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April 29, 2026

AIT304 β€” Final One-Shot Exam Sheet

AIT304 β€” Final One-Shot Exam Sheet

Exam: 70 marks | 3 hrs | Pick best 1 from each Q pair (Q11/12, Q13/14, Q15/16, Q17/18, Q19/20) Every question below appeared in 3–4 consecutive papers. These are not maybe β€” these ARE the exam.

MODULE 1 β€” Introduction to Robotics

Q11: Robot Configurations (8M) β€” EVERY paper

Four workspace configurations. Label joints: R = revolute (rotation), P = prismatic (linear).

Config Joints Motion Use Case
PPP (Cartesian/Gantry) 3 Prismatic x, y, z linear Large-area assembly, laser cutting
RPP (Cylindrical) 1R + 2P Rotate base + 2 linear Pick & place at height
RRP (SCARA) 2R + 1P Fast planar + vertical PCB assembly, precision placement
RRR (Articulated) 3 Revolute Humanlike, most flexible General purpose, welding, surgery

Diagram format (exam): Draw arm sketch for each β€” label base, joints (R/P), links, end-effector.

Q11(b): Anatomy of Robotic Manipulator (8M) β€” 3/4 papers

[Base] β†’ [Link1] β†’ [Joint1/R] β†’ [Link2] β†’ [Joint2/R] β†’ [End-Effector]
                                                               ↑
                                              [Sensors] ← [Controller] ← [Actuators]
Component Function
Base Fixed mounting platform
Links Rigid segments between joints
Joints R (rotate) or P (linear slide) β€” create DOF
Actuators DC/stepper/servo motors driving joints
Sensors Encoders, limit switches β†’ feedback
End-Effector Gripper/tool/sensor at tip
Controller Processes sensor data, sends commands to actuators

DOF = number of independent motions = number of joints 6-DOF robot = 3 position (x,y,z) + 3 orientation (pitch, roll, yaw)

Q12: Gripper Types + Force Numerical (6M) β€” 2/4 papers

Type Mechanism Limitation
Mechanical 2–3 fingers, hydraulic/pneumatic force Complex for irregular shapes
Magnetic Electromagnet on/off Ferrous materials only
Vacuum Suction cups Smooth surfaces only
Adhesive Sticky/gecko material Research stage

Force Numerical (appeared twice β€” gift marks):

F = m(g + a) / (n Γ— Β΅)

m = mass (kg), g = 9.8 m/sΒ², a = acceleration
n = number of fingers, Β΅ = friction coefficient

Example: 140 kg, Β΅=0.2, 2 fingers, a=10 m/sΒ²
F = 140 Γ— (9.8 + 10) / (2 Γ— 0.2) = 140 Γ— 19.8 / 0.4 = 6,930 N per finger

MODULE 2 β€” Sensors, Actuators & Control

Q13(a): Sensor Characteristics (6M) β€” 3/4 papers Part A, Part B

Write name + definition + example. 1 mark each.

# Characteristic Definition Example
1 Dynamic Range Ratio max:min measurable value 0.1N–100N β†’ 1000:1
2 Linearity Output ∝ input across full range Double force β†’ double voltage
3 Resolution Smallest detectable input change 0.01mm movement detected
4 Sensitivity Output change per unit input 2V per Newton
5 Repeatability Same input β†’ same output every time 5N β†’ always 4.98V
6 Bandwidth Max signal frequency sensor can track 1kHz BW β†’ tracks up to 1000Hz
7 Calibration Adjust zero offset + gain to true value Thermometer reads +2Β°C β†’ subtract 2

Static (steady-state): Range, Linearity, Sensitivity, Resolution, Repeatability, Accuracy Dynamic (changing input): Speed of response, Dynamic error, Fidelity, Lag

Q13(b): Hall Effect Sensor (8M) β€” Jan24 + May24 | Fixed scheme

Principle: Current-carrying conductor in magnetic field perpendicular to current β†’ Hall Voltage develops perpendicular to both.

Formula:

VH = (B Γ— I) / (n Γ— e Γ— t)

B = magnetic flux density
I = current
n = charge carrier density
e = electron charge (1.6Γ—10⁻¹⁹ C)
t = thickness of conductor

Diagram:

        B (into page, ↓)

   +──────────────────────+
   β”‚                      β”‚
I β†’β”‚    [Hall Element]    β”‚β†’ I
   β”‚                      β”‚
   +──────────────────────+
        ↑            ↑
      (+)VH         (-)VH
   (Hall voltage perpendicular to I and B)

Applications (2 marks):

  1. BLDC motor commutation β€” Hall sensors detect rotor magnet position β†’ switch phase currents
  2. Speed sensing β€” count Hall pulses per revolution β†’ RPM

Exam template: Principle 3M + Diagram 3M + Application 2M = 8 marks

Q14(a): H-Bridge + PWM (6M) β€” May24, Apr25

H-Bridge: 4 switches controlling motor direction. Takes H-shape.

