Optimal control of diamagnetically levitated milli robots using automated search patterns

This paper reports early results of optimal control using diamagnetically levitated robot (DLR) systems. Levitated robots, typically 1-4 mm in size, are driven locally by printed circuit boards (PCBs) with zero friction and near-zero hysteresis. As previously reported [1, 2], these properties give the levitated system excellent repeatability at the micron and submicron levels for both positioning and trajectories. Highly repeatable systems are generally good candidates for optimal control because variability in identifying and exploiting optimized control parameters are minimized. In the data reported here, levitated milli robots are characterized, and we present experiments showing a 5× reduction in oscillations using a debouncing routine that is manually optimized in time. Manual optimization is effective in some cases, but due to the multi-degree-of-freedom (DOF) aspects of levitated robots, a more robust self-tuning method is desirable. Toward this goal, we describe experiments using automatic optimization of robot motion using a computerized search-and-test routine that varies PCB trace currents and selects optimal currents based on automatic measurement of motion error. The automatic optimization using this method has shown settling times to micron and submicron levels that are 20-40 times faster than simple bang-bang control of equilibrium currents. In one test reported here, 150-μm moves were demonstrated at 90-nm rms error with 15-ms move times.