Collaborative surface patterning through cascaded ergodic control and automatic task allocation

Coordinating groups of heterogeneous agents to accomplish multiple sequential surface patterning objectives is challenging and may be difficult or impossible to achieve manually when the number of agents does not evenly partition the tasks. One important sequential surface patterning task is the application of friction-reducing textures, where beneficial indentations are first formed in a surface then the resulting raised burr is removed via polishing, producing a surface with lower sliding friction under submerged lubrication. Here, we introduce cascaded ergodic control to enable automatic sequential surface modification by teams of mobile robots. The trajectory history of a group of leader robots is taken as the target for a group of follower robots, allowing implicit task allocation without explicit sharing of task information. We demonstrate, in both simulation and experiment, that this method matches the performance of existing ergodic control schemes and enables flexible assignment of agents to different tasks without directly communicating objectives to follower robots. Teams of indentation and polishing robots work together in physical experiments to pattern acrylic workpieces, demonstrating a process scalable to patterning of massive workpieces like airplanes or cargo ships with greater flexibility than existing methods.