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Trajectory-Level Mode Guidance for Controllable Diffusion-Based Multi-Robot Motion Planning

Tianyou Yu, Shengze Cai, Chao Xu

arXiv:2609.36530v1cs.RO

TL;DR

Motion planning admits multiple feasible solutions, but steering diffusion-generated trajectories with coarse or partial priors while preserving their diversity remains challenging. The paper combines planning costs and timestep-dependent prior injection in clean trajectory space. Experiments report controllable, diverse trajectories and collision-free multi-robot coordination.

  • Problem

    Coarse, partial, or inaccurate trajectory priors can indicate desirable modes, but integrating them into diffusion generation while preserving diverse feasible trajectories remains challenging.

    Source: §I · p. 1

  • Method

    The framework guides reconstructed clean trajectories with planning costs and progressively injects partial priors at timestep-dependent noise levels.

    Source: §I · p. 1

  • Results

    Experiments demonstrate controllable generation, diverse feasible solutions, and effective collision-free coordination across single- and multi-robot planning tasks.

    Source: §VI · p. 7

  • Takeaways & Limitations

    Partial trajectory conditioning can concentrate generations around a prior while retaining multiple distinct solutions, offering a controllable trade-off between prior guidance and diversity.

    Source: B. Effect of Partial Trajectory… · p. 5

Abstract

from arXiv · show

Motion planning often admits multiple feasible solutions, making multimodal generation valuable, particularly for flexible multi-robot coordination. Diffusion models naturally learn such trajectory distributions, yet incorporating coarse and partial trajectory priors without restricting generation remains challenging. Such priors indicate a desirable region of the solution space rather than a single solution, motivating conditioned generation that preserves multimodality. In this paper, we guide trajectory generation in the clean trajectory space and progressively incorporate trajectory priors with a timestep-dependent guidance strength. At each reverse diffusion step, the reconstructed clean trajectory provides a unified space for integrating planning costs and partial trajectory priors. Planning costs are incorporated through gradient-based refinement, while the partial prior is progressively injected at the corresponding noise levels with decreasing guidance strength. This guides generation toward the prior in early stages while gradually releasing the constraint to preserve the inherent multimodality of the diffusion model. The framework naturally extends to multi-robot planning by incorporating inter-robot collision costs. Experiments on single- and multi-robot planning tasks demonstrate controllable trajectory synthesis, diverse feasible solutions, and safe multi-agent coordination.

I. INTRODUCTION

Motion planning can have multiple feasible solutions, but controlling diffusion-generated trajectories with coarse or partial priors while preserving diversity remains challenging. The paper proposes clean-space guidance for combining planning costs and trajectory priors.

I. INTRODUCTION

  • Multiple trajectories can satisfy the same task while differing in geometry, clearance, or coordination, motivating diverse candidates that can be steered toward preferred solutions.Source: §I · p. 1

II. RELATED WORK

  • Diffusion models can represent multimodal trajectories, but learning that distribution alone does not explicitly control preferred modes, especially under partial or inaccurate priors.Source: §I · p. 1

I. INTRODUCTION

  • Clean-space guidance combines planning costs with timestep-dependent prior injection to steer generation while preserving multimodality; the framework is evaluated on single- and multi-robot tasks.Source: §I · p. 1

A. Constrained Trajectory Planning

  • Constrained optimization and heuristic methods yield deterministic solutions; MPC models dynamics and obstacles explicitly, but ambiguous instructions are difficult to express as precise constraints or costs.Source: A. Constrained Trajectory Planning · p. 2
  • Conditioned imitation can regress toward the mean of feasible behaviors, while CVAEs model diverse distributions but remain limited in capturing trajectory multimodality.Source: A. Constrained Trajectory Planning · p. 2

B. Denoising Diffusion Models

Diffusion models offer multimodal generation, while explicit control over preferred trajectory modes remains challenging in multi-robot planning. The formulation treats planning as conditional trajectory generation, with task constraints and optional priors guiding feasible trajectories.

