An analysis of the inverse kinematics for a 5-DOF manipulator

This paper proposes an analytical solution for a 5-DOF manipulator to follow a given trajectory while keeping the orientation of one axis in the end-effector frame. The forward kinematics and inverse kinematics for a 5-DOF manipulator are analyzed systemically. The singular problem is discussed after the forward kinematics is provided. For any given reachable position and orientation of the end-effector, the derived inverse kinematics will provide an accurate solution. In other words, there exists no singular problem for the 5-DOF manipulator, which has wide application areas such as welding, spraying, and painting. Experiment results verify the effectiveness of the methods developed in this paper.     

Adaptive inverse dynamics control of robots with uncertain kinematics and dynamics

It has been about two decades since the first globally convergent adaptive tracking controller was derived for robots with dynamic uncertainties. However, not until recently has the problem of concurrent adaptation to both the kinematic and dynamic uncertainties found its solution. This adaptive controller belongs to passivity-based control. Though passivity-based controllers have many attractive properties, in general, they are not able to guarantee the uniform performance of the robot over the entire workspace. Even in the ideal case of perfect knowledge of the manipulator parameters, the closed-loop system remains nonlinear and coupled. Thus the closed-loop tracking performance is difficult to quantify, while the inverse dynamics controllers can overcome these deficiencies. Therefore, in this work, we will develop a new adaptive Jacobian tracking controller based on the inverse manipulator dynamics. Using the Lyapunov approach, we have proved that the end-effector motion tracking errors converge asymptotically to zero. Simulation results are presented to show the performance of the proposed controller.