Trajectory Tracking Control Of Space Manipulators With Prescribed Performance

Technological development in robotics has significantly promoted its applicationsin aerospace science, while at the same time the increasing emphasis from outer spaceactivities has also place much more requirements for space manipulators. When spacemanipulators are capturing or interacting with non-cooperative targets, their overallkinematics and dynamics are changing and thus are difficult to be determined exactly.Based on those concerns, this paper conducts the research of trajectory tracking controlof space manipulators in the presence of kinematic and dynamic uncertainties as well asexternal disturbances.The kinematics and dynamics models are firstly deduced from GeneralizedJacobian Matrix and Lagrange equations. The Virtual Manipulator and DynamicallyEquivalent Manipulator are described to make analogies between fix-basedmanipulators and space manipulators. Moreover, the position/attitude coupling andnon-holonomic properties are analyzed to give insight into the unique dynamicproperties of the free-floating space manipulator.For the free-flying space manipulators, the linear in parameter property is utilizedto design the inverse Jacobian adaptive control law. It is shown that by appropriatelychoosing controller parameters, the tracking errors of the closed-loop system can berendered to be asymptotically stable and the upper bounds of the2norm of theposition and velocity tracking errors can be regulated to any desired value. Dissipationanalysis interprets that the prescribed2disturbance attenuation ability can also beguaranteed. Then considering the nonlinear parameterization property for free-floatingspace manipulators, neural networks are designed to approximate the lumpeddisturbances. Combining the time-varying filter and backstepping techniques, theclosed-loop system is proved to be asymptotically stable and has2small gaindisturbance attenuation ability. For the designed controller, it is shown that any small2upper bound of the position and velocity tracking error can be achieved by tuningthe controller parameters, which means that the designed control law can be used toguarantee both steady-state and transient tracking performances.To relax the assumption of Jacobian singularity free in the application ofpreviously designed adaptive inverse Jacobian controller, this paper proposed a controlbased strategy to avoid the singularity issues. The singularity configurations of bothfree-flying and free-floating space manipulators are analyzed. Then from its physicalconfigurations, the singular subspace in task-space is analyzed. Thus if the actual tracking trajectory can always be confined in the non-singular subspace even in thepresence of the uncertainties, the corresponding singularity avoidance problem cans besolved, which means the singularity avoidance problem can be transformed to thecontrol issues with transient requirements for tracking errors. Further, an errortransformation based controller is proposed to achieve that purpose. By designingnonlinear time-varying state transformations, the transient requirements for trackingerrors are changed to the stability requirements of the transformed errors. By designingadaptive backstepping controller to realize the uniformly ultimately bounded stability ofthe transformed errors, the prescribed performance control of original tracking errorscan be achieved, which further ensures the trajectories always stay in non-singularsubspace which solves the singularity avoidance problem.In the end, a two-link planner space manipulator model is set up to illustrate theeffectiveness of the proposed controllers. Simulation results show that the proposedcontroller can effectively handle model uncertainties, external disturbances andJacobian singularity problems.