Robotics Basics: From Measurements to Motion
Published:
Start with one ordinary task
Intuition first. Ask an arm to pick up a cup. “Pick it up” is a task description. The hardware needs commands such as joint-position targets, velocities, or torques. Between those two levels lie questions about where the cup is, how to reach it, and whether the fingers have actually made contact.
A successful system must connect the meanings of those commands to measurements from the real robot. A neural network does not remove that requirement.
The minimum vocabulary
| Term | Meaning | Example |
|---|---|---|
| Configuration | Coordinates describing the robot’s arrangement | Joint angles \(q\) |
| State | Information needed to model its evolution | Positions and velocities |
| Observation | Sensor information available to the system | Images and encoder readings |
| Pose | Position and orientation relative to a frame | Gripper pose in the base frame |
| Trajectory | Desired motion with timing | A gripper path traversed in two seconds |
| Control input | Command acting on the system | Joint torque or velocity target |
A path specifies geometric motion without necessarily specifying when each point is reached. A trajectory adds timing. A control law uses the current information to produce commands. The Modern Robotics course develops these distinctions.
A minimal mathematical model
A discrete-time description is
Here \(x_t\) is physical state, \(u_t\) the input, \(y_t\) the measurement, and \(w_t,v_t\) represent disturbances and measurement noise. A controller acts on measurements or an estimated state, not necessarily on the exact \(x_t\) used by a simulator.
Worked example: an action needs units and a duration
Suppose a one-dimensional robot is at 0.40 metres and receives a velocity command of 0.10 metres per second for 0.20 seconds. Under an ideal constant-velocity model,
The number 0.10 would mean something entirely different if the interface expected a position target in metres. A policy can output numerically plausible values and still be incompatible with the controller receiving them.
The ideal model also ignores acceleration and disturbances. A fresh measurement tells the system whether the expected displacement actually occurred.
Where learning enters
A learned perception model can estimate cup pose from an image. A learned dynamics model can predict consequences of candidate commands. A policy can imitate demonstrated actions or improve through reward feedback. These choices place learning at different interfaces; none is automatically required for every component.
For example, a learned policy might provide joint targets at a lower frequency while a conventional feedback controller tracks them more frequently. Evaluate both the high-level decisions and the tracking behaviour.
Read the foundations before the paper chapters
- Kinematics and frames: relate joints to gripper motion.
- Sensors and state estimation: turn imperfect measurements into useful information.
- Dynamics and feedback: understand how commands produce and correct motion.
- Robot-learning basics: compare demonstrations, rewards, and learned models.
These prepare learned MPC, residual RL, rapid motor adaptation, and ACT.
References
- Lynch, K. M., & Park, F. C. Modern Robotics: course and book resources.
- Tedrake, R. Underactuated Robotics: Introduction.