Robot task space PID type regulation with prescribed performance guaranties

A prescribed performance regulator for the generalized position of the robot arm endpoint in the task space is proposed. The control input which incorporates a transformed error guarantees a prescribed performance regarding the response of the endpoint generalized position error. The use of two different forms of this transformed error will be presented and compared. Mathematical proof of the controller´s success in fulfilling the desired goals is given. A simulation of a three degrees of freedom robot is used to confirm the theoretical findings for both cases of the transformed error.