Cable-driven parallel robots (CDPRs) have been widely used in engineering fields because of their significant advantages including high load-bearing capacity, large workspace, and low inertia. However, the impact of convergence speed and solution accuracy of optimization approaches on optimal performances can become a key issue when it comes to the optimal design of CDPR applied to large storage space. An adaptive adjustment inertia weight particle swarm optimization (AAIWPSO) algorithm is proposed for the multi-objective optimal design of CDPR. The kinematic and static models of CDPR are established based on the principle of virtual work. Subsequently, two performance indices including workspace and dexterity are derived. A multi-objective optimization model is established based on performance indices. The AAIWPSO algorithm introduces an adaptive adjustment inertia weight to improve the convergence efficiency and accuracy of traditional particle swarm optimization (PSO) algorithm. Numerical examples demonstrate that final convergence values of the objective function by the AAIWPSO algorithm can almost be 14∼20% and 19∼40% higher than those by the PSO algorithm and genetic algorithm (GA) for the optimal design of CDPR with different configurations and masses of end-effectors, respectively.

This paper proposes a fuzzy proportion integration differentiation (PID) control strategy based on an adaptive whale optimization algorithm (FPID-AWOA) for trajectory tracking of a cable-driven parallel robot (CDPR). A mechanical prototype, and kinematic and dynamic models of the CDPR are established. Thus, new fuzzy rules are developed and a new fuzzy PID controller is designed. Subsequently, the AWOA is introduced to optimize quantization and scale factors of the fuzzy PID controller to obtain the optimal solution. Among them, AWOA is an improvement on WOA. Numerical examples show that the fuzzy PID control strategy based on adaptive whale optimization algorithm (FPID-AWOA) has higher CDPR trajectory tracking accuracy than the traditional fuzzy PID control strategy, the fuzzy PID control strategy based on whale optimization algorithm (FPID-WOA), and the fuzzy PID control strategy based on particle swarm optimization (FPID-PSOA). In comparison with the FPID and FPID-PSOA, the experimental results show that the trajectory tracking error of the proposed FPID-AWOA is reduced by 51.2% and 19.5% in the $X$ -axis direction, respectively, 64.2% and 49.7% in the $Y$ -axis direction, respectively, and 29.1% and 12.2% in the $Z$ -axis direction, respectively. Note to Practitioners —The motivation of this article stems from the need to develop efficient trajectory tracking control algorithms for practical applications of CDPRs. Fuzzy PID control is widely used in CDPRs because of its good robustness and fast response speed. However, the fuzzy parameter selection depends on experience, and the efficiency is low. In order to obtain high quality quantization and scale factors quickly, we propose FPID-AWOA. It uses AWOA to find the optimal quantization and scale factors, which makes the fuzzy PID control get better performance. FPID-AWOA can also be applied to control other robots. In future research, we will extend the proposed approach to multiple CDPRs working collaboratively as well as to mobile operational requirements.

Cable-driven parallel robots (CDPRs) are a kind of mechanism with large workspace, fast response, and low inertia. However, due to the existence of various sources of error, it is unavoidable to bring uncertain cable lengths and lead to pose errors of the end-effector. The inverse kinematic model of a CDPR for picking up medicines is established by considering radii of fixed pulleys. The influence of radii of fixed pulleys on errors of cable lengths is explored. Error transfer model of the CDPR is constructed, and uncertain sources of cable lengths are analyzed. Based on evidence theory and error transfer model, an evidence theory-based uncertainty analysis method (ETUAM) is presented. The structural performance function for kinematic response is derived based on the error transfer model. Belief and plausibility measures of joint focal elements under the given threshold are obtained. Kinematic error simulations show that errors of cable lengths become larger with the increase of radii of fixed pulleys. Compared with the vertex method and Monte Carlo method, numerical examples demonstrate the accuracy and efficiency of the ETUAM when it comes to the kinematic uncertainty analysis of the CDPR.

The high nonlinearity and underactuated characteristics of the cable-driven parallel hoisting robot (CDPHR) make vibration suppression control under compound motion a challenging problem. Meanwhile, in practical applications, the speed feedback values required for controlling CDPHR usually need to be measured by indirect methods, which introduces errors into precise control. In addition, the problem of the single-period transmission blank of the swing angle data existing in practical applications affects the vibration suppression performance of the controller. To address these problems, an adaptive feedback tracking control method is proposed in this article. A virtual equivalent system composed of springs, dampers, and mass blocks is designed to replace the speed feedback parameter, enabling precise positioning of the rotation and payload lifting motions for CDPHR, while achieving rapid suppression of payload swing and online identification of mass. Further, a data transmission method based on the experimental platform is designed, which ingeniously uses timestamps to achieve real-time synchronization of sensor and encoder data. Finally, the effectiveness and superior of the control method are verified through experiments on a self-built experiment platform.

By introducing the subinterval perturbation method (SIPM), a hybrid compound function/subinterval perturbation method (HCFSPM) is presented for a dual-crane system (DCS) with large interval variables. The HCFSPM employs the SIPM to decompose a large interval variable into several subinterval variables with small uncertain levels. The interval kinematic compound function vectors and their inverses are approximated by the first-order Taylor and Neumann series, respectively. Based on the monotonic technique, the bounds of original luffing angle vectors are derived. Compared with the first-order compound function/interval perturbation method and the Monte Carlo method, numerical examples verify the effectiveness of the HCFSPM at conducting uncertain kinematic analysis of the DCS, especially when it comes to large uncertain levels.