Passive realizations of series elastic actuation: effects of plant and controller dynamics on performance and passivity of haptic rendering

Official URL: https://risc01.sabanciuniv.edu/record=b2766861_(Table of contents)

Safe and natural physical human-robot interactions (pHRI) require precise control of the impedance behaviour of the robot at the interaction port. Series elastic actuation (SEA) is a commonly used interaction control paradigm for pHRI, as it can provide interactions with excellent stability robustness and high rendering fidelity. Series elastic actuation relies on a compliant element placed between the actuator and the interaction port and the utilization of the model of this compliant element to implement closed-loop force control. The compliant element relaxes the strict stability bounds on the controller gains induced due to non-collocation and bandwidth limitations and provides excellent stability robustness for interaction control. Series damped elastic actuation (SDEA) extends SEA by introducing a viscous dissipation element parallel to the series elastic element. SDEA can, not only help increase the force control bandwidth of SEA but also provide additional advantages, in terms of improving energy efficiency, reducing undesired oscillations, and alleviating the need for D-control terms. Velocity sourced impedance control (VSIC) is the most commonly used force control architecture for S(D)EA, as its cascaded control architecture with a robust inner motion control loop can effectively eliminate parasitic forces, leading to good rendering performance. Model reference force control (MRFC) is an alternative approach that promises to improve interaction control performance compared to VSIC, as the knowledge of the plant model enables feedforward action to react to inputs more quickly. iii In this thesis, we establish the necessary and sufficient conditions for frequency domain passivity of series (damped) elastic actuation (S(D)EA) while rendering null impedance, ideal springs, and Voigt model under VSIC. Furthermore, we rigorously study the effect of omitting the damping force induced on the serial compliant element in closed-loop control and provide the necessary and sufficient conditions for the passivity of interaction when only the deflections of the serial elastic element is used to estimate the interaction forces. This model captures a common implementations of SEA, where the inherent damping effects on the serial elastic element is ignored. We introduce passive physical equivalents for S(D)EAs under closed-loop control to help establish an intuitive understanding of the passivity bounds and to highlight the effect of different plant parameters and controller terms on the closed-loop performance of the system. Through the passive physical equivalents, we rigorously compare the effect of different plants dynamics (e.g., SEA and SDEA) and different cascaded controller architectures (e.g., P-P and P-PI) on the system performance. Moreover, we show that passive physical equivalents establish a natural means for effective impedance analysis. Furthermore, we compare the effect of measuring and omitting the damping force of the series elastic element on the closed-loop rendering performance of the system. We also study a reduce order model for the implementation where the damping force of the series elastic element is omitted, by replacing the robust inner motion control loop by a low-pass filter. We establish passivity conditions and physical equivalents for this reduce order model and compare the results with the full-order model to study the effects of this simplifying assumption on the stability and rendering performance of the system. We further extend our study to alternative control algorithms, such as model reference force control (MRFC). We present sufficient conditions for passivity of S(D)EA under MRFC during null impedance and ideal spring rendering. We prove that overestimation of robot inertia and underestimation of the stiffness of the series elastic element can ensure coupled stability of interaction for SEA under MRFC during null impedance rendering, as long as a lower limit on damping compensation is not violated. We demonstrate the validity of passivity conditions and the performance of haptic rendering through systematic simulation studies, as well as comprehensive set of physical experiments where we experimentally verify the passivity bounds and demonstrate the impedance rendering performance under different plant dynamics and different controller architectures.