      +Vcc
     |    |
    [S1] [S3]
     |    |
     A────B   ← motor between A and B
     |[M] |
    [S2] [S4]
     |    |
    GND  GND
State Switches ON Effect
Forward S1 + S4 A→Motor→B
Reverse S3 + S2 B→Motor→A
Brake S1 + S3 Motor shorted β€” stop
Coast All OFF Motor coasts

Never: S1+S2 or S3+S4 together β†’ short circuit.

PWM (Pulse Width Modulation):

Duty cycle D = (t_ON) / T

90%: β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–‘  β†’ Full speed
50%: β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–‘β–‘β–‘β–‘β–‘  β†’ Half speed
10%: β–ˆβ–‘β–‘β–‘β–‘β–‘β–‘β–‘β–‘β–‘  β†’ Low speed

Motor sees average voltage = duty cycle Γ— Vcc. High duty = fast motor. H-Bridge = direction. PWM = speed. Both needed for full motor control.

Q14(b): Stepper vs Servomotor (8M) β€” Jun23, May24, Apr25 β€” 3 STRAIGHT YEARS

Aspect Stepper Motor Servomotor
Definition Brushless, open-loop, step-wise Motor + encoder + controller
Movement Discrete steps (1.8Β°/step) Smooth, continuous
Control loop Open-loop Closed-loop
Feedback None β€” counts steps Encoder feedback
Precision Fixed step angle Sub-degree, very high
Torque Fixed; drops fast >1000RPM Maintained at any speed
Speed Limited High speed capable
Cost Cheaper More expensive
Error handling Loses steps silently Self-corrects via feedback
Noise High Low
Power High (holds torque always) Lower (corrects only when needed)
Applications 3D printers, CNC, scanners Robot arms, drones, industrial

Memory: Stepper = BLIND walker (counts steps, can’t verify). Servo = GPS walker (always knows position).

Q13/14: On-Off Controller vs PID (Apr25)

On-Off Controller: Binary β€” output fully ON or fully OFF.

  • Error > 0 β†’ ON. Error < 0 β†’ OFF.
  • Never settles β€” oscillates forever around setpoint.
  • Example: Thermostat (25Β°C setpoint β†’ heater cycles 24–26Β°C)

PID Controller:

u(t) = Kp·e(t) + Ki·∫e(t)dt + Kd·de(t)/dt
Term Reacts to Fixes Problem
P Current error Fast response Steady-state error remains
I Accumulated past error Eliminates steady-state error Slow, oscillation risk
D Rate of error change Dampens oscillation Amplifies noise

Control System Block Diagram (5 components, 1M each):

Setpoint β†’ [Ξ£] β†’ Controller β†’ Actuator β†’ Plant β†’ Output
            ↑                                        |
            └──────────[Sensor/Feedback]β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”˜

MODULE 3 β€” Vision & Kinematics

Q15: Seven Stages of Robot Vision (14M) β€” EVERY PAPER | 2 marks per stage

Write name + 2-line description each.

  1. Sensing β€” Image acquisition via CCD/CMOS camera. Converts real scene to digital image.

  2. Pre-processing β€” Noise removal, filtering (Gaussian blur, edge enhancement). Improves image quality for next stage.

  3. Segmentation β€” Divide image into meaningful regions (foreground/background, objects). Uses thresholding or region-growing.

  4. Description β€” Extract features from segments (shape, size, color, texture, moments). Converts regions to numerical descriptors.

  5. Recognition β€” Classify/identify objects based on features. Match descriptors to known models.

  6. Interpretation β€” Assign semantic meaning to recognized objects. Determines scene understanding for robot decision-making.

  7. Camera Sensor Hardware Interfacing β€” Connect vision pipeline output to robot controller. Translate image analysis to robot commands.

This is the most predictable question in the entire paper. Memorize cold.

