A mobile drive unit including a docking head assembly is provided. The docking head assembly is configured with two or more actuator assemblies to lift an inventory holder and tilt the inventory holder in two or more directions. The direction of tilt and an associated angle may be determined based on a location of a center of gravity of the inventory holder relative to the mobile drive unit. The direction of tilt and the associated angle may also be determined based on information describing external forces acting on the inventory holder.