Sliding mode control of spatial mechanical systems decoupling translation and rotation

This paper looks at the robust trajectory control of spatial mechanical systems using sliding mode techniques. Two distinctions of the proposed method from reported methods are: (1) The measure of attitudinal error used is intrinsically defined, Euclidean-geometric, and intuitive. From Euler's theorem it follows that given a desired and actual attitude of a rigid body there exists an axis and angle of rotation relating the two attitudes. This defines a relative rotation vector, which is used as an intrinsically defined, intuitive measure of error. Reported methods use algebraic differences of entities such as generalized coordinates representing attitude. While functionally correlated to attitudinal error, these measures are not intrinsically defined. (2) A novel, dynamically nonlinear sliding function is used that results in a simple control law. The parameters of this function are dynamically and geometrically intuitive. Simulation results are given for a spacecraft tracking a complex desired trajectory.