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The aim of this investigation is to nd a control for spacecraft rendezvous maneuver in the known elliptical orbit. Model Predictive Controller is used to calculate control for nonlinear system described by equations of spacecraft relative motion. For comparison purpose, model based on Gaussian Variational Equations is introduced. It gives possibility to assess, which type of model is more suitable for rendezvous problems with highly elliptical orbits and relatively large separation between spacecrafts. Variable-mass deputy vehicle is considered. MPC problem includes constraints on control signals, nal state and amount of used propellant.

Growing research interest in space robotic systems capable of accurately performing autonomous manipulation tasks within an acceptable execution time has led to an increased demand for lightweight materials and mechanisms. As a result, joint flexibility effects become important, and represent the main limitation to achieving satisfactory trajectory tracking performance. This paper addresses the nonlinear adaptive output feedback control problem for flexible-joint space manipulators. Composite control schemes in which decentralized simple adaptive control-based adaptation mechanisms to control the quasisteady state robot subsystem are added to a linear correction term to stabilize the boundary layer subsystem, are proposed. An almost strictly passivity-based approach is adopted to guarantee closed-loop stability of the quasi-steady state subsystem. Simulation results are included to highlight the performance and robustness to parametric uncertainties and modeling errors of the proposed composite control methodologies.

The use of harmonic drive gear boxes in space robotic applications offer several attractive properties, such as high reduction ratio, compact size, low mass, and coaxial assembly. However, the flexibility effects of this type of gear mechanism in the joints of robotic manipulators are significant enough to make real-time control challenging. This paper addresses the problem of fuzzy adaptive trajectory control of space manipulators that exhibit elastic vibrations in their joints and that are subject to parametric uncertainties and dynamics modeling errors. The developed control scheme uses a fuzzy adaptation mechanism that varies in real-time the gains of a slow control term designed to stabilize the rigid dynamics, and a linear correction term to further reduce the elastic vibrations at the joints. The proposed controller is validated in numerical simulations in a trajectory tracking scenario by a flexible-joint manipulator. Simulation results suggest that the controller is robust to uncertainties in joint stiffness coefficients and to modeling errors, and yields improved tracking performance compared with conventional flexible-joint control strategies.

Lightweight space robotic systems are known to exhibit elastic effects in their gearboxes, which contribute greatly to the motion of their end-effector. When accurate end-effector positioning is required, such flexible joint vibrations must be taken into account in both the modeling and control of space manipulators. This paper presents an analysis and a comparative numerical simulation study of previous studies on advanced control schemes for flexible joint robots. More specifically, a linear PD control, a rigid-based indirect adaptive control, an indirect adaptive composite control, a nonlinear backstepping control, a transpose Jacobian composite control, and a direct adaptive composite control methodologies are considered. The performance of the controllers is illustrated in a 12.6 × 12.6 m square trajectory tracking scenario by a two-link flexible joint space manipulator.

Flexible effects in the joints of large space robots make their real-time operation a challenging task, especially when accurate endpoint positioning is required. The problem is further aggravated when the flexible joint stiffness matrix is not well known. This paper discusses the application of a model reference adaptive control (MRAC) composite system for tracking the endpoint of a flexible joint space robotic manipulator. The composite control scheme consists in a flexible control term designed to damp the joint vibrations plus a Transpose Jacobian rigid control term for which the control gains are adapted using a novel direct MRAC adaptation law. Numerical simulations show that the adaptive composite controller can maintain stability and good tracking performance despite significant uncertainties in the joint stiffness coefficients. Nomenclature ) , ( q q C & r = rigid centrifugal and Coriolis matrix x e , y e = model reference endpoint position error, ref x – x and ref y – y i I = inertia of link i , n i , , 1 K = m J = motor inertia matrix i m J = inertia of motor i , n

The end effector of a free-flying flexible space robot is tracked along a planar trajectory using inverse flexible dynamics control (IFDC) and fuzzy logic system adaptive control (FLSAC) strategies for comparison. The robot is required to track its end effector between two points in two-dimensional space while maintaining the orbiting rigid spacecraft at a fixed position in space. Simulation results show the IFDC strategy produces a trajectory that fails to reach its commanded final position by a large margin in both coordinates. The FLSAC strategy produces a more accurate trajectory closer to the commanded final position in both coordinates but at a greater computational time burden. Sporadic high magnitude driving torque “spikes” are experienced similar to the “bursting phenomenon” encountered with adaptive control systems. Spacecraft reactive translation and attitude disturbance is minimal in each case but slightly greater for IFDC. Notation

