# Real-Time Spatial Trajectory Planning for Urban Environments Using Dynamic Optimization

arXiv: https://arxiv.org/abs/2305.02621 · HTML: https://mlsanity.com/paper/2305.02621/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 May 2023.

## Built on by (most cited first, 1 of 1)

- [Reachable Sets-based Trajectory Planning Combining Reinforcement Learning and iLQR](https://mlsanity.com/paper/2503.17398/) (2025)

## Abstract (arXiv)

Planning trajectories for automated vehicles in urban environments requires methods with high generality, long planning horizons, and fast update rates. Using a path-velocity decomposition, we contribute a novel planning framework, which generates foresighted trajectories and can handle a wide variety of state and control constraints effectively. In contrast to related work, the proposed optimal control problems are formulated over space rather than time. This spatial formulation decouples environmental constraints from the optimization variables, which allows the application of simple, yet efficient shooting methods. To this end, we present a tailored solution strategy based on ILQR, in the Augmented Lagrangian framework, to rapidly minimize the trajectory objective costs, even under infeasible initial solutions. Evaluations in simulation and on a full-sized automated vehicle in real-world urban traffic show the real-time capability and versatility of the proposed approach.