BS Robotics & Artificial Intelligence
What the Robotics & AI domain tests
The BS Robotics & Artificial Intelligence domain samples vectors, matrices, probability, basic physics, and introductory AI ideas such as search, sensing, and learning. Expect conceptual questions plus small calculations rather than deep coding.
Core rules and concepts
- A 2D rotation by angle θ counterclockwise uses [[cosθ, −sinθ], [sinθ, cosθ]] acting on a column vector. Rotations preserve length.
- Transform order matters: rotating then translating is not the same as translating then rotating. State the frame and the order.
- Feedback control compares a measured value with a set point; error drives correction. Stability and overshoot are separate issues.
- In search, breadth-first search finds the shortest path in an unweighted graph; depth-first search can use less memory but may not.
- In probability, P(A|B) is not P(B|A). Bayes’ rule updates a prior with the likelihood.
Worked example
Rotate vector v = (1, 0) by +90° counterclockwise. Reasoning: cos 90° = 0 and sin 90° = 1, so the matrix is [[0, −1], [1, 0]]. Multiplying gives x′ = 0(1) − 1(0) = 0 and y′ = 1(1) + 0(0) = 1, so v′ = (0, 1). If you get (0, −1), you have used a clockwise rotation or the wrong sign convention.
Traps that cost marks
Mixing degrees and radians, multiplying matrices in the wrong order, treating row and column vectors interchangeably, reversing conditional probabilities, and assuming a model that fits training data will generalize. In sensor problems, distinguish random noise from systematic bias.