Human–robot cooperative tasks require physical human–robot interaction (pHRI) systems that can adapt to individual human behaviors while ensuring robustness and stability. This paper presents a dual-loop control framework combining an admittance outer loop and a neural adaptive inner loop based on the Robust Integral of the Sign of the Error (RISE) approach. The outer loop reshapes the manipulator trajectory according to interaction forces, ensuring compliant motion and user safety. The inner-loop Adaptive RISE–RBFNN controller compensates for unknown nonlinear dynamics and bounded disturbances through online neural learning and robust sign-based correction, guaranteeing semi-global asymptotic convergence. Quantitative results demonstrate that the proposed adaptive RISE controller with neural-network error compensation (ARINNSE) achieves superior performance in the Joint-1 tracking task, reducing the root-mean-square tracking error by approximately 51.7% and 42.3% compared to conventional sliding mode control and standard RISE methods, respectively, while attaining the smallest maximum absolute error and maintaining control energy consumption comparable to that of RISE. Under human–robot interaction scenarios, the controller preserves stable, bounded control inputs and rapid error convergence even under time-varying disturbances. These results confirm that the proposed admittance-based RISE–RBFNN framework provides enhanced robustness, adaptability, and compliance, making it a promising approach for safe and efficient human–robot collaboration.
Chen et al. (Wed,) studied this question.