X-ACTA: eXtended Analytic Center Tension distribution Algorithm for fixed and mobile cable-driven-parallel-robot

Cable-driven parallel robots (CDPRs) present diverse configurations and complex control challenges, which can be addressed by deep reinforcement learning (DRL) by learning their nonlinear dynamics. However, DRL methods often require extensive training time, and the resulting policies do not generalize well to different robot configurations or varying numbers of actuators. In this article, we introduce a novel DRL approach for controlling CDPRs that does not depend on the specific robot configuration. Our method trains an actuator-level policy that controls each motor to achieve its target cable length, in contrast to conventional DRL approaches that learn to control the entire robot to reach a desired end-effector position. To the best of our knowledge, this is the first work to apply DRL to control CDPRs using an actuator-level policy. This approach offers two main advantages: (i) a single shared policy can be applied to any CDPR configuration, regardless of actuator count, and (ii) reliance on inverse kinematics, avoiding the more challenging forward kinematics problem. Training is performed in simulation, and the learned policy is successfully transferred to a real CDPR. Experimental results show that the actuator-level policy (ALP) surpasses traditional reinforcement learning methods in both robustness and precision. We further control a real 8-motor CDPR with 3D motion using a policy trained on a simulated 4-motor planar CDPR operating in 2D. This illustrates that the proposed method is applicable to any CDPR configuration, independent of actuator number or placement.

Cable-Driven Parallel Robots (CDPRs) are a type of parallel mechanism in which cables are used as actuators. Due to the two levels of redundancy and numerous constraints within the CDPR actuation, joint and operational spaces (together known as the tri-space), tracking a given trajectory in the operational space while satisfying constraints in tri-space simultaneously is challenging. To the best of the authors' knowledge, there does not exist any tri-space control framework, which is robust, effective, and directly applicable to several architectures of redundantly actuated CDPRs. This paper proposes a tri-space control framework that combines Reactive Control (RC) and Iterative-Learning Control (ILC) to perform repetitive tasks in the operational space. The framework allows the tracking of operational space trajectories online with feasible cable forces, while avoiding undesirable situations such as cable-link interference, joint interference, and loss of manipulability. On the other hand, by finding an optimal parameter in the null space using a novel parameterization of a null space vector, the performance can be improved through ILC when the task is repeatedly executed. Simulation and hardware results on various Multilink Cable-Driven Robot (MCDRs) and Hybrid Cable-Driven Robots (HCDRs) show that the proposed tri-space control framework can be conveniently and effectively applied to the real-time control of different CDPRs.

Cable-driven manipulators exhibit strong nonlinearities and low structural stiffness, which make precise control challenging under time-varying uncertainties and external disturbances. This paper presents a time-delay-estimation (TDE)-based adaptive fractional-order nonsingular terminal sliding mode (AFONTSM) control strategy for cable-driven robots. A robust controller is constructed within a TDE-based model-free framework by combining fractional-order nonsingular terminal sliding mode error dynamics with a fast terminal sliding mode reaching law. The main contribution is a new adaptive law that introduces an adaptive exponential term into the update gain to form a nonlinear adaptive mechanism. This design improves adaptive regulation under different operating conditions by suppressing noise-induced chattering during smooth tracking while preserving or enhancing the adaptive gain during trajectory reversal. Lyapunov analysis proves the ultimate uniform boundedness of the tracking error. Experimental results show that, compared with the baseline method, the proposed controller reduces RMSE by 34.52% and 31.11%, ITAE by 33.79% and 32.97%, and ISCT by 6.69% and 17.77% for the two joints, respectively. Further comparisons with recently reported adaptive laws demonstrate that the proposed law provides faster adaptive response, more stable gain evolution, and improved chattering suppression. Additional payload tests further verify the robustness and repeatability of the proposed method.