SoGuDiff: Socially Guided Diffusion for Steerable, Norm-Grounded Robot Navigation

• Social conventions vary by culture, environment, and task, while many existing planners and learned policies commit to one behavior.Source: §I · p. 1
• Unlike discrete binary navigation primitives realized by separately trained models, SoGuDiff specifies graded, continuous styles using one model.Source: §I · p. 1
• SoGuDiff frames social navigation as a continuously parameterized family in one conditional diffusion planner, with four style axes specified at deployment.Source: §I · p. 1
• Per-axis classifier-free guidance steers axes independently and composes styles at inference, although training demonstrations label only one axis each.Source: §I · pp. 1–2
• Single-axis sweeps trace an efficiency–sociality tradeoff that strictly dominates fixed-behavior baselines, and styled behavior transfers to real-world deployment.Source: §I · p. 2

A. Social Robot Navigation and Adjustable Behavior

• Most reactive, learned, and optimization-based methods fix social behavior through their designed reward or tuned cost; multi-objective RL conditions on preferences but selects actions one step at a time.Source: A. Social Robot Navigation and… · p. 2

B. Social Conventions and Behavior Specification

• Social norms extend beyond proxemics to passing, encounter resolution, group respect, and legible movement; SoGuDiff grounds its four axes in these conventions and uses costs to generate style-labeled demonstrations.Source: B. Social Conventions and Behavior… · p. 2

C. Diffusion Planning and Controllable Generation

• Prior diffusion-planning work composes score estimates or steers generation at sampling time, including constraint composition, traffic rules, legibility, and social-navigation task variants.SoGuDiff’s stated distinction is its continuous, per-axis style control interface rather than discrete specifications.Source: C. Diffusion Planning and Controllable… · p. 2
• SoGuDiff uses one planner with continuous signed style values and composes axes at inference, unlike ComposableNav’s discrete binary instructions and separately trained primitive models.Its demonstrations vary one style axis at a time, while conditioning lets one model represent their combinations.Source: C. Diffusion Planning and Controllable… · p. 2

III. PROBLEM FORMULATION

• The scene context comprises the robot’s current state, goal, nearby pedestrian states, and local occupancy map; trajectories are executed in receding-horizon fashion.Admissibility requires controls to realize the trajectory while respecting kinematic limits and avoiding pedestrians and static obstacles.Source: §III · p. 2
• The style vector specifies four conventions—proxemic conservatism, passing side, yielding, and group deference—with signed values controlling convention strength and direction.The robot must generate a trajectory that reaches the goal, conforms to the requested style, and satisfies admissibility requirements.Source: §III · pp. 2–3

IV. METHODOLOGY

• SoGuDiff’s methodology combines a style-conditioned diffusion model, compositional guidance, a feasibility projection layer, and demonstrations labeled on one style axis at a time.The pipeline is overviewed in Fig. 2.Source: §IV · p. 3

A. Style-Conditioned Diffusion Model

• The conditional DDPM learns to reverse progressively added Gaussian noise by predicting the noise given the trajectory, diffusion step, scene context, and style vector.At inference, trajectories are denoised with the DDIM sampler for efficiency.Source: A. Style-Conditioned Diffusion Model · p. 3
• A token-based encoder jointly processes robot state, goal, pedestrian, occupancy-map, and style inputs before conditioning the one-dimensional U-Net denoiser.Absent pedestrians are masked, while the denoiser generates trajectories through residual blocks that cross-attend to encoded tokens.Source: A. Style-Conditioned Diffusion Model · p. 3
• Structured categorical dropout trains the model on unconditional, scene-only, and scene-plus-single-axis conditions, alongside the fully conditioned pattern.These patterns support joint and per-axis inference schemes.Source: A. Style-Conditioned Diffusion Model · p. 3

