The control problem for the multivariable and nonlinear dynamics of robotic manipulators and autonomous vehicles is solved with the use of a flatness-based control approach which is implemented in successive loops. The state-space model of these robotic systems is separated into two subsystems, which are connected between them in cascading loops. Each one of these subsystems can be viewed independently as a differentially flat system and control about it can be performed with inversion of its dynamics as in the case of input–output linearised flat systems. The state variables of the second subsystem become virtual control inputs for the first subsystem. In turn, exogenous control inputs are applied to the first subsystem. The whole control method is implemented in two successive loops and its global stability properties are also proven through Lyapunov stability analysis. The validity of the control method is confirmed in two case studies: (a) control of a 3-DOF industrial rigid-link robotic manipulator and (b) control of a 3-DOF autonomous underwater vessel. The novel control method can simplify significantly the solution of the nonlinear control problem for robotic manipulators and vehicles. Unlike global linearisation-based control schemes, the proposed flatness-based method in successive loops does not need any changes in state variables of complicated state-space model transformations.
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