A multi-method framework for establishing an angular acceleration reference in sensor calibration and uncertainty quantification

Robots are increasingly being used across various sectors, from industry and healthcare to household applications. In practice, a pivotal challenge is the reaction to unexpected external disturbances, whose real-time feedback often relies on (noisy) sensor measurements. Subsequent inverse-dynamics calculations demand noise-amplifying numerical differentiation, leading to impracticable results. Although much effort has been spent on establishing direct measurement approaches, their measurement uncertainty quantification has not or yet insufficiently been tackled in the literature. Here, we propose a multi-method framework to develop an angular acceleration reference and provide evidence that it can serve as a measurement standard to calibrate various kinematic sensors. Within the framework, we use Monte-Carlo simulations to quantify the uncertainty of a direct measurement sensor recently developed by our team; the inertial measurement cluster (IMC). For angular accelerations up to 21 rad/s², the standard deviation of the IMC was on average only 0.3 rad/s² (95% CI: [0.28,0.31] rad/s²), which constitutes a reliable data-sheet record. Further, using least-squares optimization, we show that the deviation of IMC with respect to the reference was not only less on the level of angular acceleration but also on the level of angular velocity and angle, when compared to other direct and indirect measurement methods.