B. Compositional Guidance and Sampling

• Each style-axis guidance delta is measured relative to the scene-conditioned estimate, so style adjusts rather than re-specifies the scene conditioning.The total guidance weight is held constant and divided equally among active nonzero axes.Source: B. Compositional Guidance and Sampling · p. 3
• Setting an axis weight to zero removes its contribution and increasing it strengthens that behavior, independently of the desired style value.This allows axes to be adjusted and combined without retraining.Source: B. Compositional Guidance and Sampling · p. 3
• A joint conditional query uses all style tokens with one guidance weight, but lacks per-axis control; all conditioning variants run in one batched forward pass.The denoiser also generates candidate trajectories in parallel, and a goal-directed objective selects the lowest-cost candidate.Source: B. Compositional Guidance and Sampling · p. 4

C. Feasibility Projection

• The projection tracks the selected trajectory with a soft-constrained optimal control problem under the robot dynamics, actuation limits, and obstacle-clearance constraints.The described implementation uses a unicycle model and acados.Source: C. Feasibility Projection · p. 4
• Moving pedestrians and static occupancy-map obstacles enter the clearance constraints, with slack penalties discouraging violations without hard-bounding them.Static obstacles use zero velocity, and moving obstacles are propagated at constant velocity over the planning horizon.Source: C. Feasibility Projection · p. 4
• After a fixed-budget SQP solve, a trajectory is accepted only when maximum slack and deviation from the selected trajectory fall below fixed thresholds; otherwise, the system commands a controlled stop.The slack threshold preserves clearance inflation so accepted trajectories remain collision-free relative to physical obstacle radii.Source: C. Feasibility Projection · p. 4
• The diffusion model handles social behavior, style, and multimodality, while the separate projection handles kinematic feasibility and collision avoidance.The kinematic model can be substituted, keeping learned behavior modular from enforced constraints.Source: C. Feasibility Projection · p. 4

D. Demonstration Generation

• The demonstration planner samples candidate trajectories and selects those minimizing a weighted multiterm social and goal cost for each scene and style vector.It retains several distinct low-cost candidates per scene rather than only the single optimum, preserving multimodality in the training distribution.Source: D. Demonstration Generation · p. 4
• The social cost combines norm-grounded terms, while each style axis adjusts one interpretable scale rather than a free weight.Spatial zones interpolate between Hall’s intimate, personal, and social distances; temporal terms use the corresponding distance divided by typical walking speed as an anticipation horizon.Source: D. Demonstration Generation · p. 4
• Each demonstration carries a non-zero label on only one axis, so the model never observes composed styles during training; composition occurs entirely at inference.The scheme can use human-annotated or real-world pedestrian data with similar single-axis labels instead of the sampling planner.Source: D. Demonstration Generation · p. 4

A. Experimental Setup

• The baseline evaluation uses 500 randomized CrowdNav scenes with one to ten ORCA-driven pedestrians, who react to one another but not to the robot.Scenes use random robot start and goal poses and remain open and unmapped to accommodate baselines.Source: A. Experimental Setup · p. 5
• A separate set of 500 geometric scenarios covers corridors, head-on encounters, overtaking, crossing, and stationary or walking groups for style evaluation.Baselines include reactive, learning-based, graph and transformer policies, and an optimization-based planner; learned baselines use the same random scenario distribution.Source: A. Experimental Setup · p. 5
• Outcome metrics include success, timeout, collision, time to goal, and path length; social-conduct metrics are rates grounded in Hall’s interpersonal zones.Social measures include clearance, personal-space intrusion, passing-side bias, time-to-collision infractions, path cutoffs, and group splits.Source: A. Experimental Setup · p. 5
• Table II reports success, efficiency, and proximity metrics for SoGuDiff and baselines across 500 random crowd scenes.The caption identifies bolded best values, underlined second-best values, and holonomically trained baselines marked with †.Source: Table II · p. 5

