Lesson 07 · Book chapter pointer
Sensors
Read the chapter source: sensors.tex — do not treat this note as the book.
Learning goals
- Split proprioceptive from exteroceptive sensing without hand-waving.
- Name the quantity a sensor actually measures versus the quantity you wanted.
- Treat noise, bias, quantization, and bandwidth as part of the spec.
- Place encoders, IMUs, range sensors, and cameras on one comparison board.
- Explain why global pose sensors do not retire the rest of the stack.
Teaching note
Sensors are not oracles. They are transducers with a favorite quantity, a bandwidth, a bias, and a way of failing that looks like confidence. Proprioceptive sensors watch the robot: encoders, current sense, IMUs bolted to the chassis. Exteroceptive sensors watch the world: cameras, lidars, bump switches, GPS. The classification is about the source of the signal, not about how expensive the part was. A camera used as an optical mouse is still looking outward.
The teaching move is to force a sentence of the form “this device measures X and I will infer Y.” An encoder measures angle (or ticks). You infer wheel travel only after you assume a radius and no slip. An IMU measures proper acceleration and angular rate. You infer attitude only after you integrate and fight bias. A lidar measures time of flight along rays. You infer occupied space only after you assume the beam hit the thing you think it hit.
Noise is not a moral failing. It is a budget. White-ish noise you can average if you have time. Bias you cannot average away; you must estimate it or calibrate it. Quantization is the grid the world is forced onto. Saturation is a lie that looks like a number. Bandwidth is how late the truth arrives. When a student says “the IMU is bad,” ask which of those words they mean.
Global pose — GPS, motion-capture, a lighthouse — is a gift that disappears the moment you enter a warehouse, a forest, or a cheap indoor lab. Use it to grade your estimator, not to skip learning one. The later uncertainty chapters are what you do when the gift is gone.
A single lab beats a catalog: log wheel ticks, IMU yaw rate, and a tape-measure ground truth down a hallway. Plot odometry vs truth. The residual is slip, scale, and time sync. That plot is the first page of localization. Then go read the book chapter for operating principles and the sensor zoo this note will not reprint.
A useful sensor model is \(z = h(x) + v\), with \(v\) described — not merely “small.” If you cannot write \(h\), you are not measuring what you think.