This work introduces Model-Based Diffusion via Constraint Optimization and Adaptive Scheduling (MD-COAS) for SRMP that unifies the inexact Augmented Lagrangian Method (iALM) soft diffusion prior with a Convex Feasible Set (CFS)-based hard projection operator, and adaptively schedules and co-optimizes safety enforcement, along with diffusion scheduling.
Abstract
Single-Robot Motion Planning (SRMP) in highly non-convex constrained environments, where robots must satisfy collision-free guarantees, dynamic feasibility, and task-related constraints, is challenging under complex constraints and computational limits. Recent Model-Based Diffusion (MBD) approaches recast the SRMP as trajectory optimization that samples from a posterior over trajectories, using known dynamics, and analytically estimates the score function from rollout samples to guide diffusion denoising toward a low-cost, clean trajectory without demonstration learning. While existing works further adapt MBD to constrained environments and showcase promising performance, they are still limited by (1) enforcing safety either via soft feasibility diffusion priors or hard projection operators, but lack a unified framework to integrate both, and (2) fixing safety enforcement to neglect the changing of diffusion scheduling. Therefore, we introduce Model-Based Diffusion via Constraint Optimization and Adaptive Scheduling (MD-COAS) for SRMP that unifies the inexact Augmented Lagrangian Method (iALM) soft diffusion prior with a Convex Feasible Set (CFS)-based hard projection operator, and adaptively schedules and co-optimizes safety enforcement, along with diffusion scheduling. Experiments demonstrate that our method achieves higher safety \&success rates, faster convergence, and lower final costs than baseline planners on randomly generated highly non-convex 2D benchmarks and a 7-DoF robot arm avoidance task.
This work introduces Model-Based Diffusion Optimal Control (MDOC), a model-based diffusion planner that efficiently produces dynamically feasible trajectories without relying on data, and shows that MDOC's safety mechanism naturally scales to multi-robot planning settings through Conflict-Based Search.
Trajectory optimization for multi-robot systems remains a critical challenge, particularly when navigating highly non-convex, non-linear, and non-differentiable environments. While Model-Based Diffusion (MBD) has recently emerged as a promising sampling-based optimization paradigm for single-robot trajectory generation, extending it to multi-robot systems results in a centralized, high-dimensional inference problem that (i) suffers from poor sample efficiency due to the curse of dimensionality and (ii) requires global access to all robots'dynamics, constraints, and objectives. To address this, we propose Distributed Model-Based Diffusion (DMBD), a distributed server-robot framework that decomposes the reverse diffusion process into local conditional reverse diffusion processes. This decomposition enables each robot to iteratively perform denoising independently within its own control subspace while conditioning on the current trajectory estimates of the other robots that are aggregated and broadcast by the server. Extensive simulations in goal swapping, multi-floor coverage, parking, and rush-hour scenarios demonstrate that DMBD achieves strong scalability, solving many challenging coordination tasks in sub-seconds and significantly outperforming existing baselines.
Haejoon Lee, Xinyi Wang, Taekyung Kim et al.· 0 citations
Diffusion policies generate multimodal robot action sequences from demonstrations, but steering them toward deployment-time constraints typically relies on differentiable guidance costs. This excludes many practical safety constraints, such as binary collision checks, joint limits, and black-box rollout costs that are nondifferentiable. We propose Gradient-free Robot Action generation via Combined diffusion-MPPI posterior mean Estimation (GRACE), which guides a pretrained diffusion policy with Model Predictive Path Integral (MPPI) control using only forward cost evaluations. Building on the common score-ascent structure of diffusion and MPPI, GRACE constructs a cost-conditioned guidance posterior at each reverse step and estimates its mean with a single MPPI update centered at the diffusion reverse mean. For differentiable costs, GRACE recovers conventional gradient guidance under a first-order, matched-covariance approximation. GRACE attains higher success rates than diffusion-based and sampling-based baselines in simulation. On a real 7-DoF manipulator, GRACE avoids a deployment-time obstacle that the unguided prior collides with in every trial. Code and experiment videos are available at https://anonymous.4open.science/w/grace-70BB/.
