Question

Consider an omnidirectional robot with a ring of eight sonar sensors that are fired sequentially. Your robot is capable of accelerating and decelerating at 50 cm/s2. It is moving in a world filled with sonar-detectable fixed obstacles. The maximum range of the sonar sensors is 5 m. Given the bandwidth of your sonar sensors, compute your robot's maximum speed ensuring no collisions.

Answer 1

Answer:

The maximum velocity is 2.23 m/s.

Explanation:

Given that,

Deceleration = 50 cm/s²

Range = 5 m

Let the maximum speed of robot is $v_{max}$

We need to calculate the maximum velocity

Using equation of motion

$v^2=u^2+2as$

Where, v = maximum velocity

U = initial velocity

s = distance

Put the value into the formula

$v^2=0+2\times0.5\times5$

$v^2=5\ m/s$

$v =2.23\ m/s$

Hence, The maximum velocity is 2.23 m/s.