Phase control for a legged microrobot operating at resonance

We present an off-board phase estimator and controller for leg position near the resonance of the Harvard Ambulatory MicroRobot's (HAMR) two degree-of-freedom transmission. This control system is a first step towards leveraging the significant increase in stride length at transmission resonance for faster and more efficient locomotion. We experimentally characterize HAMR's transmission and determine that actuator phase is a sufficient proxy for leg phase across the range of useful operating frequencies (1–120Hz). An estimator is developed to determine actuator phase using off-board position sensors and it converges within a cycle on average. We also fit a nonlinear dynamic model of the transmission to the experimental data, and utilize the model to determine a suitable open-loop resonant leg trajectory and define feed forward control inputs. This resonant (100Hz) trajectory is theoretically 50% more efficient than pre-resonant high speed running trajectories. The controller converges to this trajectory in 0.05 ± 0.02 seconds (5.3 ± 2.4 cycles) in air, and in 0.05 ± 0.01 seconds (4.7 ± 0.6 cycles) under perturbations that approximate ground contact.