Practical Design Considerations for Performance and Robustness in the Face of Uncertain Flexible Dynamics in Space Manipulators

Low frequency dynamics introduced by structural flexibility can result in considerable performance degradation and even instability in on-orbit, robotic manipulators. Although there is a wealth of literature that addresses this problem, the author has found that many advanced solutions are often precluded by practical considerations. On the other hand, classical, robust control methods are tractable for these systems if the design problem is properly constrained. This paper investigates a pragmatic engineering approach that evaluates the system’s stability margins in the face of uncertain, flexible perturbation dynamics with frequencies that lie close to or within the bandwidth of the nominal closed-loop system. The robustness of classical control strategies is studied in the context of both collocated (joint rate) and non-collocated (force/torque and vision-based) feedback. It is shown that robust stability and performance depend on the open-loop control bandwidth of the nominal control law (as designed for a simplified, rigid plant). Namely, the designed bandwidth must be constrained to be lower than the minimum flexible mode frequency of the unmodeled dynamics by a given factor. This strategy gives credence to popular heuristic methods commonly used to reduce the effect of unmodeled dynamics in complex manipulator systems.

Estimation of Vibration Characteristics of a Space Manipulator From Air Bearing Supported Test Data

Space manipulators have attracted much attention due to their implications in on-orbit servicing in recent years. Air bearing based support equipment is widely used for ground test to offset the effect of gravity. However, an air bearing support introduces a new problem caused by additional inertial and mass properties. Additional mass and inertial load will influence the dynamics behavior, especially stiffness information and vibration response of the whole ground test system. In this paper, a set of procedures are presented to remove the influence of air bearings and identify the true equivalent joint stiffness and damping from the test data of a motor-braked space manipulator with an air bearing support. First, inertia parameters are identified. Then, the equivalent joint stiffness and damping are determined by using a genetic algorithm (GA) method. Finally, true vibration characteristics of the manipulator are estimated by removing the additional inertia caused by the air bearings. Moreover, simulations and experiments are carried out to validate the presented procedures.

A Novel Analytical Inverse Kinematics Method for SSRMS-Type Space Manipulators Based on the POE Formula and the Paden-Kahan Subproblem

Space manipulators which have a similar symmetrical structure with seven revolute joints, such as the space station remote manipulator system (SSRMS), can be called SSRMS-type space manipulators. The analytical inverse kinematics of an SSRMS-type manipulator can be solved by locking a single joint; the locked joint (joint 1, 2, 6, or 7) can be determined by configuration analysis. Although widely used in establishing the kinematics of SSRMS-type manipulators, the Denavit-Hartenberg (DH) method has a singular problem when two adjacent joint axes are nearly parallel. To avoid this problem, this paper proposes a novel analytical inverse kinematics method for SSRMS-type manipulators based on the product of exponentials (POE) formula and the Paden-Kahan subproblem. Because of the symmetrical structure, an SSRMS-type manipulator degrades to two kinds of 6-degree-of-freedom (DOF) manipulators when locking a single joint (joint 1, 2, 6, or 7). The analytical inverse kinematics of these two kinds of 6-DOF manipulators is solved by combining the Paden-Kahan subproblems and geometric and algebraic methods, respectively. The proposed approach is not only singularity free compared with the traditional DH-based methods but also more accurate than the POE-based numerical solution. The simulation results verify the efficiency of the proposed approach.