Applicability of Residuals Reduction Algorithm (RRA) for incomplete data

[Ana de Sousa]

Hi all,

I'm working with some data and considering using the Residuals Reduction Algorithm (RRA).

My datasets are

1. Leg extension exercise: I collected markers data and force platform data (both feet). But I'm missing the forces on the chair as the person is seated.
2. Seated cycling: I collected markers data and pedal forces. But I'm missing forces from seat and handles.

The RRA documentation suggests it's best for gait analysis with complete ground reaction forces. Given my missing data, does it still make sense to use RRA?

Thanks!

[Thomas Uchida]

RRA attempts to reduce F_residual in the equation F = ma + F_residual. If you don't have all of the external forces (F), you have more unknowns than equations (F_measured + F_unknown = ma + F_residual) which cannot be solved uniquely unless you provide additional information or make assumptions. One approach could be to add kinematic constraints, which would generate reaction forces that (might) estimate F_unknown.

[Ana de Sousa]

Thanks a lot for your response, Thomas.

In our cycling analysis, we are using the marker positions and external forces applied to the feet to calculate the joint moments through ID. However, since we do not have data on the forces exerted at the seat, the computed residual wrench encompasses these unmeasured forces, which do not necessarily have to be minimal. Therefore, this uncertainty raised the question of whether the RRA is appropriate in this context. If we understand correctly, the purpose of minimising residuals is to refine the model by adjusting for discrepancies between the modeled forces and the actual forces, thereby achieving dynamic consistency. However, in this case, the residuals are not solely due to modeling inaccuracies but also include the effects of missing force data, which cannot be minimised.

Could you clarify your suggestion on using kinematic constraints? Would be, e.g., that we constrain certain segments to be fixed or to follow a specific motion, then minimise the forces and adjust the model accordingly? How would this approach compare to simply using ID, given the incomplete data? Would this method provide more reliable estimates or better dynamic consistency?

Thank you for your insights!