In this paper, we propose a new digital feedback law for controlling unicycles in a sampled-data scenario. More in detail, two open problems are solved. First, assuming piecewise constant control and sampled-data measures of the state, we consider the problem of driving one unicycle toward a desired position in the plane with a target fixed orientation. Then, we tackle the problem of forcing a network of unicycles to a desired formation with the same orientation when assuming asynchronous sampled-data communication and piecewise constant controls. The design relies upon discrete-time passivitybased arguments yielding the first feedback law (within the digital literature) that employs single-rate sampling while keeping into account the effects of digital devices. The results are finally illustrated through simulations aimed at showing the benefits of the proposed controller to recover the same performances under the continuous-time control law, whose performances are unavoidably lost when implemented in practice.