Human subject experiments are performed to evaluate the influence of artificial intelligence (AI) process management on human design teams solving a complex engineering problem and compare that to the influence of human process management. Participants are grouped into teams of five individuals and asked to generate a drone fleet and plan routes to deliver parcels to a given customer market. The teams are placed under the guidance of either a human or an AI external process manager. Halfway through the experiment, the customer market is changed unexpectedly, requiring teams to adjust their strategy. During the experiment, participants can create, evaluate, share their drone designs and delivery routes, and communicate with their team through a text chat tool using a collaborative research platform called HyForm. The research platform collects step-by-step logs of the actions made by and communication amongst participants in both the design team's roles and the process managers. This article presents the data sets collected for 171 participants assigned to 31 design teams, 15 teams under the guidance of an AI agent (5 participants), and 16 teams under the guidance of a human manager (6 participants). These data sets can be used for data-driven design, behavioral analyses, sequence-based analyses, and natural language processing.