A Geometric Perspective on Moment Arm Estimation Using Force/Torque Sensors

This paper presents a novel geometric approach to estimate the moment arm, or mass center, of an unknown robot end effector using a wrist-mounted force/torque sensor (FTS). Measuring the end effector contact wrench with the environment is important in a variety of applications, but FTS measurements usually include the effects of gravity. An accurate estimate of the end effector mass center is required to compensate for gravity in these measurements. Existing methods described in the literature seem to require an open kinematic chain, as they sample measurements from multiple sensor orientations and compute an estimate using least squares methods. The present study aimed to investigate a geometric method for estimating the moment arm using measurements from only one sensor orientation, which may be better suited for closed kinematic chains. This paper presents a geometric interpretation of the torque vector equation, and proposes four geometric techniques to estimate the mass center of an unknown end effector. Whereas least squares methods rely on multiple measurements to account for unknown values, the proposed geometric techniques must incorporate some a priori knowledge of the moment arm to compensate for the missing information in the system. Each geometric technique was tested using both simulated and experimental measurements. Results from preliminary experiments indicate that the proposed method has a susceptibility to noise.