I drew a lot of inspiration from Marco Reps video Hi-Res Pressure Sensor Matrix with the LattePanda when I started this project.  Since our application requires a much smaller matrix, we decided to use a flex PCB to arrange the sensor lines and interface connectors.   There are several choices in the market for piezoresistive material.  We selected Velostat and one other type as our starting point.  The components of the sensor matrix are shown in the image below - note that both piezoresistive samples are shown, only one at a time is sandwiched between the pair of flex PCBs.

4x4 pressure sensor components
A single PCB can serve as the top or bottom of the sensor matrix. Only 1 sheet of piezoresistive material is needed.

Since cost was a concern, I looked for a way to have a single flex PCB serve as the top and bottom of the matrix.  The solution was to put the connector fingers symmetrically on the diagonal on both sides of the PCB with only half of the fingers 

Sensor matrix construction
(Left) I used Coreldraw to dimension the sensor matrix. (Center) This allowed me to test the symmetry of the connector fingers. (Right) A detailed view of the connector fingers in EAGLE CAD.

In order to measure the resistance a little analog wizardry is needed in the form of an interface board.  This is shown in the image below. 

Sensor matrix connected to interface board
The sensor matrix measure the resistance at row/column intersections with the help of the interface board. The interface helps the microcontroller row-scan the matrix.

Once we got the interface board operational, I connected it to a PIC 18F26K22 development board that I use in my classes.  With the accompanying SD-card we can record days worth of pressure sensing data.  The image below shows the completed prototype.

Completed sensor prototype
I used one of my development boards for this first prototype. The dev board contains a lot of peripherals that are not used in this project. Excuse the rats nest of wires, they will be eliminated in the next revision.

One of my main objectives is to characterize the frequency response of the sensor elements so that we know the bandwidth and consequently know what phenomena we can reliably observe.  In order to accomplish this, I built a small testing platform from 2020 series T-Slot Aluminum Extrusion and laser cut acrylic.  The solenoid is actuated with an external circuit.  Using the scale below the sensor matrix and the size of the solenoid head, we can determine the pressure being applied to the matrix.  This allows us to convert the resistance readings into PSI.

Testing stand for sensor matrix
I built a small testing stand that uses a solenoid to apply pressure to the sensor matrix. With the small scale and known cross section of the solenoid head, we can derive the equivalent pressure.