Task planning under constraints

The autonomy of embedded systems, in particular robots, comes from their capability to plan their next actions. Although, it becomes critical to ensure the safety of the behaviour as the systems are exposed to human interaction more and more (eg. Autonomous cars, toy UAVs, cobots in manufacturing and so on).
The goal of the thesis is to study task planning under constraints: select the best sequence of actions while optimising several criteria like efficiency, safety and other domain specifics. The thesis involves two main axes, the first is to study how to model the systems constraints in a manner that can be understood both by the human experts and the planning algorithm (eg. Using Operational Design Domain or Dynamic Assurance Case to evaluate system’s safety). Ontologies and knowledge graphs would probably be adequate to model the constraints. The model would benefit from their expressivity and the already-existing tooling. The second main axis is the improvement of the planning algorithm to leverage those models. Those models shall have a generic structure since it is necessary to represent many natures of constraints: safety, efficiency/cost, social “confort”, shared resources on the critical path, type and quantity of interactions between the agents, geometric feasibility, ...
As the thesis is aimed at robotic autonomous systems, it will be important to demonstrate and evaluate the system on real-world use cases.

Learning to focus: Physics-Informed Deep Learning for Super-Resolved Ultrasonic Phased-Array Imaging

This PhD aims to develop a new class of ultrasonic focusing methods for phased-array imaging by combining deep learning, physics-based modeling, and optimal transport theory. The first research axis introduces a reweighted, probabilistic extension of the Total Focusing Method (TFM), where per-isochrone focusing weights are iteratively estimated by a shared convolutional network and normalized using a neural time-of-flight field. This iterative, differentiable framework enables more adaptive, interpretable, and robust imaging in heterogeneous or uncertain media.

The second axis proposes a full reformulation of TFM as a Wasserstein barycenter problem, in which each partial image is modeled as an empirical distribution in a joint space of spatial coordinates and ultrasonic amplitude. A physically meaningful transport cost, based on geodesic distances that minimize time-of-flight variations with respect to selected emitters, encodes the acoustic geometry directly in the metric. The resulting grid-free barycenters yield sharp, physically consistent reflector localization and open new opportunities at the interface between optimal transport and ultrasonic phased-array imaging. Overall, the thesis aims to merge physics, machine learning, and geometric optimal transport to formulate next-generation reconstruction methods for ultrasonic imaging.