The mechanism
A goal states a desired outcome or constraint. A plan describes a route or trajectory intended to reach it. An action executes over time and returns progress or a terminal outcome. These objects can fail at different boundaries: a goal may be unreachable, a path may collide, an initially valid path may become stale, or execution may fail to follow it. ROS 2 actions provide a long-running goal/feedback/cancellation interface, while a planning scene supplies robot and environment state for collision and constraint checks. Neither an accepted goal nor a successful planning call proves physical completion. The worked path bound below is deliberately simple. No motion planner or robot actuator runs in this lesson, and the bound is not a safety certificate.
- The goal names a target and its acceptable tolerance in a declared frame.
- Planning uses the current scene to find a path satisfying geometric and kinematic constraints.
- Execution follows a timed command and reports observed progress, not merely the planned coordinates.
- A changed obstacle or cancellation request is handled as a new event; completion is checked against actual state.
Science and assumptions
Goals, plans and actions are different objects · explicit relationship
Traversal time is at least path length divided by the maximum permitted speed.
Symbols and units
- T
- Traversal duration
s
- L
- Length of the chosen feasible path
m
- vmax
- Positive upper bound on path speed
m/s
A cart’s collision-free path is 2 m long and its speed is bounded by 0.5 m/s. Even with instantaneous acceleration and no pauses, traversal needs at least 4 s. A new obstacle forces a 2.5 m detour, raising that lower bound to 5 s. A plan computed before the obstacle appeared cannot be treated as currently collision-free. If cancellation is requested after motion begins, a later stopped state must be observed; the request itself does not prove zero velocity or erase the distance already traveled.
Assumptions A kinematic lower bound with no acceleration or stop-time model. It assumes the named path is feasible; it does not certify collision avoidance or physical safety.
Engineering example
A cart’s collision-free path is 2 m long and its speed is bounded by 0.5 m/s. Even with instantaneous acceleration and no pauses, traversal needs at least 4 s. A new obstacle forces a 2.5 m detour, raising that lower bound to 5 s. A plan computed before the obstacle appeared cannot be treated as currently collision-free. If cancellation is requested after motion begins, a later stopped state must be observed; the request itself does not prove zero velocity or erase the distance already traveled.
Distinctions and tradeoffs
Planning success or action acceptance is not evidence that a robot reached the goal.
Replanning can restore feasibility after scene changes but costs time and depends on sufficiently current observations.
Language or learned policies need a distinct planning and action boundary before their goals become motion.
Specifications and interfaces
- Mechanism boundary
- Why can an accepted plan still fail to reach its goal?
A kinematic lower bound with no acceleration or stop-time model. It assumes the named path is feasible; it does not certify collision avoidance or physical safety.
- Evidence type
- Authored worked example
Worked explanation with a bounded numeric or state example. This lesson does not claim an executing implementation of an external model or platform.
Interfaces
- Declared input and state Input
- The goal names a target and its acceptable tolerance in a declared frame.
- Checked outcome Output
- Distinguish accepted goals, feasible plans, executed motion and observed completion under explicit geometric and timing limits.
Check your understanding
A 2.5 m path has a 0.5 m/s speed limit. What is its ideal minimum traversal time?
- 1.25 s
- 5 s
- No time is needed once the goal is accepted
Answer and reasoning
5 s
Distance divided by the maximum speed gives a lower bound; acceleration and delays can only add time under these assumptions.
Evidence and scope
This is a worked explanation, not an executing external platform, model or robot. The quantities and fixtures are authored. Source scope is recorded in the automation learning review manifest; no source benchmark or private system behavior is claimed. A kinematic lower bound with no acceleration or stop-time model. It assumes the named path is feasible; it does not certify collision avoidance or physical safety.
The worked example explains this mechanism. General numerical labs are a reference; they do not execute this lesson’s full mechanism.