Configuration error function design and application to fixed-time geometric terminal sliding-mode control on SE(3)

Abstract For addressing the position and attitude control of a fully-actuated 6-degree-of-freedom (6-DOF) rigid body, a new configuration error function is designed, and the configuration error vector is deduced as the gradient of this function, where the configuration stands for the set of position and attitude and is described by the nonlinear manifold SE(3). Based on the newly designed configuration error function, a geometric terminal sliding-mode controller is proposed to stabilize the configuration tracking errors of rigid body in a bounded fixed time considering disturbances. Simulations for close range rendezvous and docking of a spacecraft in an elliptical orbit illustrate the effectiveness of the proposed control scheme.

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