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Motion planning

The computational problem of finding a collision-free sequence of valid configurations connecting a system’s start and goal states.

Version
v1 · 2026-09-08 · History
Domain-specific #
5673
Origin domain
robotics and computational geometry
Subdomain
robotics and computational geometry
Aliases
Path planning, Piano mover’s problem

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

  1. 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

Local relationship map for Motion planningParents appear above the current abstraction, mutual partners to the right, and children below. Node labels state whether each abstraction is prime or domain-specific; colors identify relation types.Motion planningDOMAINPrime abstraction: Planning — is a kind ofPlanningPRIME

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.

Hierarchy path (1) — routes to 1 parentless root

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

Computed from structural-signature embeddings · 2026-09-08