Control and evaluation of series elastic actuators with nonlinear rubber springs

Series elastic actuators primarily use linear springs in their drivetrains, which introduces a design tradeoff: soft springs provide higher torque resolution at the cost of system bandwidth, whereas stiff springs provide a fast response but lower torque resolution. Nonlinear springs (NLSs) potentially incorporate the benefits of both soft and stiff springs, but such springs are often large. An NLS design was recently proposed that combines a variable radius cam with a rubber elastic element, enabling a compact spring design. However, the rubber introduces hysteresis, which can lead to poor torque tracking if not accounted for in the controller. To overcome this limitation, we here propose a state observer that captures hysteretic effects exhibited by the rubber to provide an accurate estimate of actuator torque. We perform torque-control experiments with this observer on an actuator testbed and compare the performance of the NLS to both soft and stiff linear metal springs. Experiments show that the NLS exhibits improved output impedance compared to both linear springs, and comparable bandwidth to the stiff linear spring up to 1.5 Hz. However, the hysteresis in the urethane rubber introduces instability in higher-frequency conditions, suggesting that future NLS designs can be improved by use of a different rubber as the elastic element.