Control Engineering Primer
PID, state-space, optimal control, path planning, and trajectory generation connected to robot and autonomous-vehicle implementation.
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Articles · 6Browser Labs · 8
Read the first step: Control Engineering Primer: PID Control — Working Across Three Time Scales →Background and reading guide Basic functions, calculus and vectors; follow the definitions alongside the equations.
- Articles · Fundamentals · 7 min
Control Engineering Primer: PID Control — Working Across Three Time Scales
PID is not merely three gains. This primer connects its intuition and equations to sampling, saturation, anti-windup, tuning, safety, ROS 2, and real implementation checks.
Background and reading guide
Basic functions, calculus and vectors; follow the definitions alongside the equations.
- Browser Labs · Hands-on · 2 min
Experiment with PID in Python — gains, delay and saturation
Reproduce how measurement delay, actuator limits and integral windup change PID tracking on the same second-order model.
Background and reading guide
The roles of P, I and D. The browser Lab requires no Python installation.
- Articles · Fundamentals · 5 min
Control Engineering Primer: State Observers and the Linear Kalman Filter
Sensor readings are not the state itself. This primer explains observability, Kalman predict/update equations, covariance, numerical examples, control integration, robot implementation, and fault-safe behavior.
Background and reading guide
Basic functions, calculus and vectors; follow the definitions alongside the equations.
- Browser Labs · Hands-on · 3 min
Run a Kalman filter in Python: noise, missing data and outliers
Compare Q, R and outlier gating on one synthetic trajectory using estimation error and rejected observations.
Background and reading guide
Matrix multiplication and the prediction/update outline of a Kalman filter.
- Articles · Fundamentals · 5 min
Control Engineering Primer: LQR — State Feedback From Explicit Priorities
LQR derives state-feedback gains from a state-space model and a quadratic cost. This primer covers Riccati equations, observability, PID/MPC tradeoffs, robot implementation, numerical intuition, and safety.
Background and reading guide
Basic functions, calculus and vectors; follow the definitions alongside the equations.
- Articles · Fundamentals · 6 min
Control Engineering Primer: Model Predictive Control — Acting Within Constraints
Model Predictive Control predicts future behavior with a model, optimizes a constrained input sequence, applies only its first move, and repeats. This primer covers equations, tuning, safety, implementation, and current examples.
Background and reading guide
Basic functions, calculus and vectors; follow the definitions alongside the equations.
- Articles · Fundamentals · 5 min
Control Engineering Primer: Path Planning — A*, Dijkstra, RRT, RRT*, and PRM
Path planning is not drawing a shortest line. This primer compares grid and continuous-space algorithms while accounting for robot footprint, map uncertainty, computation, SLAM/Nav2 integration, and safety.
Background and reading guide
Basic functions, calculus and vectors; follow the definitions alongside the equations.
- Articles · Fundamentals · 4 min
Control Engineering Primer: Trajectory Generation — Minimum Jerk, Quintics, and Trapezoidal Profiles
A path says where to travel; a trajectory says when and with what velocity, acceleration, and jerk. This primer covers minimum-jerk, quintic, trapezoidal profiles, constraints, safety, and ROS 2 integration.
Background and reading guide
Basic functions, calculus and vectors; follow the definitions alongside the equations.
- Browser Labs · Hands-on · 3 min
Pure Pursuit Lab — compare fixed-lookahead path tracking
Change fixed lookahead and inspect tracking error, steering and targets on a shared vehicle model.
Background and reading guide
Basic angles, distances and speed. No Python installation required.
- Browser Labs · Hands-on · 3 min
Adaptive Pure Pursuit Lab — scale lookahead with speed
Compare speed-scaled lookahead with PP, including acceleration and minimum/maximum bounds.
Background and reading guide
Basic angles, distances and speed. No Python installation required.
- Browser Labs · Hands-on · 4 min
Regulated Pure Pursuit Lab — speed through curves and near the goal
Separate lookahead from speed regulation and compare curvature limits, speed floors, final approach and actual vehicle speed.
Background and reading guide
PP/APP and basic distance/speed. No Python installation required.
- Browser Labs · Hands-on · 3 min
Stanley Lab — steering from front-axle cross-track and heading error
Separate front and rear axle errors and compare gain, speed and steering constraints in your browser.
Background and reading guide
Basic distance, angles and vehicle models. No Python installation required.
- Browser Labs · Hands-on · 4 min
MPC Lab — re-solve a curvature sequence within a horizon and steering limits
Change the horizon, weights and steering limit, and compare predicted paths, solver convergence and failure handling in your browser.
Background and reading guide
Basic distances, angles and vehicle models. Matrices and optimisation help with the equations. No Python installation required.
- Browser Labs · Hands-on · 3 min
Path-tracking comparison Lab — run PP, APP, RPP, Stanley and MPC under the same conditions
Run five trackers together on one vehicle, path, initial state and steering limit, and compare cross-track error, smoothness and completion with shared metric definitions.
Background and reading guide
Reading the PP, Stanley and MPC Labs first makes the results easier to interpret. No Python installation required.