Methods for controlling the sorting and sequencing of objects are provided. In some embodiments, a method includes receiving sensor data of a plurality of dental appliances, each dental appliance associated with an identifier including (a) group data indicating a group to which the dental appliance belongs, and (b) sequence data indicating a sequential position for the dental appliance within the group. The method can include controlling a sorting cell to direct each dental appliance into one of a plurality of buffer locations based on the group data for the dental appliance, where each buffer location is configured to hold a set of dental appliances belonging to the same group; and controlling a sequencing cell to sequence the set of dental appliances associated with each buffer location by placing each dental appliance into a position within the corresponding set of dental appliances based on the sequence data for the dental appliance.