Abstract: This talk addresses the problem of constrained reach controllability in two dimensions. Considering a nonlinear controlled dynamics (given by an ODE) within a two-dimensional simplex, the goal is to design a feedback control—either continuous or piecewise continuous—that can steer any point inside the simplex to the outside, subject to the additional restriction that exit is only allowed through one of its faces. We will present sufficient conditions to determine whether a given control constitutes a solution, as well as a result ensuring the existence of solutions for affine dynamics.