  We rigorously show the mean-field limit for a large class of swarming
individual based models with local sharp sensitivity regions. For instance,
these models include nonlocal repulsive-attractive forces locally averaged over
sharp vision cones and Cucker-Smale interactions with discontinuous
communication weights. We construct global-in-time defined notion of solutions
through a differential inclusion system corresponding to the particle
descriptions. We estimate the error between the solutions to the differential
inclusion system and weak solutions to the expected limiting kinetic equation
by employing tools from optimal transport theory. Quantitative bounds on the
expansion of the 1-Wasserstein distance along flows based on a weak-strong
stability estimate are obtained. We also provide different examples of
realistic sensitivity sets satisfying the assumptions of our main results.
