This article presents a local control approach to linear vehicle platooning. Linear platoon systems are sets of vehicles that use local or global perception capabilities to form a train configuration, without any hard grip element. Public transportation is beginning to interest in platoon systems as a technological base to conceive new services. The main problem related to platoon system’s control corresponds with maintaining inter-vehicle distance. In literature, the platoon’s geometry control problem is treated according to two approaches: global or local vehicle control. This paper focuses on a local approach which does not require sophisticated sensors and/or costly road equipment. This local control approach intends to obtain very good global matching to arbitrary trajectories, only from local perception which consists in measuring the vectorial distance between a given vehicle and its predecessor. The behavior of each platoon vehicle is determined from a physics inspired multi agent interaction model based on a virtual spring-damper. Furthermore, stability, platoon safety properties are checked using physics and mathematical proofs. Finally, simulation is used to measure trajectory error and inter-vehicle distance evolution.