B. Denoising Diffusion Models

  • Diffusion models can preserve distributional diversity, but do not by themselves explicitly control preferred modes using trajectory-level information.Source: B. Denoising Diffusion Models · p. 2

C. Multi-Robot Motion Planning

  • Multi-robot planning couples trajectories through environmental, dynamic, and collision constraints; existing approaches face limits with continuous trajectories, partial priors, or effective exploration.Source: C. Multi-Robot Motion Planning · p. 2
  • The framework uses planning costs and partial priors in clean trajectory space, and trains on single-agent data while generating multiple agents jointly at inference.Source: C. Multi-Robot Motion Planning · p. 2

III. PROBLEM FORMULATION

  • Planning is formulated as conditional generation of N trajectories given start and goal states and task constraints; an available prior guides generation but is not a hard constraint.Source: §III · p. 2

IV. METHOD

At sampling time, a pretrained diffusion model reconstructs clean trajectories and applies task guidance before constructing the preceding noisy state. The diffusion process learns a trajectory prior through forward noising and reverse denoising.

A. System Overview

  • At each reverse step, the pretrained model reconstructs a clean trajectory, applies planning-cost and optional prior guidance, then maps the guided estimate to the preceding noisy state.Source: A. System Overview · p. 3
  • Task-specific guidance is applied only during sampling, allowing controllable generation while preserving the pretrained model's multimodality without modifying or retraining it.Source: A. System Overview · p. 3

B. Trajectory Diffusion Model

  • The forward process progressively adds Gaussian noise to clean trajectories, and the reverse process estimates clean trajectories from noisy states to construct successive transitions.Source: B. Trajectory Diffusion Model · p. 3

C. Cost-Guided Planning

The method applies task-cost guidance to the reconstructed clean trajectory, then uses that guided estimate to construct the preceding noisy state. This avoids relying on costs applied directly to highly noisy states.

C. Cost-Guided Planning

  • Planning costs act on the reconstructed clean trajectory because trajectory quality and feasibility concern clean trajectories, while highly noisy states may offer limited meaningful guidance.Source: C. Cost-Guided Planning · p. 3
  • The planning cost explicitly models task likelihood, and its gradient provides a local direction for modifying the clean-trajectory estimate without additional training.Source: C. Cost-Guided Planning · pp. 3–4
  • Cost refinement is jointly performed with trajectory-prior guidance, incorporating task feasibility and prior information in the same reconstructed clean space.Source: C. Cost-Guided Planning · p. 4

D. Trajectory Guidance

Trajectory priors are incorporated in reconstructed clean trajectory space, where masked waypoints are guided by the prior and unmasked waypoints remain diffusion-generated. The guided trajectory is also refined by planning costs before returning to diffusion space.

D. Trajectory Guidance

  • Trajectory guidance applies coarse priors in reconstructed clean trajectory space, while unmasked waypoints remain determined by diffusion.Source: D. Trajectory Guidance · p. 4

1) Denoised Trajectory Guidance:

2) Noisy-State Trajectory Guidance:

Noisy-state guidance maintains the prior at the corresponding diffusion noise level and applies a decreasing guidance weight. The mask preserves diffusion and cost guidance at unmasked waypoints.

2) Noisy-State Trajectory Guidance:

E. Cost Function

The planning cost jointly evaluates trajectory feasibility and motion quality through penalties for speed, obstacle clearance, goal deviation, inter-robot collisions, and irregularity.

E. Cost Function

  • The planning cost combines five penalties to evaluate trajectory feasibility and motion quality.The terms address velocity, obstacle clearance, goal deviation, inter-robot collisions, and trajectory irregularity.Source: E. Cost Function · p. 4
  • Velocity, obstacle-clearance, and goal costs penalize excessive speed, insufficient distance from obstacles, and terminal position error.Source: E. Cost Function · p. 4
  • The multi-robot collision and smoothness costs penalize insufficient pairwise separation and second-order trajectory differences.Source: E. Cost Function · pp. 4–5

V. EXPERIMENTS

In single-agent tests, partial trajectory conditioning concentrates samples around the prior while preserving multiple distinct solutions. The experiments use a task-agnostic diffusion model and compare prefix and uniformly sparse conditioning.

