Autonomous laundry washing and drying systems and methods

A method of load balancing a heat pump in fluid communication with a plurality of combination washing and drying machines, comprising:

• receiving, at a controller in operable communication with the plurality of combination washing and drying machines, a washing and drying cycle status of each one of the plurality of combination washing and drying machines, each one of the plurality of combination washing and drying machines comprising a single tub for sequential washing and drying of a load of laundry;
• identifying an available one of the plurality of combination washing and drying machines comprising an empty single tub configured to receive a load of laundry;
• determining, based on one or more load characteristics of the load of laundry, a washing and drying cycle duration and temperature profiles of the load of laundry;
• and
• determining a washing and drying cycle start time of the identified available one of the plurality of combination washing and drying machines based on the determined washing and drying cycle duration and temperature profiles, a cycle status of each one of a remainder of the plurality of combination washing and drying machines, and staggering washing and drying cycles between the identified available one of the plurality of combination washing and drying machines and the remainder of the plurality of combination washing and drying machines to balance load on the heat pump.