B. Simulation Results

• Sweeping proximity style traces a TTG–PSI tradeoff frontier that strictly dominates fixed-behavior baselines.The comparison covers 500 random crowd scenes; other style axes exhibit similar tradeoffs.Source: B. Simulation Results · pp. 5–6
• Single-axis sweeps move their associated metrics monotonically: MeanD rises from 2.27 m at −1 to 3.28 m at +1, while passing-side bias shifts from +0.763 to −0.705.Yielding reduces TCR from 1.03% to 0.19% and PCR from 3.00% to 0.58%; group deference reduces GSR from 20.00% to 7.54%.Source: B. Simulation Results · p. 6, Table III · p. 6
• Cross-axis couplings occur: increased proxemic conservatism improves yielding and group-adherence metrics, and side preference and yielding also increase group adherence and mean clearance.These secondary effects reflect shared geometry and styles’ shared commitment to sociality.Source: B. Simulation Results · p. 6
• Composed styles work despite training only on single-axis demonstrations: with all axes at +1, MeanD is 2.87 m, cutoffs are 0.18%, group splits are 0.97%, and right-side passing is preferred (+0.405).The [0, +1, +1, 0] style induces right-side passing and yielding; [0, −1, +1, −1] exhibits left-side passing and greater group agnosticism.Source: B. Simulation Results · p. 6, Figure 5 · p. 6, Table IV · p. 7
• Composition is nonlinear: assertiveness can dominate group deference in conflicting styles, and axis adherence is generally attenuated relative to corresponding single-axis styles.Composed styles nevertheless generally remain interpretable and consistent with their component axes, including in conflicting configurations.Source: B. Simulation Results · pp. 6–7

C. Ablations

• Joint guidance fails to compose passing-side bias coherently for the [−1]4 style when trained on single-axis demonstrations, whereas joint-axis demonstrations let it replicate the expert accurately.Per-axis guidance does not replicate the expert in that joint-demonstration setting; matching guidance to demonstration format produces the best results.Source: C. Ablations · p. 7, Table V · p. 7
• The single-axis scheme approaches joint composition using only single-axis-labeled demonstrations and permits a unique guidance weight for each axis.Increasing total guidance weight strengthens adherence up to saturation, but also compresses differences between intermediate and extreme style values and slightly lowers success as trajectories move off the training manifold.Source: C. Ablations · p. 7
• The imitated planner generally matches and sometimes exceeds the online expert, while remaining agnostic to demonstration source.For proxemic and left-passing styles, the expert’s stronger group adherence causes timeouts, whereas the imitated policy implicitly characterizes and avoids groups.Source: C. Ablations · p. 7
• Removing feasibility projection reduces successes and raises timeouts and collisions; the resulting 4.08 m mean clearance reflects stalled motion, not caution.Source: C. Ablations · p. 7, Table V · p. 7
• Physical demonstrations show distinct left-side and right-side passing styles on a repeated test.Source: Figure 6 · p. 7

D. Real-World Deployment

• Collision-free, distinctly styled behavior is reproduced on a Jackal at 10 Hz across repeated per-axis and composed-style trials.The trials also include neutral and runtime-varying styles.Source: D. Real-World Deployment · p. 7

VI. DISCUSSION

• The projection layer makes assumptions and offers no safety guarantees; constant-velocity pedestrian estimates and solver nonconvergence constrain its safety role.A controlled-stop fallback reduces but does not eliminate collision severity.Source: §VI · p. 7
• Overly conservative proxemic styles can freeze in dense crowds, while style guidance raises likelihood rather than guaranteeing the requested behavior.Source: §VI · p. 7
• Conflicting composed styles can let one axis dominate, excessive guidance weights degrade continuous control, and implicit group characterization makes deference harder to learn.Source: §VI · pp. 7–8
• SoGuDiff spans continuous social behaviors and strictly dominates fixed-behavior baselines over an efficiency-vs-sociality tradeoff.Source: §VI · p. 8
• Adaptive style selection based on perceived social setting is proposed as a natural extension.Source: §VI · p. 8