A new approach for cellular robots is presented. The single elements of the robot are triangular cells, which can change their shape by means of linear actuators at each edge. The novelty concerns the connection of autonomous cells at their edges rather than at the vertices. In this way, unstructured triangular meshes can be formed. The robot can self-reconfigure and thus can reproduce almost arbitrary planar shapes. In a similar way, the system has been realized with tetrahedrons in a simplified way within a previous work. The self-reconfigurable system shall serve as a basis for programmable matter. The present paper includes the mechatronic design, its components and the kinematic model of the cellular robot. In order to reduce positioning errors, a model is developed, which considers compliance and clearance in the links and joints. Based on a simplified mechanical model using elastic trusses, the positioning errors can be predicted. The parameters of these models are identified from simple motion sequences. Furthermore, the nonlinearity of actuators is identified and corrected. In this way, the desired triangular shapes can be prescribed without measuring the position of the cells.