Consider an omnidirectional robot with a ring of eight $70KHz$ sonar sensors that are fired sequentially. Your robot is capable of accelerating and decelerating at $50c\frac{m}{s^2}.$ It is moving in a world filled with sonar$-$detectable fixed $($nonmoving$)$ obstacles that can only be detected at $5$ meters and closer. Given the bandwidth of your sonar sensors$,$ compute your robot's appropriate maximum speed to ensure no collisions.

Design an optical triangulation system with the best possible resolution for the following conditions: specify $b($as in figure $4\mathrm{.}15)$:

$($a$)$ the system must have sensitivity of $1cm$ at a range of $2$ meters.

$($b$)$ The PSD has a sensitivity of $0\mathrm{.}1mm.$

$($c$)f=10cm.$

Perception

$263$

Identify a specific digital CMOS$-$based camera on the market. Using product specifications for this camera, collect and compute the following values. Show your derivations:

Dynamic range

Resolution $($of a single pixel$)$

Bandwidth

Stereo vision. Solve the system given by equations $(4\mathrm{.}60)$ and $(4\mathrm{.}61)$ and find the optimal point $(x,y,z)$ that minimizes the distance between the optical rays passing through tilde$(p{)}_l$ and tilde$(p{)}_r.$ For doing this, observe that these two equations define two distinct lines in the $3$D space. The problems consists in rewriting these two equations as the difference between $3D$ points along these two lines. Then, impose that the partial derivatives of this distance with respect to ${}_l$ and ${}_r$ equal zero. From this, you will obtain the two points along the two lines at minimum distance between each other. The optimal point $(x,y,z)$ can then be found as the middle point between those points.