1: Q1: A wheeled robot moves in the plane and every wheel rolls without slipping. Which statement is neces-sarily true at every instant?
40s
The axes of all wheels are parallel to each other.
The axes of all wheels either meet in a single point (the ICC) or are all parallel.
The axes of all wheels intersect in exactly one point, the ICC.
The velocity vectors of all wheel contact points have equal magnitude.
2: Q2: A differential-drive robot is commanded with vl = −vr and vr > 0. Which line is correct?
40s
R = ∞, ω = 0: straight ahead
R = 0, ω = 2vr /l: rotation in place about the robot centre
R = l/2, ω = 2vr /l: rotation about the left wheel
R = 0, ω = vr /l: rotation in place about the robot centre
3: Q3: Which of the following drives has no non-holonomic constraint?
30s
Synchro drive
Mecanum-wheeled drive
Differential drive
Ackermann (car) drive
4: Q4: A train must stay on its rails. A differential-drive robot cannot move sideways. Both are “constraints”,but not of the same kind. Which row classifies them correctly?
40s
Both are holonomic.
Train: non-holonomic (removes directions of motion). Robot: holonomic (removes poses).
Both are non-holonomic.
Train: holonomic (removes poses from the configuration space). Robot: non-holonomic (removes directions of motion, but no poses).
5: Q5: A synchro drive’s wheels are mechanically coupled: one motor spins every wheelat the same rate, and a second motor rotates every wheel about its own vertical axis through the sameangle, so the wheels always point in the same direction. Which statement is false?
50s
Two motors are enough to command both the robot’s speed and its direction of travel.
Because every wheel can be steered, the robot has no non-holonomic constraint.
The robot can change its direction of travel on the spot, by steering the wheels without driving them.
At any instant the robot’s velocity must be parallel to the common wheel direction.
6: Q6: True or false? “A wheel encoder is a sensor, therefore in the Bayes-filter formulation encoder readingsmust enter as measurements zt and be processed in the correction step.”
30s
True
False
7: Q7: A time-of-flight range sensor computes d = v · t/2. The factor 12 is there because
40s
the sensor averages the outgoing and returning signal speeds.
half of the emitted energy is absorbed by the object.
the measured time covers the round trip: emitter → object → receiver.
the emitter and receiver are two separate devices.
8: Q8: A sonar aimed at a smooth wall at 45◦ incidence returns either a maximum-range reading or the (muchlarger) distance to some object behind the wall. The dominant error mechanism is
40s
the wide opening angle.
specular reflection.
crosstalk between neighbouring sensors.
the temperature dependence of the speed of sound.
9: Q9: Which group contains only active sensors?
40s
Ultrasound, laser range finder, monocular camera
Bumper, tactile switch, infrared proximity sensor
Ultrasound, laser range finder, infrared proximity sensor
10: Q10: You must choose a depth sensor for a robot that maps a sunlit atrium with glass balustrades and blackleather furniture, at ranges up to 15 m. Why is a Kinect-style structured-light sensor the wrong choice?Pick the two decisive reasons.
40s
Its operational range is limited to roughly 5 m.
It cannot produce a dense range image.
Sunlight, dark surfaces and specular surfaces all defeat the projected IR pattern.
It is more expensive than a 2-D LiDAR.
11: Q11: True or false? “Since probabilities lie in [0, 1], a probability density function p(x) can never take avalue greater than 1.”
30s
True
False
12: Q12: True or false? “If P (x, y | z) = P (x | z)P (y | z) then P (x, y) = P (x)P (y).”
30s
True
False
13: Q13: In P (x | z) = η P (z | x)P (x), the normaliser η
50s
depends on x and must be recomputed for every hypothesis.
is itself a probability and therefore lies in [0, 1].
equals P (z)−1 , is the same for all x, and is obtained by making the posterior sum to 1.
encodes the prior and disappears if the prior is uniform.
14: Q14: Which of the following is not among the assumptions underlying the Bayes filter as presented in thelecture?
40s
The world is static: it changes only through the state transitions the model describes.
The models P (z | x) and P (x | u, x′ ) are exact, with no approximation error.