Motion planning¶
The computational problem of finding a collision-free sequence of valid configurations connecting a system’s start and goal states.
Core Idea¶
The carrier is configuration space rather than raw workspace, feasibility differs from optimality, kinodynamic variants add differential constraints and a planned path does not guarantee safe real-world execution under model error. Obstacles and constraints carve forbidden regions from configuration space; a search, sampling or optimization method connects start to goal through the remaining free region and may then parameterize the path in time. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.
Scope of Application¶
Motion planning belongs to robotics and computational geometry and is useful where the analyst can specify the typed robotics and computational geometry carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, then evaluate the moving system and degrees of freedom, configuration space, start and goal sets, obstacle geometry and collision model, free-space and validity constraints, kinematic or dynamic transition model, path or trajectory representation, feasibility and completeness, cost objective and optimality, uncertainty and execution boundary are explicit.
Clarity¶
The abstraction clarifies a crowded vocabulary by making the moving system and degrees of freedom, configuration space, start and goal sets, obstacle geometry and collision model, free-space and validity constraints, kinematic or dynamic transition model, path or trajectory representation, feasibility and completeness, cost objective and optimality, uncertainty and execution boundary are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test.
Manages Complexity¶
Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Motion planning. Motion planning compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.
Abstract Reasoning¶
- Identify the carrier. State what the elements, states, objects, or observations are: the typed robotics and computational geometry carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the moving system and degrees of freedom, configuration space, start and goal sets, obstacle geometry and collision model, free-space and validity constraints, kinematic or dynamic transition model, path or trajectory representation, feasibility and completeness, cost objective and optimality, uncertainty and execution boundary are explicit independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of robotics and computational geometry because they reuse the typed robotics and computational geometry carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, Obstacles and constraints carve forbidden regions from configuration space; a search, sampling or optimization method connects start to goal through the remaining free region and may then parameterize the path in time., and type the carrier, state every parameter and convention in the definition, test that the moving system and degrees of freedom, configuration space, start and goal sets, obstacle geometry and collision model, free-space and validity constraints, kinematic or dynamic transition model, path or trajectory representation, feasibility and completeness, cost objective and optimality, uncertainty and execution boundary are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Motion planning Domain-specific
Parents (1) — more general patterns this builds on
-
Motion planning is a kind of Planning Prime
The proposed strict upward parent is
prime:planning.
Neighborhood in Abstraction Space¶
Motion planning sits in a crowded region of the domain-specific corpus (34th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.
Family — Convex Geometry & Spatial Partition (35 abstractions)
Nearest neighbors
- Curve — 0.91
- Kinematic diagram — 0.91
- Visibility (geometry) — 0.90
- Line–line intersection — 0.90
- Automated planning and scheduling — 0.90
Computed from structural-signature embeddings · 2026-09-08