LoGoPlanner: Logic & Geometry Planning

• LoGoPlanner is an integrated framework that leverages logic and geometry to optimize planning, control, and decision-making in logistics, manipulation, and navigation domains.
• The framework utilizes knowledge graphs, Answer Set Programming, and multi-objective optimization to handle dynamic system constraints and uncertainty.
• Recent advancements incorporate metric-aware visual navigation, employing transformer-based models and diffusion strategies to enhance real-world robotic performance.

LoGoPlanner refers to a suite of frameworks and algorithms that leverage logic and geometry in the context of planning, optimization, and control for complex systems—especially in logistics, robotic manipulation, and embodied navigation domains. Across the literature, the term “LoGoPlanner” is associated with three main paradigms: (i) declarative logistics optimization with semantic knowledge graphs and Answer Set Programming (ASP), (ii) logic-geometric task and motion planning under uncertainty (as “Logic-Geometric Planner”), and (iii) localization-grounded end-to-end navigation policies with metric-aware visual geometry. Each instantiation operationalizes logic at the core of system representation and encapsulates geometry as a first-class optimization or inference principle.

1. Declarative Logistics with Knowledge Graphs and ASP

The LoGoPlanner framework for logistics is designed to model, optimize, and visualize supply chain architectures in industrial co-design environments, where requirements and system constraints are continuously evolving. The architecture comprises four primary modules:

1. Knowledge-Graph Extraction: Facts describing entities (e.g., countries, production sites, transport means) and their interrelations are encoded as RDF triples in an ontology (MarkLogic triple store), queried via SPARQL, and exposed through a JSON REST API. JSONata transformations convert these results into ASP fact syntax (Dietz et al., 2023).
2. ASP Translation and Grounding: Extracted facts are combined with a fixed library of ASP rules encoding logical, structural, and integrity constraints (choice, assignment, sourcing, transportation, etc.). The clingo solver performs grounding and computes stable models subject to optimization criteria.
3. Optimization: Objective functions—such as minimizing total transport distance, cost, or resilience penalties—are encoded in ASP via #minimize statements. The solver explores multi-objective trade-offs, leveraging lexicographic optimization or Pareto front enumeration.
4. Result Visualization: Solutions (stable models) are exported (CSV) and rendered in an interactive Dash+Plotly web application, presenting scatter-matrix KPIs and world-map visualizations of chosen logistics plans.

This pipeline is tightly integrated with CI/CD infrastructure: any ontology update (e.g., site, transport route, or metric modifications) triggers a regeneration and reoptimization sequence, propagating changes automatically from semantic data source to visual solution dashboard.

2. Knowledge Graph Structure and Extraction Mechanisms

The knowledge graph central to LoGoPlanner logistics encodes object classes (OWL): Country, ProductionLocation, WarehouseLocation, Part, and TransportMean; object properties: locatedIn, partProduceableAt, transportMeanAtSite, transportRoute, productionPlan; and numeric attributes (e.g., distance, capacity). The data acquisition workflow involves:

• Manual or semi-automated population (spreadsheets, subject-matter interviews, protégé editing)
• Reasoning with SWRL to materialize inverse relations and enforce domain/range semantics (validated by SHACL)
• Automated pipelines (Jenkins) for consistency checking, data enrichment, and re-deployment to the triple store

Each queryable configuration is transformed into ASP ground facts for logical optimization (Dietz et al., 2023).

3. Logic Program Encoding and Optimization in ASP

The ASP encoding prescribes both the permissible solution space and the optimization landscape:

• Facts enumerate entities and relationships (e.g., country(aCountry), transportRoute(aH,bH,ship,7)).
• Rules formalize the domain structure (location identification, transport symmetry, routability), including multi-hop route construction and production plan dependencies.
• Choice Rules enforce assignment constraints (e.g., each part is produced at exactly one viable location, sourcing multiplicity for resilience).
• Integrity Constraints ban undesirable solutions (such as double-sourcing from the same country).
• Optimization Directives (via #minimize) enable linear aggregation of KPIs; distances, costs, and resilience penalties are computed as explicit functions over solution assignments.

Multi-objective optimization is implemented by stacking minimization statements in a user-specified order or by Pareto front enumeration. A concrete example demonstrates assignment, routing, and cost minimization for an instance with 4 parts, 3 production sites, and multiple transport means. The canonical output consists of stable models specifying part-site assignments, multihop routing, and metric evaluations (Dietz et al., 2023).

