Controls is the implementation, in terms of actuator efforts, of a motion plan

Definition of Plan

A plan is often of 2 forms in trajectory planning

1. Time-scaled trajectory

Our time parameter $t$ is the timestamp reaching the indicated states

• can visualise this as a key-framed timeline
• place keyframes on timestamps and note the desired state at that time

1. Index-parameterised trajectory

Our index parameter $\tau$ is simply a scalar $\in [0,1]$

• not time dependent
• index can be understood as a “completeness” of the plan

Feedback Control

We need feedback or close-loop control as…

• our environment and agent is noisy —> the measurements and actions we take are never perfect
• we need a way to detect how off we are from the target (plan)

<aside> 👉 There are 2 key steps to feedback control

1. Measure error between reference and current state
2. Take actions to minimise this error.

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