Development of a Cable-Driven Hyper-Redundant Robot with Flexure Hinges-Based Modules

Development of a Cable-Driven Hyper-Redundant Robot with Flexure Hinges-Based Modules 1st Marzia Piemontese CREO Lab Universit` a Campus Bio-Medico di Roma Rome, Italy [email protected] 2nd Lucia Tontini CREO Lab Universit` a Campus Bio-Medico di Roma Rome, Italy [email protected] 3rd Nevio Luigi Tagliamonte CREO Lab Universit` a Campus Bio-Medico di Roma Rome, Italy [email protected] 4th Loredana Zollo CREO Lab Universit` a Campus Bio-Medico di Roma Rome, Italy [email protected] 5th Clemente Lauretti CREO Lab Universit` a Campus Bio-Medico di Roma Rome, Italy [email protected] Abstract—This paper presents a novel cable-driven hyperredundant robot featuring flexure hinges-based compliant modules. The 12-degrees-of-freedom fully 3D-printed manipulator employs six universal joints with Bowden cable actuation for decoupled control. Two backbone-based inverse kinematics algorithms are developed and compared against traditional methods. Experimental validation using motion capture demonstrates joint accuracy below 8.59 deg and the capability of the system to carry 200 g payload. The heuristic algorithm achieves 0.41 mm position accuracy with less than 2 ms cycle time, significantly outperforming Jacobian-based approaches. Index Terms—Hyper-redundant robots, inverse kinematics, compliant modules, continuum manipulators I. INTRODUCTION Hyper-redundant robots (HRR) are manipulators with significantly more degrees of freedom (DOF) than their task space dimension, offering enhanced dexterity for applications from inspection to minimally invasive surgery [1]. However, HRRs face challenges in mechanical design, actuation system, and kinematic control. Structurally, HRRs are categorized as rigid-joint robots (using universal joints) [2] or continuum robots (relying on elastic backbones) [3]. Flexure hinge-based designs [4] combine compactness with predictable kinematics, though adoption remains limited due to material fatigue and unstable instantaneous centers of rotation (ICR). Cable transmission systems [5] enable lightweight remote actuation but introduce complex non-linear mappings and friction issues. Kinematically, traditional Jacobian-based inverse kinematics methods prove inadequate for real-time applications due to computational expense and singularities. Heuristic algorithms [3] avoid these issues but often lack shape constraints essential for confined environments. Identify applicable funding agency here. If none, delete this. This work addresses these limitations through a novel cabledriven HRR with: (1) 12-DOF 3D-printed design combining continuum and rigid-joint advantages, (2) Bowden cable actuation enabling decoupled control, and (3) real-time backbonebased inverse kinematics algorithms. II. DESIGN AND CONTROL A. Mechanical Design The proposed HRR (Fig. 1) features a 12-DOF kinematic structure based on six universal joints with alternating actuation (six modules have a directly attached cable, and six a passing cable). The robot features six compliant modules based on the flexure hinges from [4], representing their first application to HRR systems. Each module is SLA 3D-printed in Flexible 80A resin, eliminating friction and maintenance issues of traditional joints. The actuation system utilizes Bowden cables (PTFE sheaths, Nylon-covered steel wires) arranged on orthogonal planes for decoupled 3D control. Six MG996R servomotors provide ±π/4rad range through capstan-driven antagonistic pairs, resulting in 1.1 kg total mass. B. Control Architecture The control architecture integrates two novel inverse kinematics algorithms based on backbone curve computation using fourth-order B´ ezier parameterization. The heuristic approach performs backbone computation followed by optimization that minimizes positional error between robot configuration and reference curve, while incorporating joint limit constraints and end-effector target requirements. The augmented Jacobian method extends the standard analytical Jacobian with additional constraint rows that enforce alignment of the joint frame origins with the target backbone curve, incorporating regularization terms for joint limit avoidance and singularity avoidance. 