PccDiffuser: Multi-solution Motion Planning for Continuum Robots
Authors: Ke Qiu, Sifan Chen, Si Wang, Rong Xiong, Yue Wang, Haojian Lu
Abstract
We present the PccDiffuser, a conditional diffusion framework for continuum robots that learns a multimodal distribution over complete configuration-space paths and samples multiple candidate solutions in parallel, which are subsequently converted into an executable trajectory by time allocation considering actuator constraints. Under the piecewise constant-curvature model, we use exponential co-ordinates to describe the robot kinematics, and use graph neural network to encode a variable number of environment obstacles. Analytical differential kinematics is incorporated in the denoising process to improve terminal accuracy and whole-body clearance. On a mixed test set comprising workspace with zero to four obstacles, PccDiffuser achieved a success rate of 91%. Compared with existing sampling- and optimisation-based benchmarks, it delivered both a higher success rate and greater computational efficiency, with the latter advantage becoming more substantial when sampling more candidate solutions. Experiments on a three-section tendon-driven continuum robot further demonstrate consecutive planning, multi-solution planning, and whole-body obstacle avoidance.
Continuum robots provide intrinsic compliance, high dexterity, and safe physical interaction, enabling navigation and manipulation in confined and unstructured environments. Despite recent advances in sensing and control, heightening the need for precise motion generation, most widely used planning libraries are grounded in rigid-body assumptions, creating a critical gap for fast and practical tools for continuum robots. To address this, we present CR-Solver, a two-stage, optimization-based solver for the motion generation of tendon-driven continuum robots. Our method unifies inverse kinematics, path following, and trajectory planning within a single constrained nonlinear optimization framework. Leveraging GPU-accelerated parallel optimization, CR-Solver delivers fast, accurate, and constraint-aware solutions. We validate our approach on three tasks, demonstrating significant speedups over traditional CPU-based solvers while achieving a consistently high success rate above 95% and millimeter-level accuracy. The solver is implemented in pure Python, reducing the barrier to adoption and offering a practical, extensible foundation for continuum robots' high-performance motion planning.
Follow-the-leader (FTL) motion exploits the unique morphology of continuum robots (CRs) to navigate confined spaces by having the body retrace the path of the tip. While extensively studied, existing FTL methods typically assume a fixed base or a single degree-of-freedom insertion mechanism, limiting their applicability to practical systems in which CRs are mounted on robotic manipulators with fully actuated SE(3) base pose. This paper presents a sampling-based motion planner for FTL motion of manipulator-mounted CRs that jointly considers robot configuration and base pose. The key idea is to decouple global shape search from base pose determination by computing the base pose through a closed-form geometric construction, thereby avoiding iterative optimization during online planning. The approach supports general forward models and enables efficient planning by shifting the majority of computation offline. We establish theoretical guarantees including resolution complete shape search and converging tip tracking throughout waypoint traversal and interpolation. Experiments on 120 simulated paths over 3 test classes demonstrate 0% tip error and 1.9% mean shape deviation (w.r.t. robot length) at 100% success rate. We validate the practicality of our approach on a 6-DOF tendon-driven CR mounted on a serial manipulator. Code and visualization available at https://continuumroboticslab.github.io/sb-ftl-cr-planner/.
Chengnan Shentu, Nicholas Baldassini, Oluwagbotemi D. Iseoluwa +2
Diffusion-based motion planners have demonstrated strong performance in generating diverse and high-quality robot trajectories in cluttered environments with multiple feasible solutions. However, existing approaches typically operate on fixed-length waypoint sequences, making the learned model resolution-dependent, thereby preventing zero-shot generalization across resolutions. In this work, we propose Function-Space Diffusion for Motion Planning (FSD-MP), a diffusion-based motion planner that models trajectories as continuous functions and performs diffusion directly in function space, achieving discretization-invariant trajectory generation. We define a mode-wise forward process in the spectral domain, driven by Gaussian noise with a Matérn-type covariance, and parameterize the reverse process with a boundary-compatible Discrete Sine Transform-based Fourier Neural Operator (DST-FNO) that preserves start-goal constraints across resolutions. We evaluate FSD-MP on 2D point robot and 7-DoF Franka manipulator planning benchmarks. Our method achieves competitive planning performance at the training resolution and generalizes zero-shot across resolutions up to 16× higher, preserving consistent planning behavior without retraining. These results demonstrate that function-space diffusion provides an effective framework for discretization-invariant motion planning.