Lidar Safety Envelopes (Robotics & Computer Science)

In autonomous vehicle design, a lidar sensor scans the surroundings by emitting light pulses across a specific field of view. The domain of the range-finding function is restricted by the sensor's physical limits: the horizontal scanning angle $\theta$ is restricted to $\left[-\frac{\pi}{3}, \frac{\pi}{3}\right]$ radians, and the radial distance $d$ is restricted to $[0.1, 150]$ meters.

To determine how the vehicle should respond to obstacles, software engineers program a piecewise control function $A(d)$ to evaluate safety zones:

Determine the vehicle's response and safety state if an obstacle is detected at a distance of:

1. $d = 2\text{ meters}$
2. $d = 10\text{ meters}$
3. $d = 80\text{ meters}$