Passivity guaranteed stiffness control with multiple frequency band specifications for a cable-driven series elastic actuator

Abstract

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 frequencyband optimization problem into the H∞ 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∞ synthesis method achieved more accurate and robust stiffness control performance with guaranteed passivity.

Variable Stiffness Control with Strict Frequency Domain Constraints for Physical Human-Robot Interaction

“…In this paper, a cable-driven series elastic actuator (SEA) system that has been used in our previous works [21], [22], [27], [28], is used for simulation and experimental validation. Its mechanical design is shown in Fig.…”

“…To further demonstrate the performance, simulations of variable impedance control are conducted and compared with a gain-fixed passivity-based PID method. The parameters of the PID are the same as in our previous work [21], and remain constant during the variable impedance control. During the simulations, the desired stiffness changes according to the sequence {0.71K s , 0.32K s , 0.51K s , 0.25K s , 0.56K s , 0.65K s , 0.91K s , K s }.…”

“…In our previous work [21], [22], we improved stiffness rendering performance by restricting constraints on accuracy, actuator limitation, disturbance attenuation and noise rejection into their specific frequency ranges. Strict full frequencydomain passivity was guaranteed for constant stiffness control in [21].…”

“…In our previous work [21], [22], we improved stiffness rendering performance by restricting constraints on accuracy, actuator limitation, disturbance attenuation and noise rejection into their specific frequency ranges. Strict full frequencydomain passivity was guaranteed for constant stiffness control in [21]. In this paper, we extend the methods to variable stiffness control by scheduling the gains, and the desired stiffness can be smoothly varied online while all the performance constraints are guaranteed.…”

“…The passivity constraint is relaxed in such a way that it is only required for the low frequency range. These are the two key differences between this paper and the previous two [21], [22]. Simulations and experiments are performed to validate the methods and arXiv:2008.03663v1 [cs.RO] 9 Aug 2020 compared with a gain-fixed passivity-based PID method.…”