Q16: Rotation Matrices (14M) β€” EVERY paper

Three fundamental rotation matrices:

R1(Ο†) β€” about fΒΉ axis (Yaw):        R2(Ο†) β€” about fΒ² axis (Pitch):
|1    0      0   |                   | cos Ο†   0   sin Ο†|
|0  cos Ο†  -sin Ο†|                   |   0     1     0  |
|0  sin Ο†   cos Ο†|                   |-sin Ο†   0   cos Ο†|

R3(Ο†) β€” about fΒ³ axis (Roll):
| cos Ο†  -sin Ο†  0|
| sin Ο†   cos Ο†  0|
|   0       0    1|

Memory pattern: kth row and kth column = identity. Remaining 2Γ—2: diagonal = cosΟ†, off-diagonal = Β±sinΟ†. Inverse = Transpose: R⁻¹(Ο†) = Rα΅€(Ο†)

Composite Rotation Rule:

  • Fixed frame axis β†’ PREMULTIPLY: R ← Rk(Ο†) Γ— R
  • Current/mobile frame axis β†’ POSTMULTIPLY: R ← R Γ— Rk(Ο†)

Worked Problem (from notes β€” exam type):

Problem: Rotate M about fΒΉ of fixed F by Ο† = Ο€/3. Find point p=[2,0,3]α΅€ in fixed frame.

cos(Ο€/3) = 0.5,  sin(Ο€/3) = 0.866

R1(Ο€/3) = |1    0      0   |
           |0   0.5  -0.866|
           |0   0.866  0.5 |

[p]^F = R1(Ο€/3) Γ— [p]^M
      = |1    0      0   | |2|   =  [2, -2.598, 1.5]α΅€
        |0   0.5  -0.866| |0|
        |0   0.866  0.5 | |3|

To find q=[3,4,0]α΅€ (fixed F) in mobile M:
[q]^M = R1α΅€(Ο€/3) Γ— [q]^F
      = |1    0      0   | |3|   =  [3, 2, -3.464]α΅€
        |0   0.5   0.866| |4|
        |0  -0.866  0.5 | |0|

Q16(b): Differential Drive Kinematics

v = (v_r + v_l) / 2       (linear velocity)
Ο‰ = (v_r - v_l) / L       (angular velocity, L = wheel separation)

Pose update:
Ξ”x = v Γ— cos(ΞΈ) Γ— Ξ”t
Ξ”y = v Γ— sin(ΞΈ) Γ— Ξ”t
Δθ = Ο‰ Γ— Ξ”t
Condition Result
v_r = v_l Straight line (Ο‰ = 0)
v_r = -v_l Rotate in place (v = 0)
v_r = 0 Arc curving left

Degrees of Maneuverability: Ξ΄M = Ξ΄m + Ξ΄s (range: 2–3) Holonomic: any direction instantly (Mecanum). Non-holonomic: direction constrained (car, diff drive).

MODULE 4 β€” Localization & Mapping

Q17(a): Odometry Error Model (8M) β€” ALL 4 papers

Definition: Localization by integrating wheel encoder velocity over time to estimate position. Also = dead reckoning.

Estimation equations:

Ξ”s = (Ξ”sR + Ξ”sL) / 2          (average displacement)
Δθ = (Ξ”sR - Ξ”sL) / L          (heading change)
Ξ”x = Ξ”s Γ— cos(ΞΈ + Δθ/2)
Ξ”y = Ξ”s Γ— sin(ΞΈ + Δθ/2)

4 Error Sources (exam β€” name all 4):

  1. Wheel slippage β€” wheels slip on surface; encoder counts rotation but robot didn’t move that far
  2. Unequal wheel diameters β€” manufacturing tolerances cause systematic drift over time
  3. Encoder resolution limits β€” discrete step size; quantization error in position measurement
  4. Surface irregularities β€” bumps/slopes cause unexpected motion not captured by encoders

Key limitation: Errors accumulate unboundedly over time. Cannot rely on odometry alone for long navigation.

Q17(b): SLAM (6M) β€” ALL 4 papers

Definition: Robot builds map of unknown environment while simultaneously localizing itself within that map.

SLAM variables:

  • X β€” robot path (sequence of poses over time)
  • M β€” map of environment (landmarks, occupancy grid)
  • U β€” odometry/control inputs
  • Z β€” sensor observations

Goal: Estimate P(Xβ‚œ, M | Z₁:β‚œ, U₁:β‚œ) β€” joint probability of path and map given all data.

SLAM Types Comparison:

Feature Visual SLAM Graph-Based SLAM Particle Filter SLAM
Input Camera images Any sensor Any sensor
Map type 3D feature points Pose graph Particle cloud
Key idea Feature tracking Nodes=poses, edges=constraints Multiple pose hypotheses
Loop closure Feature matching Graph optimization Resampling
Robustness Lower (needs texture) Higher Moderate

Particle Filter SLAM β€” 6 steps:

  1. Initialize N particles with random poses + equal weights
  2. Motion update β€” move each particle per odometry + noise
  3. Measurement update β€” weight each particle by sensor consistency
  4. Resampling β€” select particles proportional to weight
  5. Mapping β€” build map using highest-weight particles
  6. Iterate

Q18: Kalman Filter Localization (14M) β€” ALL 4 papers

Purpose: Optimal pose estimation from noisy odometry + noisy sensor observations. Maintains Gaussian belief (mean + covariance).

