Finite-Time Synchronous Motion Control for Pneumatic Muscle-Actuated Parallel Robots in Cartesian Space

Pneumatic muscles, being biomimetic actuators with excellent flexibility and high power density, are highly favored in the field of flexible robots. Nevertheless, the accompanying problems, including high nonlinearities, time-varying parameters, hysteresis, etc., also bring a lot of trouble to their motion control. Moreover, for multiple motion chain systems, such as pneumatic muscle-actuated (PMA) parallel robots, most existing results have not considered the motion synchronization problem among motion chains, adversely affecting the overall motion performance. Therefore, this article develops a synchronous motion control (SMC) method for PMA parallel robots in Cartesian space, which not only guarantees the asymptotic tracking performance of end effectors, but also makes tracking errors and synchronization errors converge to near the origin in the adjustable finite time. Specifically, the proposed method compensates for the synchronization errors of end effectors in the coordinate axis directions, significantly improving motion accuracy; meanwhile, the elaborately modified coupling errors can successfully avoid the singularity problem at special positions. For all our knowledge, this article proposes the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">first</i> finite-time adaptive SMC method analyzed and designed in Cartesian space, to obtain <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rapid</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">accurate</i> tracking performance <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">without</i> prior knowledge of model information. Finally, rigorous theoretical analysis is provided through the extended finite-time stability theorem, and adequate hardware experiments are carried out to verify the feasibility of the proposed method.