Feedback control of many magnetized: Tetrahymena pyriformis cells by exploiting phase inhomogeneity

Biological robots can be produced in large numbers, but are often controlled by uniform inputs. This makes position control of multiple robots inherently challenging. This paper uses magnetically-steered ciliate eukaryon {Tetrahymena pyriformis) as a case study. These cells swim at a constant speed, and can be turned by changing the orientation of an external magnetic field. We show that it is possible to steer multiple T. pyriformis to independent goals if their turning - modeled as a first-order system - has unique time constants. We provide system identification tools to parameterize multiple cells in parallel. We construct feedback control-Lyapunov methods that exploit differing phase-lags under a rotating magnetic field to steer multiple cells to independent target positions. We prove that these techniques scale to any number of cells with unique first-order responses to the global magnetic field. We provide simulations steering hundreds of cells and validate our procedure in hardware experiments with multiple cells.