[douglas]

One planetary facility and one system facility stack, in a multiplicative manner. A robotoid III and a system robotoid I multiply resource production by 1.3 * 1.1 = 1.43, for a combined 43% bonus. If you get level 3 system robotoids, the combined bonus is 69%.

Edit: Note that the increase from the system robotoid will not be shown on the individual planet display, but is taken into account for your total empire income.