Adaptive tracking controller with exponential restrictions for robotic manipulators

In this work, we design a control solution to solve the tracking trajectory problem for the joints of a robot manipulator. The control considers a proportional derivative (PD) structure with adaptive gains. The adaptation law of the gains is obtained using a Barrier Lyapunov function, which considers a logarithmic form and a time-varying bound through a decreasing exponential. The Barrier design enforces an exponential decrement of the tracking error with a prescribed velocity. The designed control is implemented numerically for a model of a two-degrees-of-freedom robot manipulator. The results are compared with a classical PD controller showing that the designed control performs better in the tracking task. The adaptive PD has a smaller mean square error than the classical PD. The designed control is tested with different convergence parameters, and the results show how the exponential bound enforces a prescribed velocity.