4. Logic-Geometric Planning under Uncertainty

A distinct line, denoted LoGoPlanner (“Logic-Geometric Planner”), extends logic-geometric programming (LGP) for uncertain, constrained manipulation and hybrid planning. Here, the methodology integrates:

• Logic Layer: Encodes discrete contact/tool-use modes as sequences (“skeletons”) specifying abstract actions (e.g. grasp, touch, push).
• Geometric Layer: For each skeleton, a smooth trajectory optimization is performed under imposed path and switch constraints derived from the logic plan.

In stochastic settings, the framework interprets planning as inference: the posterior trajectory distribution, conditioned on the logic profile, is approximated as a mixture of Gaussians, each component corresponding to a logic skeleton. Optimizing controller design involves:

• High-level logic search for promising skeletons (A*, greedy, pruning)
• For each, constrained NLP trajectory optimization, Laplace approximation for covariance, and mixture model assembly
• On-line execution by blending or switching among locally linear feedback controllers, with mode weights adapting to observations/disturbance

A major implication is the ability to trade off efficiency versus robustness dynamically: modes exploiting contact or redundancy are favored under high uncertainty due to their smaller posterior volume, as seen in both toy and complex manipulation scenarios (Ha et al., 2020).

5. Localization-Grounded Visual Navigation

Recent work adapts the LoGoPlanner paradigm to end-to-end navigation policy learning, specifically for mobile robots in unstructured environments (Peng et al., 22 Dec 2025). The framework features:

• Visual-Geometry Backbone: A Video Geometry Grounded Transformer (VGGT) that encodes sequences of RGB and depth frames into metric-aware patch embeddings using intra- and inter-frame multi-head attention (with RoPE), explicitly preserving metric scale.
• Metric-Aware Geometry Reconstruction: Auxiliary heads regress local 3D points and camera-to-world transforms per frame. Multi-frame features are aggregated into a latent world-point representation, decoded into dense metric point clouds.
• Policy Conditioning: Implicit localization is performed by predicting the robot’s chassis pose and goal in local coordinates directly from the visual features, without external calibration or SLAM. Policy input combines state and geometry queries cross-attended to pose/point tokens; outputs are synthesized via a denoising diffusion model to generate a collision-free trajectory.

The approach is jointly trained with metric-scale odometry and point reconstruction losses, leveraging large-scale visual-trajectory data. In simulation, the system yields a consistent 27.3% success-rate improvement over strong oracle-localization baselines and exhibits robust generalization to novel spaces and embodiments. Ablations demonstrate the necessity of metric grounding and auxiliary tasks for optimal performance (Peng et al., 22 Dec 2025).

6. Performance, Visualization, and Application Domains

LoGoPlanner exhibits high scalability and practical deployment characteristics across modalities:

• The logistics pipeline manages industrial-scale knowledge graphs (e.g., 29 locations, 34 parts, over 2,600 choice-points), with solver optimizations reducing inference latency from minutes to seconds.
• Visualization modules provide interactive dashboards, scatter-matrix KPI exploration, and geospatial mapping of plan instances, streamlining co-design iteration.
• In manipulation, the logic-geometric mixture approach enables responsive adaptation to disturbances and selection of robust contact modes based on likelihood feedback.
• For navigation, metric-consistent embedding and geometry memory directly elevate performance in both simulation and real-world robotic agents.

Supported application domains include supply chain optimization under volatility, automatic re-planning in collaborative engineering, resilient manipulation in uncertain or contact-rich settings, and mobile navigation in human-centric environments (Dietz et al., 2023, Ha et al., 2020, Peng et al., 22 Dec 2025).

7. Integration with Broader Research and Benchmarks

LoGoPlanner’s methodologies intersect with broader logic-based planning and reasoning benchmarks. For example, the LogiPlan framework (Cai et al., 12 Jun 2025) probes the logical planning and consistency verification capabilities of LLMs via relational graph generation, cycle detection, and path inference under tight structural constraints. While not a direct implementation, LogiPlan’s formulation of logical acyclicity, plan instance generation, and multi-relational query answering parallels core LoGoPlanner abstractions, further indicating the relevance of logic-geometric composition and optimization techniques in the evaluation and advancement of both symbolic AI and embodied intelligence.

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References:

• "A Logic Programming Approach to Global Logistics in a Co-Design Environment" (Dietz et al., 2023)
• "Probabilistic Framework for Constrained Manipulations and Task and Motion Planning under Uncertainty" (Ha et al., 2020)
• "LoGoPlanner: Localization Grounded Navigation Policy with Metric-aware Visual Geometry" (Peng et al., 22 Dec 2025)
• "LogiPlan: A Structured Benchmark for Logical Planning and Relational Reasoning in LLMs" (Cai et al., 12 Jun 2025)