Nonlinear control of a fully actuated robotic hand using high-order sliding mode and feedback linearization controllers

The increasing adoption of prosthetic devices in medical applications introduces complex and variable load conditions, particularly due to the diverse nature of user disabilities. To address the resulting control challenges, this paper proposes a novel High-Order Fully Actuated Sliding Mode Controller (HOFA-SMC) implemented to enhance robustness under system uncertainties and non-linearities. The proposed controller incorporates a proportional-integral (PI) framework to structure the high-order terms and effectively mitigate the chattering commonly associated with sliding mode control. Stability of both the HOFA-SMC and a feedback Linearization controller (FLC) is established using Lyapunov theory. A detailed simulation study is conducted on a full hand model, comprising four 4-degree-of-freedom (DOF) fingers and a 3-DOF thumb, implemented in Python. The controllers are evaluated across three test scenarios: flexion, extension, and ball grasping. Results indicate that HOFA-SMC achieves rapid trajectory convergence (within 0.2 s) and robust performance under varying uncertainty conditions. A comparative analysis further confirms the superiority of HOFA-SMC over traditional SMC and FLC approaches in trajectory tracking and control stability.