Introduction
Safe autonomous navigation requires reasoning not only about how other agents may move, but also about which maneuvers are compatible with the surrounding environment. Hamilton–Jacobi (HJ) reachability can provide a framework for collision avoidance under worst-case interactions. Environmental constraints can already be included in HJ formulations, but combining geometry and multi-agent interaction can significantly increase problem dimensionality. Standard pairwise formulations may also consider maneuvers that are feasible in open space but incompatible with the actual environment.
This thesis investigates how environmental geometry can be incorporated into HJ differential games and whether environmental and interaction safety can be handled separately and then composed, avoiding a fully high-dimensional formulation.
Goals
- HJ foundations: study optimal control, differential games, reachability analysis and pairwise collision avoidance.
- Environment-aware formulation: include geometric information through constraints, dynamics, or admissible control strategies, characterizing environment-compatible actions for each agent and incorporate them into the pairwise HJ game.
- Validation: compare open-space, directly constrained and compositional formulations in corridors, curved passages and intersections, balancing safety and conservatism.
- Learning extension: explore how environmental geometry can be incorporated into differential games and whether environmental and interaction safety can be handled separately and then composed afterwards, while retaining HJ reachability as the safety framework.
Requirements
- Knowledge of Python;
- Basic knowledge of control theory and dynamical systems;
- Interest in robotics, autonomous systems and software development (interest in machine learning/deep learning is a plus).
Contact
Marco Doria Fragomeni: marco.doria@polimi.it
Stefano Arrigoni: stefano.arrigoni@polimi.it