5-Step Process + Schematic:

β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”
β”‚  Initialize  β”‚ xΜ‚β‚€, Pβ‚€
β””β”€β”€β”€β”€β”€β”€β”¬β”€β”€β”€β”€β”€β”€β”˜
       ↓
β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”
β”‚   Predict    β”‚ x̂ₖ⁻ = Fβ‚–x̂ₖ₋₁ + Bβ‚–uβ‚–
β”‚ (Motion Upd) β”‚ Pₖ⁻  = Fβ‚–Pₖ₋₁Fβ‚–α΅€ + Qβ‚–
β””β”€β”€β”€β”€β”€β”€β”¬β”€β”€β”€β”€β”€β”€β”˜
       ↓
β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”
β”‚   Observe    β”‚ Get sensor measurement zβ‚–
β””β”€β”€β”€β”€β”€β”€β”¬β”€β”€β”€β”€β”€β”€β”˜
       ↓
β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”
β”‚   Update     β”‚ yβ‚– = zβ‚– - Hβ‚–x̂ₖ⁻           (innovation)
β”‚(Measurement) β”‚ Kβ‚– = Pₖ⁻Hβ‚–α΅€(Hβ‚–Pₖ⁻Hβ‚–α΅€+Rβ‚–)⁻¹  (Kalman gain)
β”‚              β”‚ xΜ‚β‚– = x̂ₖ⁻ + Kβ‚–yβ‚–            (corrected state)
β”‚              β”‚ Pβ‚–  = (I - Kβ‚–Hβ‚–)Pₖ⁻          (corrected covariance)
β””β”€β”€β”€β”€β”€β”€β”¬β”€β”€β”€β”€β”€β”€β”˜
       ↓ (loop back to Predict)

Variable meanings:

  • Fβ‚– = state transition matrix (motion model)
  • Bβ‚– = control input matrix; uβ‚– = control input (odometry)
  • Qβ‚– = process noise covariance; Rβ‚– = measurement noise covariance
  • Hβ‚– = observation matrix; zβ‚– = sensor measurement
  • Kβ‚– = Kalman gain β€” key: how much to trust sensor vs prediction

Key insight: High Kβ‚– β†’ trust sensor more. Low Kβ‚– β†’ trust model more.

MODULE 5 β€” Path Planning & Navigation

Q19(a): Dijkstra’s Algorithm (8M) β€” 3/4 papers

Purpose: Shortest path in weighted graphs. No heuristic.

Steps:

1. dist[start] = 0; dist[all others] = ∞
2. Mark all UNVISITED; put in priority queue
3. REPEAT:
   a. Pop node u with min distance
   b. Mark VISITED
   c. For each unvisited neighbor v:
      new_dist = dist[u] + edge(u,v)
      IF new_dist < dist[v]: dist[v] = new_dist
4. STOP when goal popped

Worked trace (5-node, exam-style):

Nodes: A(start)β†’E(goal)
Edges: A-B:4, A-C:2, B-C:1, B-D:5, C-D:8, C-E:10, D-E:2

        A
       / \
      4   2
     B─1─C
     |   |
     5   10
     |   |
     D─2─E
     (D-E:2, B-D:5, C-D:8)

Step 1: dist={A:0, B:∞, C:∞, D:∞, E:∞}
Step 2: Visit A β†’ B=4, C=2
Step 3: Visit C(min=2) β†’ B=min(4,3)=3, D=10, E=12
Step 4: Visit B(min=3) β†’ D=min(10,8)=8
Step 5: Visit D(min=8) β†’ E=min(12,10)=10
Step 6: Visit E(min=10) β†’ GOAL

Shortest path: A→C→B→D→E, cost = 10

Q19(b): Potential Field Path Planning (6M) β€” 3/4 papers

Concept: Robot = particle in force field.

  • Attractive force Fatt: pulls toward goal (increases with distance from goal)
  • Repulsive force Frep: pushes away from obstacles (increases near obstacles)
  • Net force: F = Fatt + Frep β†’ robot moves along gradient
U(q) = Uatt(q) + Urep(q)
F = -βˆ‡U(q)

Local Minima Problem: Robot trapped where Fatt = Frep (forces cancel). Not at goal, no net force to escape. Fix: Random walk or switch algorithm.

