Geometric Modeling And Tracking Control For Space Manipulator

With the continuous development of human space exploration activities,the space robot technology will play an increasingly important role in ensuring reliable and efficient operation of satellite and space station.Trajectory tracking control,as one of the key technologies to perform complex in-orbit service operations,has been extensively studied and achieved a great deal of results.However,these work has not considered the influence of the non-Euclidean property of configuration space SE(3)on the tracking performances of the end-effector.Although some geometric approaches(such as,spatial operator algebra,screw algebra)have been used to establish the mathematical model of the space robot,they tend to improve the computation efficiency,instead of considering whether to facilitate the tracking controller design on SE(3)via the mode-based control techniques.In addition,the intrinsic tracking control problem for the single rigid body has been extensively studied.It follows from these work that neglecting the topological property of the configuration space will result in incomplete global stability results.Based on above viewpoints,this dissertation focus on solving the geometric modeling and the relevant intrinsic tracking control problem for space robots by incorporating the standard concepts and operators from Lie group,Lie algebra and screw theory.The main contents of this dissertation are presented as follows:Relying on the standard concepts and operators from Lie group,Lie algebra and screw theory,we first establish an unified geometric modeling framework for the general multi-arm unfixed-based serial manipulator system.It is well known that the nonEuclidean property of SO(3)makes all local parameterizations fail to represent the configuration space both globally and uniquely.In order to avoid the singular or redundant description problem induced by parameterizations,we directly formulate the forward kinematics mapping of the multi-arm vehicle-manipulator system on its configuration space based on the product of exponentials formula.Then,the manipulator Jacobian is given by virtue of the adjoint transformation to describe the velocity-level behaviour of this system.Besides,the relationship among wrenches applied at the end-effector,the external forces applied at the base and the joint torques also been established in this dissertation.Since we describe the pose of the base with respect to the inertia frame by the homogeneous matrix,the body velocity of the base is the matrix value function of the elements of the homogeneous matrix.As a result,the dynamic equation of the multi-arm unfixed-base manipulator can't be directly formulated by the Lagrangian approach.In order to overcome this problem,we introduce the concepts of geometric variation and quasi-coordinates,and then formulate the dynamic equations according to the Hamilton's law of variation principle.Taking advantage of the Christoffel symbol functions,we put the equations of motion back into a vector form and give some structural properties of the dynamic model.Meanwhile,the kinematic and dynamic equations of the free-floating space manipulator are established by the proposed geometric modeling approach,which lays the foundation to construct the coordinate-free controller in the sequel.The joint-space tracking control problem for base-controlled space manipulator is solved based on the adaptive back-stepping approach and the Lyapunov function approach.In practical applications,for security reasons,the angular velocities and the control torques of the manipulator have to be limited.To this end,a command filter based adaptive nonliear controller is proposed to obtain the limited command signal and its derivative,and overcome the differential explosion problem in the design procedure of backstepping method.In order to make the pose of the base can tracking track a given smooth trajectory,we design an intrinsic robust tracking controller with guaranteed prescribed performance on the tangent bundle of SE(3).For this purpose,the trajectory tracking problem on SE(3)is transformed into a point stabilization problem of an error dynamic system in the associated Lie algebra by suitable selection of the configuration error function and position error vector.For the tracking controller design,the error transformation technique is utilized to transform the tracking error dynamics with inequality constraints to an equivalent ”unconstrained” error one.Finally,a coordinatefree robust tracking controller is designed for the ”unconstrained” error dynamics to solve the prescribed performance tracking control problem for the base.In view of the fact that the robustifying term of the above controller with guaranteed prescribed performance requires the prior knowledge of the boundary of the lumped disturbance,we propose a disturbance observer based linear sliding-mode controller with guaranteed prescribed performance for the uncertain free-floating space robot to solve the tracking control problem in task space.To this end,we derive the geometric model for the free-floating space manipulator with kinematic and dynamic uncertainty,and then formulate the prescribed performance tracking control problem in task space.To ensure the tracking error converge to the origin asymptotically and improve the robustness of the closed-loop control system against the external disturbance and modelling uncertainty,we design a linear sliding mode surface for the equivalent ”unconstrained” error dynamics.On this basis,a robust tracking controller with guaranteed performance is proposed via a sign switching function.To reduce the chattering in control input without affecting tracking performance,we design an adaptive-gain Super-Twisting disturbance observer to real-time estimate the external disturbance,and then construct a disturbance observerbased tracking controller with guaranteed prescribed performance.Considering the fact that the above control system suffers chattering and the convergence time of the tracking error vector cannot be estimated,we propose a finite-time adaptive controller with guaranteed prescribed performance to solve the trajectory tracking problem for the uncertain free-floating space robot with joint torque constraint in task space.To ensure that the convergence time of the system is independent of the initial value of the system state,we design a nonsingular fixed-time sliding mode surface for the transformed equivalent error system.In practical applications,the chattering occurred in the control input will destroy the actuator severely.To this end,we design an adaptive update law to real-time estimate the upper boundary of the lumped disturbance,which eliminates the discontinuous term in the controller.Thus,the chattering problem is avoided.Based on the estimated boundary information,we propose a finite-time reaching law to ensure that the system error converge to the boundary layer of the switching surface in spite of the uncertainties.Meanwhile,the stability analysis is presented to prove that the designed adaptive controller can fulfill the prescribed performance tracking control task despite of the joint control torque saturation constraint.