Kinematic and Dynamic Characteristics of the Free-Floating Space Manipulator with Free-Swinging Joint Failure

Abstract

For the free-floating space manipulator with free-swinging joint failure, motions among its active joints, passive joints, free-floating base, and end-effector are coupled. It is significant to make clear all motion coupling relationships, which are defined as "kinematic coupling relationships" and "dynamic coupling relationships," inside the system. With the help of conservation of system momentum, the kinematic model is established, and velocity mapping relation between active joints and passive joints, velocity mapping relation between active joints and base, velocity mapping relation between active joints and end-effector. We establish the dynamic model based on the Lagrange equation, and the system inertia matrix is partitioned according to the distribution of active joints, passive joints, and the base. Then, kinematic and dynamic coupling relationships are explicitly derived, and coupling indexes are defined to depict coupling degree. Motions of a space manipulator with free-swinging joint failure simultaneously satisfy the first-order nonholonomic constraint (kinematic coupling relationships) and the second-order nonholonomic constraint (dynamic coupling relationships), and the manipulator can perform tasks through motion planning and control. Finally, simulation experiments are carried out to verify the existence and correctness of the first-order and second-order nonholonomic constraints and display task execution effects of the space manipulator. This research analyzes the kinematic and dynamic characteristics of the free-floating space manipulator with free-swinging joint failure for the first time. It is the theoretical basis of free-swinging joint failure treatment for a space manipulator. Passive joints Base Space manipulator End-effector − Figure 1: Kinematic model of the n-DOF space manipulator with free-swinging joint failure.3 International Journal of Aerospace Engineering R 3×n represents the contribution of θ to angular momentum L. J LM and J AM can be expressed as J LM = j LM1 , j LM2 ,⋯,j LMn and J AM = j AM1 , j AM2 ,⋯,j AMn , respectively, and we can find column vectors corresponding to passive joints and active joints to make up matrixesEquations (6) and (7) can be expressed in matrix form T P T ∈ R 3+p ×1 and the Jacobian matrix iswhere J eA v is the first three rows of J eA . The kinematic coupling index is the manipulability of J vePA . For the task to eliminate the base attitude deflection when regulating passive joints, we select the task velocity vector as v ωbP = θ T P , ω T 0 T ∈ R p+3 ×1 and the Jacobian matrix iswhere J bA ω is the last three row vectors of J bA . The kinematic coupling index is the manipulability of J ωbPA . To eliminate base attitude disturbance, we keep ω 0 ≡ 0 [28]. For general space tasks, we should select v task = v task1 , v task2 ,⋯,v task f T ∈ R f ×1 according to controlled passive units for current task requirements. f is the dimensionality of v task . Then, the corresponding row vectors from J t need to be taken out to construct the Jacobian matrix:...