Study on inverse kinematics and trajectory tracking control of humanoid robot finger with nonlinearly coupled joints

It is a challenging problem to derive closed-form solution of inverse kinematics of the humanoid robot fingers with nonlinearly coupled joints. This paper presents a novel quasiclosed-form solution of inverse kinematics for such fingers. On the assumption that the angles of the two coupled joints are equal, an approximate closed-form solution of finger's inverse kinematics is derived firstly. Utilizing the approximate solution as the ancillary variables, the problem of inverse kinematics is converted to determination of the joint angles from the approximate solution instead of the fingertip position. Based on the properties of the approximate solution, it is found that the approximate solution of the coupled joint plays the most important role in the joint angle derivation. In practical implementation, a ID look-up table and the linear interpolation to the approximate solution of the coupled joint are used to compute the accurate joint angles named the quasi-closed-form solution. Simulation results show that the proposed method exhibits good accuracy, though its computational cost is slightly higher than that of the approximate solution. Furthermore, a trajectory tracking controller is developed, formed with a combination of feedforward, feedback and a saturation control. The controller does not require the explicit use of dynamic modeling parameters. Lyapunov based stability analysis indicates that the finger system with the proposed controller can be asymptotically stable. Experiments are finally performed to demonstrate the correctness of the proposed solution of inverse kinematics and the trajectory tracking control algorithm.