Asymmetric Integral Barrier Lyapunov Function-Based Human–Robot Interaction Control for Human-Compliant Space-Constrained Muscle Strength Training

In this article, an asymmetric integral barrier Lyapunov function (AIBLF)-based control scheme is proposed for human–robot interaction (HRI), with which robot-aided human-compliant space-constrained muscle strength training can be achieved. First, an admittance model is exploited to generate compliant desired trajectory with the input of human–robot interaction torque. Then, on the basis of the super-twisting algorithm, a nonlinear observer is built to estimate and further compensate for the lumped disturbance applied to the robotic driving joint, including the active torque from human subject, the robotic model uncertainty, the friction, etc. Finally, an AIBLF-based controller involving nonlinear observer is proposed to solve the trajectory tracking issues in addition to the general constraint of training task space, in which the AIBLF strategy is utilized to establish an asymmetric-constrained training task space with adjustable boundary effects. This approach ensures that the training environment is tailored to accommodate individual needs and preferences, promoting a safer and more comfortable training experience. The convergence of all states and stability analysis for the closed-loop system are presented via the Lyapunov stability theory. The effectiveness of the proposed control scheme is verified by a single-joint muscle strength training robot in various experiments, and it is worth noting that this method can be easily extended to other multijoint robotic systems with the demand of human compliance and space constraint.