Delft Haptics Lab

A-priori Inertia Estimation from Weight

Abstract

This MSc project was executed by Lotte Grootveld, supervised by Jack Schorsch and David Abbink. Lotte graduate in July 2015.

Abstract

Robotic lifting aids aim to reduce the forces on the operator, but may thereby also change the experienced dynamics of the lifted object. In the case of weight compensation, the experienced ratio between object’s weight and inertia is altered, exposing the operator to dynamics different from those experienced in daily life. This may affect execution of fast goal-directed movements, especially during first exposure to the altered dynamics. We hypothesize that the inertia, used in the internal model in the open-loop phase of the movement, must be estimated before movement onset and can be based on the object’s weight. In an experimental study, subjects (n=18) performed fast vertical lifting movements of virtual objects of different inertia and weight in normal gravity (baseline experiment) and under weight compensation. In the catch trial experiment, the weight was kept constant and in catch trials weight compensation was applied, resulting in an unexpectedly increased inertia. We then fitted a simple open-loop model, based on minimum jerk trajectories, to best match the generated forces for the first 75ms of each trial, by varying one parameter: the modelled inertia, i.e. the inertia estimated a priori by the subject. The trajectories in the baseline experiment are minimum jerk like and are independent of inertia, which can only be due to properly applied force profiles. The minimum jerk related force profiles increased with increasing inertia and contained a static force equal to weight. In the catch trial experiment, the force profiles for the weight compensation condition were similar to those in the normal gravity condition up to approximately 80ms. After that, the force profiles of the catch trials deviated from the normal force profile and the movement in the catch trials was characterised by skewed velocity profiles and consistent overshoots. The Variance Accounted For, a measure for goodness of fit, for all conditions in both experiments were high (with the median around 95%), implying the model fitting procedure captured the essential open-loop movement behaviour. Weight and modelled inertia were linearly related in the baseline experiment, as was hypothesized, yet a positive offset was found for small inertias. In the catch trials, the modelled inertias were higher than expected purely based on weight information, but remained closely related to inertia as in normal gravity. We conclude that a priori inertia estimation, used in the open-loop phase of fast lifting movements, strongly depends on weight information and the known weight/inertia ratio. This insight can help in designing the control for lifting aids to support the operator more naturally.