Organizations: 1* IHP – Leibniz-Institut für innovative Mikroelektronik, Frankfurt (Oder), Germany · BTU Cottbus-Senftenberg, Cottbus, Germany · Technical Center, National Academy of Sciences of Ukraine, Kyiv, Ukraine
Abstract
This paper presents an experimental study of motion planning for resilient continuum robots. In this study we mainly focused on multi-criteria decision-making, its application for path-planning algorithms, impact on the generated path and execution time. To do this, we used two well-known algorithms for path planning, namely Genetic algorithm and A star algorithm, and modified them by adding the Analytical Hierarchy Process algorithm to evaluate the quality of the paths generated. In our experiment the Analytical Hierarchy Process considers four different criteria, i.e. distance, motors damage, mechanical damage of the robot's arm and accuracy, each considered to contribute to the resilience of a continuum robot. The use of different criteria is necessary to increase the time to maintenance operations of the continuum robot. We conducted the experiments using two different simulated environments of the robot. Although we significantly simplified the robot's model and its environment, we still implemented some of the features of the environment based on the real robot prototype. In particular, one of the environments has single- as well as multi-path points, and other consists of the multi-path points only. The results show that, in contrast to A star, the performance time of Genetic algorithm does not depend on the environment's cardinality. It generates more diverse paths, which increases the robot's resilience.
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 are well suited for navigating confined and fragile environments, such as vascular or endoluminal anatomy, where contact with surrounding structures is often unavoidable. While controlled contact can assist motion, unfavorable contact can degrade controllability, induce kinematic singularities, or introduce safety risks. We present a contact-aware planning approach that evaluates contact quality, penalizing hazardous interactions, while permitting benign contact. The planner produces kinematically feasible trajectories and contact-aware Jacobians which can be used for closed-loop control in hardware experiments. We validate the approach by testing the integrated system (planning, control, and mechanical design) on anatomical models from patient scans. The planner generates effective plans for three common anatomical environments, and, in all hardware trials, the continuum robot was able to reach the target while avoiding dangerous tip contact (100% success). Mean tracking errors were 1.9 +/- 0.5 mm, 1.2 +/- 0.1 mm, and 1.7 +/- 0.2 mm across the three different environments. Ablation studies showed that penalizing end-of-continuum-segment (ECS) contact improved manipulability and prevented hardware failures. Overall, this work enables reliable, contact-aware navigation in highly constrained environments.
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.