Advantages: Simple, reactive, no global planning. Disadvantages: Local minima, fails in narrow passages.

Q20(a): BFS vs DFS (4M Part A) β€” 2/4 papers

Property BFS DFS
Data structure Queue (FIFO) Stack (LIFO)
Exploration Level by level Branch depth-first
Completeness Yes Yes (finite)
Optimality Yes (unweighted) No
Memory O(b^d) β€” HIGH O(bd) β€” LOW
Best for Shortest path Memory-constrained

BFS algorithm: Enqueue start β†’ dequeue front β†’ enqueue unvisited neighbors β†’ repeat DFS algorithm: Push start β†’ pop top β†’ push unvisited neighbors β†’ repeat

Q20(b): Voronoi vs Visibility Graph (Apr25)

Property Voronoi Diagram Visibility Graph
Path type Safest (max clearance) Shortest
Method Points equidistant from obstacles Line-of-sight to obstacle corners
Safety High (far from all obstacles) Low (grazes corners)
Path length Longer than optimal Optimal
Best for Safety-critical Time-critical

Q20(c): Navigation Architectures (Jun23, May24)

Modular architecture:

Sensing β†’ Modeling β†’ Planning β†’ Execution

Horizontal decomposition: Divide by function layer (perception / reasoning / action) Vertical decomposition: Divide by abstraction level (reactive β†’ deliberative β†’ social)

A* Algorithm (Part A β€” know formula)

f(n) = g(n) + h(n)
  • g(n): actual cost from start to n
  • h(n): heuristic estimate from n to goal
  • f(n): total estimated path cost through n

Admissibility: h(n) must never overestimate β†’ guarantees optimal path. Vs Dijkstra: Dijkstra = h=0, explores all directions. A* = guided toward goal, faster.

PART A β€” Quick Reference (3 marks each)

Question Answer
Three Laws of Robotics 1: Protect humans. 2: Obey humans (unless violates 1). 3: Self-preserve (unless violates 1+2)
Sensor vs Transducer Transducer converts energy form. Sensor = Physical→Electrical type. All sensors are transducers.
Holonomic Can move any direction instantly (Mecanum/omnidirectional). Ξ΄m=3
Non-holonomic Direction constrained (car, diff drive). Cannot move sideways. Ξ΄m=2
Ξ΄M formula Ξ΄M = Ξ΄m + Ξ΄s (Maneuverability = Mobility + Steerability)
CCD vs CMOS CCD: analog, low noise, expensive. CMOS: digital, fast, cheap, more noise
SLAM applications Autonomous vehicles, drone mapping, warehouse robots
Robot localization Determining where robot is located w.r.t. its environment
Bug algorithm Move toward goal β†’ hit obstacle β†’ follow boundary β†’ when closest to goal, resume
A* formula f(n) = g(n) + h(n); h must be admissible (never overestimate)

Examiner’s Non-Negotiables

  1. Q15 (7 Stages of Vision) β€” Every paper. 2M per stage. Memorize all 7 + 2 lines each.
  2. Stepper vs Servo (Q14b) β€” Jun23, May24, Apr25. 3 straight years. Know 12-row table.
  3. Hall Effect (Q13b) β€” Jan24, May24. Fixed 8-mark scheme: diagram 3M + principle 3M + application 2M.
  4. Sensor Characteristics (Q13a) β€” 3/4 papers. Know all 7 traits + examples cold.
  5. Robot Configurations (Q11) β€” Every paper. Draw + label all 4 (PPP/RPP/RRP/RRR).
  6. Kalman Filter (Q18) β€” All 4 papers. Write 5 steps + schematic + Kalman gain equation.
  7. Odometry Errors (Q17a) β€” All 4 papers. Name all 4 error sources + derivation sketch.
  8. Dijkstra’s (Q19) β€” 3/4 papers. Trace 5-node graph step by step with distance table.

Last-Hour Checklist

  • 7 vision stages β€” write from memory
  • R1, R2, R3 rotation matrices β€” write from memory
  • Stepper vs Servo β€” 12-row table
  • Hall Effect β€” diagram + VH formula + 1 application
  • 7 sensor characteristics β€” name + definition + example
  • H-Bridge diagram + 4 switch states
  • PWM duty cycle waveforms + formula
  • Kalman 5 steps + gain equation
  • 4 odometry error sources
  • Dijkstra trace on 5-node graph
  • BFS vs DFS β€” 5-row comparison table
  • Potential field β€” attractive + repulsive + local minima problem
  • 4 robot configurations β€” draw + label
  • Anatomy diagram β€” 7 components labeled