This article addresses both monitoring of contact transitions and estimation of unknown first-order geometric parameters during force-controlled motion. A robotic system is tasked to move an object among a sequence of contact configurations with the environment, under partial knowledge of geometric parameters (positions and orientations) of the manipulated objects and of the environment itself. The authors provide an example of a compliant motion task with multiple contacts, namely that of moving a cube into a corner. It is shown that by describing the contact configurations with different models and using the multiple model approach it is possible: (i) to detect effectively at each moment the current contact configuration and (ii) to estimate accurately the unknown parameters. The reciprocity constraints between ideal reaction forces and velocities are used as measurement equations. An Interacting Multiple Model (IMM) estimator is implemented and its performance is evaluated based on experimental data.