  Impedance control and specifically stiffness control are widely applied for
physical human-robot interaction. The series elastic actuator (SEA) provides
inherent compliance, safety and further benefits. This paper aims to improve
the stiffness control performance of a cable-driven SEA. Existing impedance
controllers were designed within the full frequency domain, though human-robot
interaction commonly falls in the low frequency range. We enhance the stiffness
rendering performance under formulated constraints of passivity, actuator
limitation, disturbance attenuation, noise rejection at their specific
frequency ranges. Firstly, we reformulate this multiple frequency-band
optimization problem into the $H_\infty$ synthesis framework. Then, the
performance goals are quantitatively characterized by respective restricted
frequency-domain specifications as norm bounds. Further, a structured
controller is directly synthesized to satisfy all the competing performance
requirements. Both simulation and experimental results showed that the produced
controller enabled good interaction performance for each desired stiffness
varying from 0 to 1 times of the physical spring constant. Compared with the
passivity-based PID method, the proposed $H_\infty$ synthesis method achieved
more accurate and robust stiffness control performance with guaranteed
passivity.