Tracking a flexible robot is simulated using nonadaptive and fuzzy logic system (FLS) adaptive control strategies with noncollocated joint rotation sensors then with a position sensor located 0.5m, 2.25m and 4.0m from the end effector. Collocated joint rotation sensors satisfy hyperstability conditions but fail to capture nonminimum phase (NMP) response that causes control action delay. A position sensor noncollocated at the end effector captures NMP response. Results are poor for nonadaptive control with a collocated rotation sensor and a noncollocated end effector position sensor but very good results are achieved for FLS adaptive control. For noncollocated sensors at 0.5m, 2.25m and 4.0m from the end effector, tracking control results for both strategies are similar but drastically deviate from the commanded trajectory as the sensor gets closer to the elbow joint. FLS adaptive control is most effective for a sensor located either at the elbow joint or end effector.

†Operational problems with robot manipulators in space relate to several factors, one most importantly being structural flexibility and subsequently significant difficulties with the control systems, especially, for position control. This paper presents a comparison of fuzzy logic system (FLS) controllers to determine an optimal design for tracking the endpoint of a two-link flexible robot. The dominant assumed mode of vibration for an EulerBernoulli cantilever beam is coupled with the nonlinear dynamics for rigid links to form an Euler-Lagrange inverse flexible dynamics robot model. A Jacobian transpose control law is adapted by a FLS with link deformation inputs and a single variable output. Simulation results for three, five, seven and nine triangular and Gaussian membership functions are compared to identify an optimal design for best tracking control and least computation time. Results show the optimal choice of FLS is three triangular membership functions at 14 min 51 sec tracking time.

rigid Euler-Lagrange dynamics model but are extended here to a flexible dynamics model based on the first assumed mode calculated using Euler-Bernoulli pinnedpinned beam theory. A square trajectory presents an ideal case for studying intense vibration effects and their control at the four orthogonal direction switches. 7 Operational problems with robots in space relate to several factors. One most important is the structural flexibility problem of a robot manipulator and subsequently significant difficulties with its control systems, especially, position control. Typically, small elastic vibrations of the links coupled with their large rigid link rotations and non-linear dynamics primarily cause these difficulties. This paper presents a control scheme for positioning the endpoint of a two-link robot manipulator modeled with assumed modes flexible dynamics while tracking a square trajectory. The dominant assumed mode vibration is derived for an Euler-Bernoulli pinned-pinned beam to model link flexibility then, coupled with nonlinear dynamics for large rotations of rigid links to formulate an EulerLagrange inverse dynamics robot model. A control law derived using the Jacobian transpose provides joint actuation for both rigid and flexible dynamics. Comparison of output trajectories shows some differences in control performance between the rigid and flexible dynamics models with the transient response characteristics demonstrating a reduction in maximum overshoot for the flexible dynamics over the rigid dynamics models but a lengthier settling time with a consistent albeit slight oscillation about the entire desired steady-state ttrajectory .

reviewed to compare their structure and performance and to identify the most effective in resolving the difficulties. 6, 7, 8, 9, 10 The operational problems with robots in space relate to several factors. One of the most important is the structural flexibility problem of the manipulator and subsequently significant difficulties with its control systems, especially, position control. This paper presents a review of previous work on advanced control schemes for manipulator endpoint positioning while tracking a square trajectory 12.6 m x 12.6 m. by a two-link flexible robot. Schemes include; command shaping, inverse dynamics, linear quadratic regulator, linear quadratic Gaussian with linearized Kalman filter, extended Kalman filter and fuzzy logic adaptive extended Kalman filter, fuzzy logic and repetitive learning. While each scheme tracks with differing degrees of precision, fuzzy logic, in some form within a control scheme, tracks consistently with a high degree of precision, flexibility and robustness. They include; inverse dynamics (IDC), linear quadratic regulator (LQR), linear quadratic Gaussian (LQG) with linearized Kalman filter, extended Kalman filter (EKF) and fuzzy logic adaptive extended Kalman filter (FLAEKF), fuzzy logic (FLC) and, repeated learning (RL). A description of a command shaping, inverse kinematics technique for tracking a square trajectory studied by Banerjee and Singhose is included for comparison. 3, 4 Their work stimulated the studies reviewed in this paper and is alluded to in previous papers. 6, 7, 8, 9, 10