generate safe and comfortable trajectories. First, a spatial-temporal graph is constructed using the autonomous vehicle, its surrounding vehicles, and virtual nodes along the road with respect to the vehicle itself. Next, the graph is forwarded into a sequential network to obtain the desired states. To support the planner, a simple behavioral layer is also presented that determines kinematic constraints for the planner. Furthermore, a novel potential function is also proposed to train the network. Finally, the proposed planner is tested on three different complex driving tasks, and the performance is compared with two frequently used methods. The results show that the proposed planner generates safe and feasible trajectories while achieving similar or longer distances in the forward direction and comparable comfort ride.

An Online Spatial-Temporal Graph Trajectory Planner for Autonomous Vehicles

TL;DR

This work tackles online trajectory planning for autonomous vehicles by modeling the planner as a sequence of spatial-temporal graphs that include the ego, surrounding actors, and virtual road-aligned nodes. A Graph Attention Network encoder–decoder processes these heterogeneous graphs to output the ego’s next pose, with softmax-based weighting over virtual nodes to capture preferred future positions, all while enforcing constraints via a simple behavioral layer and obstacle/velocity potential functions. The approach supports driving behaviors such as lane-keeping, lane-changing, car-following, and speed-keeping, and demonstrates robust feasibility across challenging tasks (driving through traffic, merging, exiting) with competitive safety and efficiency relative to two baselines. The method offers interpretability through attention maps and has potential for extension to more diverse tasks and cooperative multi-agent scenarios.

Abstract

The autonomous driving industry is expected to grow by over 20 times in the coming decade and, thus, motivate researchers to delve into it. The primary focus of their research is to ensure safety, comfort, and efficiency. An autonomous vehicle has several modules responsible for one or more of the aforementioned items. Among these modules, the trajectory planner plays a pivotal role in the safety of the vehicle and the comfort of its passengers. The module is also responsible for respecting kinematic constraints and any applicable road constraints. In this paper, a novel online spatial-temporal graph trajectory planner is introduced to generate safe and comfortable trajectories. First, a spatial-temporal graph is constructed using the autonomous vehicle, its surrounding vehicles, and virtual nodes along the road with respect to the vehicle itself. Next, the graph is forwarded into a sequential network to obtain the desired states. To support the planner, a simple behavioral layer is also presented that determines kinematic constraints for the planner. Furthermore, a novel potential function is also proposed to train the network. Finally, the proposed planner is tested on three different complex driving tasks, and the performance is compared with two frequently used methods. The results show that the proposed planner generates safe and feasible trajectories while achieving similar or longer distances in the forward direction and comparable comfort ride.
Paper Structure (19 sections, 23 equations, 9 figures, 2 tables, 1 algorithm)

This paper contains 19 sections, 23 equations, 9 figures, 2 tables, 1 algorithm.

Figures (9)

  • Figure 1: (a) A snapshot of the road presented in the Cartesian coordinate frame showing the Frenet framework formulation with respect to the reference curve (in blue), and, (b) Frenet coordinate frame of the snapshot with the ego (blue circle). The new Frenet coordinate frame (black solid dashes) is with respect to the ego position
  • Figure 2: Transformations between the Cartesian and the Frenet frames to obtain trajectory (in dashed line)
  • Figure 3: Flow diagram for the behavioral layer (see Appendix for Routine 1)
  • Figure 4: (a) The ego (in blue) is surrounded by actors (in red).(b) The behavioral layer generates kinematic constraints for the current scenario. (c) The lateral virtual nodes (in light peach) is spread out laterally along the road, respecting road boundaries. (d) The longitudinal virtual nodes (in light green) are spread out longitudinally ahead of the ego along the road. (e) Formation of graph $G_{k}$ for the given snapshot with $N_{V}=5$
  • Figure 5: Network architecture to learn online the future trajectory of the ego
  • ...and 4 more figures