Simple robust r-α tracking controllers for uncertain fully-actuated mechanical systems

We consider the problem of designing robust tracking controllers for uncertain fully-actuated mechanical systems. We propose controllers which are robust r - alpha tracking controllers in the following sense. For a prespecified rate of convergence alpha > 0 and a prespecified tolerance r > 0, a proposed controller guarantees that the system's trajectory exponentially converges to any desired trajectory with rate a and ro within the tolerance v. Controller design is based on Lyapunov functions. The main advantage of these controllers is their simplicity. These controllers do not use the regressor matrix made popular in the area of robotic control which makes them simple to implement. Application to a two-link robotic manipulator is presented. Numerical simulation results are included.