In a virtual or augmented reality system, a module with multiple contact points may provide haptic output associated with a virtual object being held or manipulated by a user's hand. A drone-like airborne device may keep such a module hovering close to the user and provide just-in-time contact and other types of haptic feedback when needed. The user experiences virtual objects with a head-mounted display and such a module that delivers multidimensional haptic feedback, including but not limited to, contact, surface stiffness, surface texture, and thermal properties of the virtual object that is in contact with the user's hand and fingers. The propellers on the drone device provide full six-degrees-of-freedom (6-DOF) force and torque feedback to the user via such a module attached to the airborne system. In some implementation, the user wears a wrist band that docks with such a module via magnets on both the wrist band and the module. The wrist band may contain multiple controls for the user to issue commands and communicate with the module. The position and movement of the module and the user's hand and fingers can be tracked by sensors that are either attached to the module or user (such as inertial measurement units, IMUs) or placed in the environment (such as cameras and laser range sensors).