Towards Estimating Normal and Shear Interface Pressures in Prosthetic Sockets via Least Squares and Mechanics Modeling

Prosthetic socket fitting remains largely manual and iterative, and objective fit metrics are still limited. Part of the challenge is the lack of long-term real-life pressure data at the residual limb--socket interface. Traditional pressure sensors are prone to drift over time, and capture only normal pressures at sparse locations within the socket, missing a critical component for biomechanical analysis: shear. Although some sensors can report both normal and shear interface stresses, these components are often difficult to decouple because of measurement crosstalk. One potential path forward is to develop models that can augment available measurements. This work introduces a testbed to evaluate model performance under sparse pressure sensing using two complementary validation signals: (i) the global wrench (\ie, total forces and moments expressed in an orthonormal frame) transmitted through the socket, by an artificial residual-limb, and (ii) local interface loads (\ie, decoupled normal and shear pressure components in a right-hand-rule orthogonal frame that lives in each instrumented location) measured by sparse sensing clusters, each composed of four capacitance-sensing channels. Rather than presenting full-field pressure estimates, the focus is on an analysis sequence that quantifies how well candidate mechanical models explain both global and local measurements under controlled conditions. A quasi-static spring--mass contact model is evaluated, and its parameters are identified via a two-stage convex least-squares problem. Validation under static loading shows that estimating constant bias terms reduces steady offsets in the wrench channels and improves agreement with local measurements. A Pareto-front sensitivity analysis further illustrates how the trade-off between global and local objectives changes when bias terms are included.