On-line estimation of variable stiffness in flexible robot joints

Abstract

Variable stiffness actuators (VSAs) are currently explored as a new actuation approach to increase safety in physical human-robot interaction (pHRI) and improve dynamic performance of robots. For control purposes, accurate knowledge is needed of the varying stiffness at the robot joints, which is not directly measurable, nonlinearly depending on transmission deformation, and uncertain to be modeled. We address the online estimation of transmission stiffness in robots driven by VSAs in antagonistic or serial configuration, without the need for joint torque sensing. The two-stage approach combines (i) a residual-based estimator of the torque at the flexible transmission, and (ii) a recursive least squares stiffness estimator based on a parametric model. Further design refinements guarantee a robust behavior in the lack of velocity measures and in poor excitation conditions. The proposed stiffness estimation can be easily extended to multi-degree-of-freedom (multi-DOF) robots in a decentralized way, using only local motor and link position measurements. The method is tested through extensive simulations on the VSA-II device of the University of Pisa and on the Actuator with Adjustable Stiffness (AwAS) of IIT. Experiments on the AwAS platform validate the approach

A pure signal-based stiffness estimation for VSA devices

“…The forgetting factor in the QR-RLS algorithm has been set to λ = 0.98. Figure 2 shows a comparison of stiffness estimation results obtained with the proposed method, with a standard off-line LS fitting, and with the residual/RLS based estimator of [14]. The new method clearly outperforms the other two.…”

“…The standard LS considers the complete batch of data and is not able to follow time-varying aspects of the flexibility parameters. On the other hand, our method [14] uses the (nominal) motor parameters, and so their imperfect identification is reflected in an error on the estimated stiffness. The proposed method returns also the estimated motor parametersB = 7.5135 [Kg·m·mm] andD θ = 0.9148 [N·mm·s/rad], which are very close to the actual ones.…”

“…(14)(15)(16) needs to collect a batch of data and is executed thus off-line, implicitly assuming that the parameter vector ξ remains constant over time. This assumption is indeed critical.…”

“…While for the torque input τ a white gaussian noise with zero mean can be assumed, noise on the measured outputs q and θ will depend on the type of sensors at hand. For instance, white noise was assumed in [15], whereas noise due to quantization and discretization of encoders was considered in [14].…”

“…This two-phase approach was used also in [12], where the second phase was replaced by a polynomial fitting based on Recursive Least Squares (RLS). This idea was revised and extended to serial VSAs in [13], [14]. A two-phase approach working on the motor side was used also in [15].…”