Robotics Fundamentals 1, Chapter 1: Challenge 3 solution (anatomy, endurance and availability)

Formulas: E(usable) = 0.8 x E          t(run) = E(usable) / P          A = t(run) / ( t(run) + t(recharge or swap) )
          energy per metre = P / v          distance on one charge = E(usable) / (energy per metre)

(a) A robot vacuum cleaner (typical features; models differ)
    Senses:   bumper switch (contact); cliff sensors (infrared, to stop at stairs); wall or distance sensors (infrared or ultrasonic); wheel encoders or an optical sensor (how far it moved); dirt sensor; battery voltage; a gyroscope or a camera or lidar on better models.
    Thinks:   which cleaning pattern to follow (spiral, zig-zag, along walls); what to do on contact (back up and turn); when to return to the dock (battery low or job finished); how to avoid stairs; where it has already cleaned (a map, on better models).
    Acts with: two drive wheels (and a caster); the brush motors and the suction fan; also a light or beeper.
    Chapters:  structure and wheels mount: Robotics Fundamentals 2; the drive motors and gears: Robotics Fundamentals 3; the differential drive: Robotics Fundamentals 4; cliff, wall and bump sensors: Robotics Fundamentals 5; encoders and gyro: Robotics Fundamentals 6; keeping a wheel speed or a heading: Robotics Fundamentals 7; the cleaning patterns and the dock return (a state machine): Robotics Fundamentals 8; battery, charging and safety (the dock, the cliff stop): Robotics Fundamentals 10.

(b) E(usable) = 0.8 x 36 = 28.8 Wh
        Vacuum, 15 W:        t = 28.8 / 15 = 1.92 h   (115 min)
        Rover, 25 W:         t = 28.8 / 25 = 1.152 h  (69 min)
        Legged robot, 90 W:  t = 28.8 / 90 = 0.32 h   (19.2 min)

(c) Availability:
        Vacuum, 3 h to recharge:                A = 1.92 / (1.92 + 3) = 1.92 / 4.92 = 0.390   (39.0 %)
        Legged robot, 1 minute (0.01667 h) swap:  t(run) = 19.2 min, so A = 19.2 / (19.2 + 1) = 19.2 / 20.2 = 0.950   (95.0 %)
    The vacuum is idle most of the time but nobody minds, because it is working while you are out; the legged robot is only useful in the field if the battery can be swapped quickly.

(d) Energy per metre and range on one charge (E(usable) = 28.8 Wh = 28.8 x 3600 = 103 680 J):
        Legged, 0.7 m/s:   P / v = 90 / 0.7 = 128.6 J/m       distance = 103 680 / 128.6 = 806 m
        Rover, 1.2 m/s:    P / v = 25 / 1.2 = 20.83 J/m       distance = 103 680 / 20.83 = 4977 m   (about 5.0 km)
    The rover goes about 6.2 times as far on the same battery (4977 / 806).

(e) Legs cost a great deal more energy per metre than wheels (here about 6 times), so choose them only where wheels cannot go (stairs, rubble, very rough ground); on flat ground, wheels win.

Check on method: convert Wh to joules by multiplying by 3600 before dividing by joules per metre, or keep both in watt-hours (energy per metre in Wh/m). A common slip is to mix watt-hours with joules.