  To function autonomously in the physical world, humanoid robots need
high-fidelity sensing systems, especially for forces that cannot be easily
modeled. Modeling forces in robot feet is particularly challenging due to
static indeterminacy, thereby requiring direct sensing. Unfortunately,
resolving forces in the feet of some smaller-sized humanoids is limited both by
the quality of sensors and the current algorithms used to interpret the data.
This paper presents light-weight, low-cost and open-source force-sensing shoes
to improve force measurement for popular smaller-sized humanoid robots, and a
method for calibrating the shoes. The shoes measure center of pressure (CoP)
and normal ground reaction force (GRF). The calibration method enables each
individual shoe to reach high measurement precision by applying known forces at
different locations of the shoe and using a regularized least squares
optimization to interpret sensor outputs. A NAO robot is used as our
experimental platform. Experiments are conducted to compare the measurement
performance between the shoes and the robot's factory-installed force-sensing
resistors (FSRs), and to evaluate the calibration method over these two sensing
modules. Experimental results show that the shoes significantly improve CoP and
GRF measurement precision compared to the robot's built-in FSRs. Moreover, the
developed calibration method improves the measurement performance for both our
shoes and the built-in FSRs.
