Bi-Modal Hemispherical Sensor: A Unifying Solution for Three Axis Force and Contact Angle Measurement

In robotic tasks that require physical interactions such as manipulation and legged locomotion, it is important to simultaneously measure contact forces and contact angles. This paper presents a unified solution for simultaneously measuring three axis contact forces and contact angles for legged locomotion or manipulation. Unlike most tactile sensors, the presented design utilizes the stress field method by sampling pressures over multiple locations within an elastomer, enabling inherently robust operation against impact and abrasive interactions. The presented sensor is designed for point-feet quadrupedal robots and can be easily scaled down for other applications such as grasping. The sampled stress distribution is mapped to output forces $f_{x}, f_{y}$, and $f_{\mathrm{z}}$ and two contact angles, $\theta$ and $\psi$ on the hemispherical sensor surface via Gaussian process regression. The prototype sensor is able track normal and shear forces accurately, achieving a normalized root mean (RMS) squared error of only 1.00%–1.36% for $f_{\mathrm{z}}$ across multiple tests with up to 180N normal force, and a normalized RMS error of 1.71%–4.67% and 1.82%–6.68% for fx and fy, respectively, with up to 80N shear force. Additionally, the footpad is able to estimate the contact location coordinates $\theta$ and $\psi$ with a normalized RMS error of 2.69%−7.51% over a range of $0-40^{\mathrm{o}}$ and 2.79%–9.62% over a range of $0-30^{\mathrm{o}}$, respectively. The footpad can estimate contact location over a maximum range of $\theta=\pm 45^{0}$ and $\psi=\pm 45^{\mathrm{o}}$, and can withstand over 450N of normal force at location $\theta =\psi =0^{\mathrm{o}}$ without reaching saturation. This prototype demonstrates the ability to simultaneously measure force in three axes and contact angles using Gaussian process regression, with the potential to explore other regression methods for embedded computing and miniaturization of the design for finger tip scale sensors.