A path-planning algorithm for encountered-type haptic devices that render multiple virtual objects in 3D space is proposed. To render multiple virtual objects with a single haptic device, the following two behaviors must be realized: (i) the device should move to the target object location in advance of the user's hand so that the user can encounter it; (ii) otherwise, the device should keep away from the user's hand, avoiding an unexpected collision. To realize such a consistent encounter, the user's hand motion must be tracked. The proposed algorithm determines the device location based on the minimum distance problem between a point (the user's hand) and a convex polyhedron constructed from the reference points of multiple objects. An automobile virtual control panel was constructed using an encountered-type haptic device in which the proposed path-planning algorithm was implemented. The validity of the proposed algorithm was confirmed and the required performances, such as the device speed and the accuracy of hand tracking were evaluated.