2025 I-RIM Conference October 17-19, Rome, Italy ISBN: 9788894580570 10.5281/zenodo.17629806 177 III. MATERIALS AND METHODS A. Comparative analysis of Inverse Kinematics approaches A comparison between the backbone-based and the traditional Jacobian algorithms was performed. The evaluation was made on 20 test trajectories of 100 points each in MATLAB simulation environment with an obstacle. Performance metrics included: position error, orientation error, cycle time, mean distance from obstacle, singular configurations count, and joint limits enforcement. All algorithms were evaluated under the same hardware conditions (Intel Core i5 @ 2.40 GHz, MATLAB R2025b). MATLAB execution times were scaled by 0.002 to estimate real-world C/C++ performance. Statistical analysis used Wilcoxon test with Bonferroni correction (p= 0.0167). B. Robot accuracy evaluation Kinematic performance was validated with the Vicon optoelectronic system (Fig. 1). The analysis evaluated joint accuracy under varying payload (0-200 g). Each test was repeated three times. Robot control was implemented through MATLAB-Arduino UNO communication generating PWM signals for six servo motors. Fig. 1: Setup used for the evaluation of the motion of the HRR. Main components are highlighted. IV. RESULTS AND DISCUSSION A. Results of the analysis of Inverse Kinematics approaches Performance comparison of heuristic, augmented-Jacobian, and conventional IK algorithms reveals significant differences across key metrics. All algorithms successfully enforced joint constraints preventing singular configurations during motion. The heuristic method demonstrates superior performance with mean position error of 0.41 mm and orientation error of 0.2 rad (Tab. I). Computational efficiency is highest with cycle times of 0.84-2.32 ms, resulting from eliminating Jacobian computation and matrix inversion. Obstacle avoidance capability is maintained across all methods with distances exceeding 50 mm, though the heuristic approach performs slightly lower (51 mm average) than Jacobian-based methods. Despite this, the heuristic IK algorithms is considered better suited for HRRs. Algorithm Heuristic IK Augmented Jacobian IK Traditional Jacobian IK Position error (mm) 0.4±1.6∗201 ±90.2∗170.1±90.3∗ Orientation error (rad) 0.2±0.2∗0.9±0.2 0.8±0.2 Mean times (ms) 1.6±0.7∗6.9±1.2∗3.1±0.5∗ Distance from obstacle (mm) 51.1±14.2∗62.9±20.8 60.4±20.8 TABLE I: Performance metrics for the compared inverse kinematics algorithms. The symbol ∗identifies statistically independent results. B. Results of robot accuracy evaluation Joint motion analysis comparing measured positions against reference commands demonstrates kinematic decoupling between joints. Payload loading reduces system responsiveness and alters positioning accuracy, with increased errors at target configurations but improved accuracy at home position where gravitational effects are minimized. The average absolute errors range from -1.49 deg to 8.59 deg at steady state. V. CONCLUSIONS AND FUTURE WORKS A novel cable-driven HRR with compliant modules based on flexure hinges is presented in this work. The 3D-printed manipulator comprises six compliant modules enabling universal joint motion, with total length of 22.8 cm and mass of 200 g. The actuation unit employs six servomotors driving Bowden cables with steel cores in PTFE sheaths for remote motor placement. Two novel backbone-based inverse kinematics algorithms were developed and validated. The heuristic algorithm achieves superior performance with 0.41 mm position error, less than 0.2 rad orientation error, and less than 2 ms cycle time, making it optimal for real-time implementation with C++ solvers. In the future, a software compensation module will be developed to mitigate positioning errors from unmodeled and nonlinear behaviors, using vision feedback or predictive modeling techniques for real-time error correction. REFERENCES [1] Z. Mu, L. Zhang, L. Yan, Z. Li, R. Dong, C. Wang, and N. Ding, “Hyper-redundant manipulators for operations in confined space: Typical applications, key technologies, and grand challenges,” IEEE Transactions on Aerospace and Electronic Systems, vol. 58, no. 6, pp. 4928–4937, 2022. [2] A. Yeshmukhametov, K. Koganezawa, and Y. Yamamoto, “Design and kinematics of cable-driven continuum robot arm with universal joint backbone,” in 2018 IEEE International Conference on Robotics and Biomimetics (ROBIO), pp. 2444–2449, IEEE, 2018. [3] M. Li, R. Kang, S. Geng, and E. Guglielmino, “Design and control of a tendon-driven continuum robot,” Transactions of the Institute of Measurement and Control, vol. 40, no. 11, pp. 3263–3272, 2018. [4] S. Koppen, M. Langelaar, and F. van Keulen, “A simple and versatile topology optimization formulation for flexure synthesis,” Mechanism and Machine Theory, vol. 172, p. 104743, 2022. [5] L. Tang, J. Wang, Y. Zheng, G. Gu, L. Zhu, and X. Zhu, “Design of a cable-driven hyper-redundant robot with experimental validation,” International Journal of Advanced Robotic Systems, vol. 14, no. 5, p. 1729881417734458, 2017. 178