Graph-Assisted Trajectory Stitching

• Graph-assisted trajectory stitching is a method that uses graph structures to reconstruct and optimize trajectories by integrating dynamic, spatial, and logical constraints.
• It employs diverse graph constructions such as latent, motion primitive, and spatio-temporal observation graphs for robust long-horizon planning and real-time applications.
• Empirical evaluations in hierarchical RL, robot navigation, and tracking demonstrate significant gains in efficiency, accuracy, and constraint satisfaction.

Graph-assisted trajectory stitching refers to a class of methodologies that leverage explicit or implicit graph structures to reconstruct, synthesize, or optimize trajectories by recombining fragments or primitives, subject to constraints dictated by dynamics, logical specifications, spatial topology, or contextual signals. This paradigm enables robust long-horizon reasoning, efficient offline learning, real-time constrained planning, and principled imputation of missing data in diverse domains such as hierarchical reinforcement learning, robot navigation, multi-object tracking, and map-constrained trajectory recovery.

1. Foundations and Methodological Variants

Graph-assisted stitching encompasses several methodological axes, characterized by the underlying domain and the nature of the graph abstraction:

• Latent/semantic graphs: In hierarchical RL and logic-constrained planning, nodes correspond to embeddings of dynamical states or subgoals, with edges representing feasible transitions parameterized by temporal or spatial step cost. Classical examples include the Temporal Distance Representation (TDR) graphs in GAS and the latent reachability graphs in SAGAS (Baek et al., 9 Jun 2025, Liu et al., 30 Nov 2025).
• Motion primitive graphs: In real-time geometric and kinodynamic motion planning, graphs are defined over spatial waypoints, velocity, and control samples. Nodes encode partial dynamical states, and edges correspond to closed-form optimal-control motion primitives; trajectories are stitched by traversing such graphs (Levy et al., 30 Dec 2024, Levy et al., 16 Oct 2025).
• Spatio-temporal observation graphs: In tracking and map matching, segments of observations (detections, GPS points) are nodes, while edges encode spatial or temporal consistency, similarity, or admissible continuation. Bayesian inference or encoder-decoder networks are employed for partitioning/matching to generate global trajectories (Lin et al., 2015, Wei et al., 29 Apr 2024).

A commonality across these domains is the explicit separation of fragment-level dynamics (often via low-level policy or closed-form integration) from high-level global composition (determined by graph search, combinatorial matching, or logic-constrained planning).

2. Graph Construction Principles

The graph construction process is highly domain-specific, but several general themes emerge:

• Embedding-based State Abstractions: Offline RL methods rely on learning a state embedding ψ: S→ℋ so that Euclidean distances reflect optimal temporal or spatial reachabilities. For example, GAS and SAGAS employ expectile-based IQL critics to train ψ such that $d^*(s, g) \approx ||\psi(s) - \psi(g)||_2$ accurately approximates the minimal number of steps under the optimal policy (Baek et al., 9 Jun 2025, Liu et al., 30 Nov 2025).
• High-Quality Node Selection: A key innovation is the Temporal Efficiency (TE) filter in GAS, where only data points whose empirical transitions closely mirror the optimal (minimal TDR cost) direction are retained. This drastically reduces graph complexity while maintaining reachability (Baek et al., 9 Jun 2025).
• Clustering and Connectivity: Selected states are clustered (e.g., sequentially in TDR space) at intervals proportional to a temporal horizon, forming graph nodes with controlled neighborhood density (edges between node pairs within a TDR distance threshold). In motion-plan graphs, states are defined as tuples of spatial and dynamical variables, connected if a closed-form primitive can bridge the gap within constraints (Levy et al., 30 Dec 2024).
• Semantic and Contextual Augmentation: For logical or task-aware planning, clusters are augmented with certified anchor nodes (e.g., states corresponding to specific propositions in an LTL task) and soft probabilistic labels denoting the likelihood of satisfying task-relevant predicates (Liu et al., 30 Nov 2025). In trajectory recovery for intelligent transportation, both micro (within-trajectory) and macro (city-level road-flow) graphs inform candidate set pruning and context-aware decoding (Wei et al., 29 Apr 2024).

3. Planning and Trajectory Stitching Algorithms

The “stitching” procedure can be described as a graph search or optimization problem, subject to problem-specific objectives:

• Shortest-Path and Subgoal Planning: The canonical RL approach, as in GAS, applies Dijkstra or A* search in the subgoal graph to select optimal sequences of latent subgoals; a trained low-level policy π_low(a | s, h_dir) is then conditioned on the direction in latent space to reach each subgoal (Baek et al., 9 Jun 2025).
• Logic-Constrained Planning: In SAGAS, the product of the latent reachability graph and a Büchi automaton encoding an LTL specification is searched (on the fly) via A* for prefix-suffix plans. Safety and satisfaction constraints are enforced by soft labels and anchor connectivity within the graph (Liu et al., 30 Nov 2025).
• Motion Primitive Sequencing: In STITCHER, a three-stage pipeline constructs a waypoint graph, a velocity graph, and then a full motion-primitive graph. Real-time A* search over this graph yields a sequence of parameterized closed-form primitives, “stitching” feasible segments into complete trajectories that strictly satisfy dynamic, actuation, and collision constraints (Levy et al., 30 Dec 2024, Levy et al., 16 Oct 2025).
• Probability-Driven Chunk Matching: In tracking or map-based estimation, MCMC-based inference matches blobs or trajectory fragments over time, with overlapping windows to “stitch” interrupted tracks based on appearance, motion, and shape priors (e.g., for occlusion handling in vision tracking (Lin et al., 2015)).
• Graph-Based Decoding: For GPS imputation, graph convolutional encoder-decoders (e.g., MM-STGED) combine micro-trajectory graphs and macro-flow graphs, using context and candidate masking derived from road-network constraints and collective patterns to decode plausible intermediate points that “stitch” sparse segments (Wei et al., 29 Apr 2024).

