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1. Path constrained unbalanced optimal transport

   https://doi.org/10.1088/1361-6544/ade21d  

   Bauer, Martin; Charon, Nicolas; Needham, Tom; Nishino, Mao (June 2025, Nonlinearity)

   Abstract Dynamical formulations of optimal transport (OT) frame the task of comparing distributions as a variational problem which searches for a path between distributions minimizing a kinetic energy functional. In applications, it is frequently natural to require paths of distributions to satisfy additional conditions. Inspired by this, we introduce a model for dynamical OT which incorporates constraints on the space of admissible paths into the framework of unbalanced OT, where the source and target measures are allowed to have a different total mass. Our main results establish, for several general families of constraints, the existence of solutions to the variational problem which defines this path constrained unbalanced OT framework. These results are primarily concerned with distributions defined on an Euclidean space, but we extend them to distributions defined over parallelizable Riemannian manifolds as well. We also consider metric properties of our framework, showing that, for certain types of constraints, our model defines a metric on the relevant space of distributions. This metric is shown to arise as a geodesic distance of a Riemannian metric, obtained through an analogue of Otto’s submersion in the classical OT setting. 

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2. Optimal Path-Planning With Random Breakdowns

   https://doi.org/10.1109/LCSYS.2021.3130193  

   Gee, Marissa; Vladimirsky, Alexander (January 2022, IEEE Control Systems Letters)
3. Optimal sequential stochastic shortest path interdiction

   https://doi.org/10.1016/j.ejor.2025.04.009  

   Borrero, Juan S; Sauré, Denis; Trigo, Natalia (November 2025, European Journal of Operational Research)
4. Optimal GPS Integrity-Constrained Path Planning for Ground Vehicles

   https://doi.org/10.1109/PLANS46316.2020.9109898  

   Maaref, Mahdi; Kassas, Zaher M. (April 2020, IEEE/ION Position, Location and Navigation Symposium)

   null (Ed.)
5. Near-optimal Smooth Path Planning for Multisection Continuum Arms

   https://doi.org/10.1109/ROBOSOFT.2019.8722778  

   Deng, Jiahao; Meng, Brandon H.; Kanj, Iyad; Godage, Isuru S. (April 2019, 2019 2nd IEEE International Conference on Soft Robotics (RoboSoft))

   We study the path planning problem for continuum-arm robots, in which we are given a starting and an end point, and we need to compute a path for the tip of the continuum arm between the two points. We consider both cases where obstacles are present and where they are not. We demonstrate how to leverage the continuum arm features to introduce a new model that enables a path planning approach based on the configurations graph, for a continuum arm consisting of three sections, each consisting of three muscle actuators. The algorithm we apply to the configurations graph allows us to exploit parallelism in the computation to obtain efficient implementation. We conducted extensive tests, and the obtained results show the completeness of the proposed algorithm under the considered discretizations, in both cases where obstacles are present and where they are not. We compared our approach to the standard inverse kinematics approach. While the inverse kinematics approach is much faster when successful, our algorithm always succeeds in finding a path or reporting that no path exists, compared to a roughly 70% success rate of the inverse kinematics approach (when a path exists). 

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