Adaptive kinematic and stiffness control of a hybrid-driven soft robot for enhanced interactions under external loads

Soft robots offer promising solutions for human-robot interaction through inherent compliance, yet achieving controllable stiffness while maintaining dexterity remains challenging. This paper introduces a novel hybrid-actuated soft manipulator that exploits the synergistic interaction between tendon-driven mechanisms and pneumatic chambers to realize continuous stiffness modulation over an extensive range. A key challenge for this system is the precise prediction of the minimum actuation pressure required across diverse configurations, which constitutes a highly nonlinear modeling problem. We address this through a Weighted Broad Learning System (WBLS) that learns these complex pressure-configuration relationships with enhanced noise tolerance. Our primary contribution lies in developing an integrated control architecture that combines the WBLS-based pressure predictor with piecewise constant curvature (PCC) kinematics to enable coordinated regulation of both robot pose and mechanical stiffness. The system incorporates a feedback-driven adaptation mechanism that monitors end-effector responses to external disturbances and dynamically compensates for load-induced deformations by adjusting robot pose and stiffness parameters to maintain desired performance. Experimental validation confirms significant stiffness adjustability, achieving more than 3.6-fold variation in axial stiffness. Under external loading conditions, the proposed approach achieves comparable trajectory precision with a reduction in average driving pressure of up to 31.83% compared to conventional rigid-stiffness strategies. Practical validation through complex object handling tasks confirms the system's effectiveness in adaptive manipulation scenarios. • Construction of a soft manipulator capable of large-scale 3D variable stiffness motion using hybrid drive principles. • Utilization of the weighted broad learning system (WBLS) method to identify the nonlinear mapping between configuration and minimum driving pressure, in conjunction with the piecewise constant curvature (PCC) model, to establish a kinematic model under no load conditions. • An adaptive optimization method for configuration and stiffness under external load is proposed, whereby the manipulator is capable of online estimation of the stiffness model and adaptive adjustment of the configuration and stiffness through end position feedback.