4. Constraint Handling and Feasibility Guarantees

Trajectory stitching must respect numerous constraints, statically or during planning:

• Dynamical and Actuation Constraints: Motion-primitives in STITCHER (double or triple integrators, jerk-limited) are constructed so that each candidate edge admits only those primitives satisfying velocity, acceleration, jerk, thrust, and actuator bounds. Violations are pruned during graph expansion (Levy et al., 30 Dec 2024, Levy et al., 16 Oct 2025).
• Semantic Goal and Safety Constraints: In SAGAS, forbidden task conditions are enforced by pruning product-graph edges whose associated soft-labeled nodes have high likelihood of violating safety or logic constraints, exploiting anchor verification during execution to guarantee task satisfaction (Liu et al., 30 Nov 2025).
• Spatial-Topological Constraints: In map-matching, graph maskings ensure decoded segments follow road connectivity, leveraging flow graphs and contextual representation to encode population-level traversal priors (Wei et al., 29 Apr 2024).
• Global Consistency and Fragment Re-linking: Swendsen–Wang-style cluster moves and shape priors enforce consistent, non-fragmented reconstructions in tracking, ensuring that occlusions or gaps are not misidentified as trajectory terminations (Lin et al., 2015).

5. Empirical Evaluations

Graph-assisted trajectory stitching yields substantial empirical gains across domains:

Method/Domain	Empirical Highlights	Reference
GAS (HRL, AntMaze)	Score 88.3 (giant-stitch) vs 1.0 prior SOTA; up to 10–18 pt performance boost via TE filtering	(Baek et al., 9 Jun 2025)
STITCHER (Quadrotor, UAV)	1–15 ms planning per 30–60 m, 10–400× faster than MIQP/penalty methods, no constraint violations	(Levy et al., 30 Dec 2024)
MM-STGED (GPS recovery)	+4–6 pp accuracy, −20–50m MAE vs. RNTrajRec and others; ablations confirm superiority of graph priors	(Wei et al., 29 Apr 2024)
SAGAS (LTL, AntMaze)	SR=91.0% vs. decoupled 83.0%, ~12% shorter trajectory length; hard LTL tasks satisfied in offline RL	(Liu et al., 30 Nov 2025)
Tracking (Video)	Recall up to 91.3%, switch IDS reduced on PETS/LHI datasets; 3–5× faster convergence vs. naive Gibbs MCMC	(Lin et al., 2015)

Stitching-centric approaches uniformly enable tasks previously infeasible with either monolithic policy training or online optimization alone (long-horizon RL, real-time replanning, occlusion-robust tracking, map-constrained interpolation).

6. Limitations and Future Directions

Current limitations include:

• Pixel-based representations: Performance in RL domains with raw image state remains inferior, attributed to representation learning limitations; more expressive contrastive or attention-based encoders are proposed (Baek et al., 9 Jun 2025).
• Manual hyperparameter selection: Graph-connectivity parameters (e.g., H_TD) typically require sweeping; future directions include adaptive or data-driven selection (Baek et al., 9 Jun 2025, Levy et al., 30 Dec 2024).
• Online adaptation and generalization: Most methods operate offline; online graph refinement, learning-based pruning, and dynamic integration with local nonlinear solvers are underexploited (Levy et al., 30 Dec 2024, Liu et al., 30 Nov 2025).
• Optimality gaps and coverage: Successful stitching hinges on sufficient data coverage or accurate dynamics approximations; failures arise in highly fragmented or low-coverage domains (Liu et al., 30 Nov 2025).

A plausible implication is that further integration of learned heuristics, representation learning, and classical graph algorithms will define the next frontier for trajectory stitching across both model-based and model-free domains.

7. Relationship to Related Paradigms

Graph-assisted trajectory stitching bridges several research lines:

• Hierarchical reinforcement learning, by separating high-level transition selection (graph search) and low-level primitive execution (policy or primitive controller).
• Combinatorial motion planning, by using graph-based search over precomputed or learned motion primitives rather than direct numerical optimization.
• Graph neural networks and message passing, particularly in data imputation, where both local structure and global flow inform plausible trajectory completion (Wei et al., 29 Apr 2024).
• Global tracking and video analysis, unifying spatio-temporal segmentation and matching via posterior sampling in graphical models (Lin et al., 2015).
• Logic-guided AI planning, integrating automata products and constraint-checking into the stitching pipeline for composite task satisfaction (Liu et al., 30 Nov 2025).

The broad applicability and extensibility of graph-assisted trajectory stitching suggest its centrality in future intelligent systems for multi-scale planning, robust estimation, and data-driven control.