Planning & Control¶
What this page solves
Planning answers "which route and which trajectory"; control answers "how to correct errors while executing". This is the most classical, interpretable part of robotics and the baseline learned policies are compared against. Required at entry level; your feedback-control and system-identification background transfers directly.
How far to go¶
| Level | Learn | Done when |
|---|---|---|
| Orientation | Paths vs trajectories, planning vs control, open vs closed loop | Explain "choosing a route" vs "correcting execution error" |
| Foundation | A*, PID and trajectory tracking | E1 and one E2 experiment done, with failures reported |
| Advanced | Sampling planners, trajectory optimisation, MPC, force / impedance control, whole-body control | Go deep on one, chosen by body and task |
Core knowledge¶
Paths and trajectories: a path is a geometric sequence of points; a trajectory adds time (velocity, acceleration). Planners usually find a collision-free path first, then time-parameterise it within velocity and acceleration limits.
Search-based planning: A* finds shortest paths on grids or graphs and is optimal if the heuristic never overestimates. Great for 2D navigation; the state space explodes in high dimensions.
Sampling-based planning: RRT and PRM sample the continuous space and connect samples into a tree or graph — suited to high-dimensional arm configuration spaces; RRT* is asymptotically optimal. Results need smoothing.
Trajectory optimisation: treat the trajectory as decision variables, minimise a cost (time, energy, smoothness) under constraints (collision, joint limits). CHOMP and TrajOpt are typical; sensitive to initialisation.
Feedback control: PID acts on the error, its integral and its rate — the most common baseline. Trajectory tracking = feed-forward (from the desired trajectory) + feedback (correcting deviation).
Model predictive control (MPC): each cycle, predict ahead with a model, solve a constrained optimisation online, execute only the first step, re-solve next cycle. Handles constraints explicitly at a computational cost; used widely in legged robots and autonomous driving.
Force and impedance control: contact tasks (peg-in-hole, wiping) cannot be position-controlled alone. Impedance control makes the end-effector behave like a spring-damper, compliant on contact instead of pushing hard.
Whole-body control: humanoids and legged robots must satisfy balance, contacts and several task goals at once, often as a prioritised quadratic programme.
Debate · model-driven vs. learning-driven¶
Model-driven (planning + MPC) is interpretable, enforces safety constraints and needs little data, but requires accurate models and struggles with complex contact and perception uncertainty. Learning-driven (imitation, RL) captures behaviours that are hard to model, but needs lots of data and fails opaquely. The trend is layering: learning decides what to do, model-based controllers do it safely.
Curated resources¶
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Main course · Modern Robotics
Ch. 9 trajectories, ch. 10 motion planning, ch. 11 control (incl. force control); pick chapters by task.
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Example library · PythonRobotics
Small visual examples of A*, RRT, MPC and more; each runs as is and is easy to modify.
Follow-along experiments¶
Self-check¶
Why must the A* heuristic not overestimate?
Overestimating can make the search abandon the truly optimal path early, losing the optimality guarantee; an admissible heuristic guarantees the shortest path.
Why do arm planners use RRT rather than A*?
Arm configuration spaces are 6–7 dimensional; gridding them explodes exponentially, while sampling never discretises the whole space.
Advantages and costs of MPC over PID?
Advantages: explicit constraints, prediction with a model, multivariable coordination. Costs: needs a model and an optimisation every cycle, heavy computation and tight real-time demands.
Why do contact tasks need impedance control?
Pure position control turns small position errors into large contact forces that can damage the part or the robot; impedance control makes force proportional to deviation, so contact is compliant.