A new class of robust control laws for tracking of robots

For the trajectory following problem of a robot manipulator, a new class of robust control algorithms is proposed. This new class of controls has several important features. First, three kinds of stability results, uniformly and ultimately bounded stability, asymptotic stability, and exponential stability, can be achieved using a control of the same form. Which kind of stability result is achieved is dependent solely upon the designer´s choice of a time-varying gain. The designer has great freedom to choose any specific control in the class. Exact knowledge of robot dynamics is required except that unknown dynamics are required to be bounded in the Euclidean norm by a second-order polynomial function with known coefficients