This research proposes a constrained motion planning framework for robot manipulators in human-robot interaction (HRI). For a non-redundant manipulator with a fully specified end-effector pose, additional requirements such as collision avoidance and self-collision avoidance are difficult to handle as simple null-space secondary tasks. This limitation makes it challenging to generate feasible joint-space trajectories in HRI environments where safety and kinematic constraints must be considered simultaneously. To address this limitation, collision- and self-collision-aware trajectories are generated using Rapidly-exploring Random Tree (RRT) and RRT* algorithms, and the resulting dataset is used to train a diffusion model that generates constraint-satisfying trajectories through guided sampling. To reduce the inference time required for iterative diffusion sampling, consistency distillation is applied, and a joint-weighted jerk regularization term is incorporated into the loss function to promote smoother trajectories by penalizing abrupt changes in joint acceleration. Simulation results show that the consistency model generates 150 trajectory candidates in less than 100 ms, maintains a high episode success rate, and substantially reduces joint and end-effector jerk when jerk regularization is applied.
Byeong-Il Ham, Hyunbin Kim, Kyung-Soo Kim· 0 citations
Robot motion planning is inherently multimodal, yet classical planners typically return only a single solution. Probabilistic formulations address this limitation by maintaining a distribution over motions, allowing the planner to reason over multiple low-cost alternatives. In robotics, however, motion samples must also satisfy strict constraints, including collision avoidance, joint limits, contact conditions, and dynamics consistency. These hard requirements make motion sampling substantially more challenging: within a limited planning budget, the ensemble must cover diverse low-cost motions while ensuring that every sample remains feasible under the relevant constraints. We propose SteinSQP (Stein Variational Sequential Quadratic Programming), a constrained Stein variational inference method for diverse feasible robot motion sampling. SteinSQP evolves an interacting particle ensemble, as in Stein variational methods, while embedding constraints directly into a kernel-space SQP subproblem. We solve the resulting constrained Stein-Newton subproblem with a GPU-friendly matrix-free primal-dual algorithm, enabling efficient batched ensemble updates. To globalize the method, we introduce an ensemble-level merit function that jointly balances objective value, constraint violation, and particle diversity. Across five constrained motion-planning tasks, SteinSQP returns fully feasible ensembles while preserving diverse motion alternatives. Compared with first-order constrained Stein baselines and serial multistart nonlinear programming, SteinSQP shows faster and more robust ensemble convergence in terms of iterations, improves particle-wise feasibility, and achieves faster batched time-to-solution on challenging robot-scale tasks.
A key limitation on the use of diffusion models in robotic planning is their inability to inherently enforce safety or dynamical constraints, which often results in physically infeasible or unsafe outputs. Hybrid approaches that employ model predictive control (MPC) to address this problem can be unstable, as poor trajectory initializations from the diffusion model prevent the MPC from converging to a safe and feasible solution. To overcome these challenges, we propose D-SafeMPC, which enhances the interaction between diffusion and control. Our method guides the reverse diffusion process with control barrier functions (CBFs) and control Lyapunov functions (CLFs) and employs an iterative-projection scheme where an MPC refines the trajectory at each denoising step. This steers sampling toward safe, goal-directed regions and provides reliable MPC warm starts. In simulations on a Franka manipulator across four scenarios (one static-obstacle and three dynamic-obstacle settings) and in a sim-to-real experiment on a physical Franka robot, D-SafeMPC improves safety, task success rates, and planning efficiency over state-of-the-art baselines. To facilitate reproducibility, our source code and experimental configurations are available in a repository at https://github.com/erdiphd/D-SafeMPC
Erdi Sayar, Ersin Dacs, J. W. Burdick et al.· 0 citations