In this paper we solve the full-consensus problem for multiple nonholonomic vehicles interacting over a directed leader-follower topology and subject to sensing constraints in the form of limited range and limited field-of-view. Remarkably, based on a polar-coordinates model transformation, the designed controller is time-invariant and smooth (in the domain of definition). Moreover, the control laws rely only on local measurements, making it well suited for implementation. The asymptotic convergence to the consensus manifold as well as the respect of the constraints is established using Lyapunov’s first method and cascaded systems theory. Realistic simulations in the Gazebo-ROS environment, which illustrate the effectiveness of our theoretical contributions, are shown in an accompanying video.