Previously, the authors have designed and implemented an active motion control "virtual crankshaft" for a free piston engine, which enables precise piston tracking of desired trajectories. With this mechanism, the volume of the combustion chamber can be regulated, and therefore the pressure, temperature and species concentrations of in-cylinder gas can be adjusted in real-time which affect the combustion process directly. This new degree of freedom enables us to conduct piston trajectory-based combustion control. In this paper, a model of the free piston engine running homogeneous charge compression ignition combustion under various piston trajectories is presented. The various piston trajectories have the ability to change the compression ratio and accommodate different piston motion patterns between the top dead center and the bottom dead center. Six reaction mechanisms are employed in the model in order to demonstrate the multi-fuel combustion ability of the free piston engine, and to describe the chemical kinetics of different fuels under various piston trajectories. Analysis of the simulation results is then presented which reveals the piston trajectory effects on the combustion in terms of in-cylinder gas temperature trace, indicated output work, heat loss and radical species accumulation process. (C) 2014 Elsevier Ltd. All rights reserved.