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Exercise08 — Holonomic, Non-Holonomic, and Underactuated Interview Traps

Companion exercises for 05-holonomic-vs-non-holonomic.md

Estimated time: 30 minutes
Prerequisite: 05-holonomic-vs-non-holonomic.md, 04-navfn-vs-smac-search-spaces.md

Self-assessment guide: If you can separate motion constraints from actuation limits without mixing them up, you are answering like an engineer instead of guessing from buzzwords.

Overview

This exercise targets the questions that usually trip people up:

  1. Why is a car non-holonomic even though it can still reach many poses?
  2. Why is a quadrotor usually called underactuated rather than holonomic?
  3. Why does sideways motion matter so much in planning?

Section A — Fast Comparison Sheet

Term Main question Safe interview answer
Holonomic Can the robot move directly in each local direction allowed by its configuration? Yes, it can move instantaneously in all independent local DOFs that matter
Non-holonomic Are there velocity directions that are forbidden even though the pose may still be reachable later? Yes, local motion is constrained by heading or curvature
Underactuated Do I have fewer independent controls than the motion variables I care about? Yes, control authority is indirect or incomplete

Comparison checklist

Your comparison is strong if it separates:

  • motion constraints from control-input limitations
  • local feasible motion from eventual reachability

  • non-holonomic examples from underactuated examples

  • [ ] Done

Section B — Trap Questions with Model Answers

Question 1 — Why is a differential-drive robot non-holonomic?

Model answer:

  • Because it cannot generate lateral velocity directly.
  • Its instantaneous motion is tied to its heading.
  • It can rotate and move forward, but not slide sideways.

Question 2 — If it can still reach the pose eventually, why is that not holonomic?

Model answer:

  • Holonomy is about local feasible motion directions, not just final reachability.
  • A robot may reach the same pose through a sequence of maneuvers while still being unable to move there directly.

Question 3 — What is the most important mathematical clue for non-holonomic behavior?

Model answer:

  • A non-integrable velocity constraint, usually written in a form like A(q)qdot = 0.
  • The key point is that the constraint lives at the velocity level and cannot be reduced to a pure position constraint.

Question 4 — Why is a mecanum robot often treated as holonomic?

Model answer:

  • Because in the common planar model it can command translation in both planar directions plus rotation.
  • That means it can correct lateral error directly instead of maneuvering to do it.

Question 5 — Why is a quadrotor usually called underactuated rather than holonomic?

Model answer:

  • Because the important issue is that translational motion is achieved indirectly through thrust and attitude control.
  • The system has fewer independent direct controls than the full motion variables people care about.

Question 6 — Is underactuated the same thing as non-holonomic?

Model answer:

  • No.
  • Underactuation is about missing independent control inputs.
  • Non-holonomy is about motion constraints on feasible local velocities.

Question 7 — Why do non-holonomic robots need different planners?

Model answer:

  • Because free cells on the map are not enough.
  • The planner must also respect heading, turning radius, and sometimes reverse motion.

Question 8 — What is the clean one-sentence distinction?

Model answer:

  • A holonomic robot can move directly in every allowed local direction, while a non-holonomic robot must maneuver because some local velocity directions are forbidden.

Interview-answer checklist

Your interview answers are strong if they mention:

  • sideways motion as the easiest intuition test for non-holonomy
  • that non-holonomic does not mean unreachable, only locally constrained
  • that underactuated is a different axis from holonomic vs non-holonomic

  • a clean example for each category, such as mecanum, car, and quadrotor

  • [ ] Done

Section C — Scenario Questions

Scenario 1 — Docking correction

Two robots miss a docking pose by 15 cm to the left.

  • Robot A: mecanum base
  • Robot B: car-like platform

Questions:

  1. Which robot can correct laterally more directly?
  2. Which robot is more likely to need a re-approach?
  3. What concept is being tested here?

Scenario 1 Answer

  • The mecanum base can correct more directly.
  • The car-like platform is more likely to need a re-approach.

  • The concept is local motion feasibility: holonomic correction versus non-holonomic maneuvering.

  • [ ] Done

Scenario 2 — Interview trap: car vs quadrotor

An interviewer asks:

“Which one is non-holonomic: a car or a quadrotor?”

Best answer shape:

  1. What should you say about the car?
  2. What should you say about the quadrotor?
  3. Why is this a trap question?

Scenario 2 Answer

  • A car is the clean classical non-holonomic example because it cannot move sideways instantaneously.
  • A quadrotor is more cleanly described as underactuated in its full dynamic model.
  • It is a trap because it checks whether you confuse motion constraints with actuation structure.

Scenario checklist

Your scenario answers are strong if they identify:

  • which property is being tested in the scenario
  • why the car example is kinematic and the quadrotor example is actuation-related

  • what mistake the interviewer is hoping you make

  • [ ] Done

Practical Takeaway

Before choosing a planner or controller, ask:

  1. Can the robot translate directly in the direction of its error?
  2. Does heading constrain local feasible motion?
  3. Are the dominant limits kinematic, dynamic, or actuation-related?

That is how you avoid mixing up holonomic, non-holonomic, and underactuated systems.