Spacecraft Integrated Attitude-position Control Using Dual Quaternions

With the rapid development of the aerospace industry,on-orbit tasks become much more diverse and complicated.Effective attitude and orbit control is the fundamental requirement of all the other on-orbit tasks.For the traditional single monolithic spacecraft system,the attitude and orbit control problems of it are usually considered separately,and arranged to achieve different control objectives based on different requirements.But for the burgeoning multi-spacecraft missions,like rendezvous and docking,on-orbit assembling and so on,a follower spacecraft is often required to synchronously and simultaneously track the desired relative translational-and orientational-motion,with respect to the leader spacecraft.This paper tries to solve six-degree-of-freedom(6-DOF)relative motion control problems of a two-spacecraft formation,which could apply to a series of practical on-orbit spacecraft tasks,include approaching,hovering,flying-around,rendezvous and docking,on-orbit assembling,on-orbit fueling and so on.To describe the integrated attitude and position motion between spacecraft,the dual quaternion formulation,and also the dualquaternion-based 6-DOF kinematics and dynamics are employed in this paper.Then based on the aforementioned background,several control methods are proposed to accomplish the 6-DOF relative tracking objectives,while some important practical issues are considered,including parameter uncertainties suppression,linear-and angular-velocity observation,translational-and orientational-constraint complying,flying safety requirement,and actuator fault tolerance,specified as follows.Based on the traditional certainty-equivalence principle,and by employing a special dual regression matrix,a 6-DOF synchronized adaptive controller is presented to solve the relative attitude and position tracking control problem for a leader-follower spacecraft formation with mass and inertia uncertainties.This controller has a brief structure and a very compact form.Then,utilizing the immersion and invariance concept,under the same background,another high-precision adaptive control method is designed,which can solve the performance degradation problem of closed-loop systems under certaitntyequivalence-based controllers.What's more,compared to relevant results,the number of filters employed in the adaptive law is significantly decreased.To provide reliable and precise estimations for situations when both relative linearand angular-velocities of the follower with respect to the leader are unmeasurable,a dualquaternion-based full-state observer is proposed.The special structure of this observer could ensure C?continuity of all estimated states,and also the global asymptotic convergence of estimation errors,irrespective of control inputs.To further achieve tracking control goals,the observer is combined with an independently designed PD-like controller.Then a special Lyapunov ”strictification” process is carried out to guarantee the essential separation property between the observer and the controller,and also the asymptotic stability of the closed-loop system.Compared to relevant results,the filter structure employed in this method is significantly simplified.Under 6-DOF motion constraints,an artificial potential function based control method is proposed for the final phase proximity operations of spacecraft autonomous rendezvous and docking.In the problem considered in this paper,on the one hand,to acquire reliable relative motion information,the attitude of the follower spacecraft should be proper controlled to keep the leader is always within the field-of-view area of the follower's sensor;on the other hand,the leader spacecraft sometime has a long-span space structure,during the proximity operations,to avoid collisions between the follower and components(for example,solar panels)of the leader,the follower is required to approach the docking port from a certain safety direction.Based on the dual quaternion formulation,an artificial potential function is built and it could effectively describe these two kinds of constraints.Then,a feedback control method is presented to ensure the follower can finally arrive at the docking port of the leader with desired relative attitude and position,while strictly complying with all specified constraints.The local minimum problem associated with the artificial potential function can be addressed by selection of control parameters that satisfies a mild condition.A 6-DOF adaptive fault-tolerant tracking controller is designed for spacecraft formation under actuator faults.First,the dual quaternion based dynamics is modified,the new model could take into account general actuator fault types,including partial energy loss,complete energy loss,zero and continuous floats,and locking.Then,by employing the sliding mode technique,a novel adaptive controller is introduced,which can help the closed-loop system achieve tracking control objectives even in the presence of actuator faults,external disturbances,and parameter uncertainties.Furthermore,benefiting from the special struture of the presented sliding manifold,tracking errors are guaranteed to be converged within a finite time,and this finite time is given in an explicit way,which means it could be directly modified by designers.Extensive numerical simulations are conducted to show the effectiveness and practical application values of all the 6-DOF relative tracking control methods proposed in this paper.