A. Implementation Details

  • A task-agnostic 1D U-Net models 60-waypoint trajectories trained on 20,000 feasible single-robot paths; DDIM uses 300 sampling steps by default.Source: A. Implementation Details · p. 5

B. Effect of Partial Trajectory Conditioning

C. Multi-Robot Planning

The position-swapping experiments test coordination and collision avoidance as robot numbers increase. With partial trajectory priors, the planner generates diverse coordination patterns while retaining safe separation and improving trajectory efficiency.

C. Multi-Robot Planning

1) Multi-Robot Position Swapping:

  • For the 4-, 6-, 8-, and 10-robot obstacle-free swaps, the planner generates collision-free trajectories; two 8-robot runs show different coordination patterns under unchanged starts and goals.The task assigns each robot another robot’s initial position as its goal, and uses a 30-waypoint Uniform-Sparse prior.Source: 1) Multi-Robot Position Swapping · pp. 5–6
  • 30-waypoint conditioning yields the lowest mean trajectory length for 4, 6, and 8 robots, while minimum inter-robot distance remains above 0.7 m across all configurations.The 30-waypoint condition is also competitive for 10 robots.Source: 1) Multi-Robot Position Swapping · p. 6, Table I · p. 6

2) Multi-Robot Planning in Obstacle Environments:

In obstacle environments, the planner balances partial-prior guidance with goal, inter-robot collision, and obstacle constraints. Denoising examples show how this guidance shapes trajectory development and coordination over time.

2) Multi-Robot Planning in Obstacle Environments:

  • With a six-waypoint prior, trajectories adapt to obstacles: one pair swaps through the central region while others exchange positions by rotating around the constrained outer region.The result balances the prior with planning costs rather than enforcing the prior rigidly.Source: 2) Multi-Robot Planning in Obstacle… · p. 6, Figure 4 · p. 7

3) Denoising Process with Prior Guidance:

  • For six obstacle-free robots, the 30-waypoint prior produces a more regular position-swapping pattern, whereas unguided trajectories develop in different directions and may take larger detours.The denoising visualization uses 500 DDIM sampling steps and shows reconstructed clean trajectories at selected steps.Source: 3) Denoising Process with Prior Guidance · p. 6
  • During denoising with a six-waypoint prior, four robots develop distinct interaction patterns, including implicit waiting, while adapting to obstacle and inter-robot collision constraints.The pink trajectory begins extending toward its goal around the 125th denoising step; no waiting action or waiting labels are specified.Source: 3) Denoising Process with Prior Guidance · p. 6
  • The multi-robot position-swapping results compare scenarios with 4, 6, 8, 8, and 10 robots; the two 8-robot runs illustrate different inference outcomes.The figure depicts trajectory progression and assigns a different color to each robot.Source: Figure 3 · p. 7

VI. CONCLUSION

The paper concludes that clean-space guidance and timestep-dependent prior injection support controllable, multimodal trajectory generation, including joint multi-robot planning with collision guidance. It identifies less structured language instructions and high-level behavior labels as future directions.

VI. CONCLUSION

  • The framework guides multimodal trajectory generation in clean space using planning costs and timestep-dependent prior injection, and extends to joint multi-robot planning with inter-robot collision guidance.Experiments demonstrate controllable generation, diverse feasible solutions, and collision-free coordination.Source: §VI · p. 7
  • Future work will explore less structured guidance, including ambiguous language instructions and high-level behavior labels, for more expressive trajectory control.Source: §VI · p. 7
  • The planning cost is evaluated on the reconstructed clean trajectory using a plug-in approximation that treats its estimate as a point estimate of the unknown clean trajectory.The appendix states that this allows the cost-based likelihood to be evaluated on the reconstructed trajectory.Source: APPENDIX · p. 7

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