Finite-time adaptive control for the dual-arm space robots with uncertain kinematics, dynamics and deadzone nonlinearities

Dual-arm space robots are capable of load transporting and coordinated manipulation for on-orbit servicing. However, achieving the accurate trajectory tracking performance is a big challenge for dual-arm robots, especially when mechanical system uncertainties exist. This paper proposes an adaptive control scheme for the dual-arm space robots with grasped targets to accurately follow trajectories while stabilizing base’s attitude in the presence of dynamic uncertainties, kinematic uncertainties and deadzone nonlinearities. An approximate Jacobian matrix is utilized to compensate the kinematic uncertainties, while a radial basis function neural network (RBFNN) with feature decomposition technique is employed to approximate the unknown dynamics. Besides, a smooth deadzone inverse is introduced to reduce the effects from deadzone nonlinearities. The adaption laws for the parameters of the approximate Jacobian matrix, RBFNN and the deadzone inverse are designed with the consideration of the finite-time convergence of trajectory tracking errors as well as the parameters estimation. The stability of the control scheme is validated by a defined Lyapunov function. Several simulations were conducted, and the simulation results verified the effectiveness of the proposed control scheme.

Shamanskii Method for Solving Parameterized Fuzzy Nonlinear Equations

One of the most significant problems in fuzzy set theory is solving fuzzy nonlinear equations. Numerous researches have been done on numerical methods for solving these problems, but numerical investigation indicates that most of the methods are computationally expensive due to computing and storage of Jacobian or approximate Jacobian at every iteration. This paper presents the Shamanskii algorithm, a variant of Newton method for solving nonlinear equation with fuzzy variables. The algorithm begins with Newton’s step at first iteration, followed by several Chord steps thereby reducing the high cost of Jacobian or approximate Jacobian evaluation during the iteration process. The fuzzy coe?cients of the nonlinear systems are parameterized before applying the proposed algorithm to obtain their solutions. Preliminary results of some benchmark problems and comparisons with existing methods show that the proposed method is promising.

An Ulm-like Cayley Transform Method for Inverse Eigenvalue Problems with Multiple Eigenvalues

We study the convergence of an Ulm-like Cayley transform method for solving inverse eigenvalue problems which avoids solving approximate Jacobian equations. Under the nonsingularity assumption of the relative generalized Jacobian matrices at the solution, a convergence analysis covering both the distinct and multiple eigenvalues cases is provided and the quadratical convergence is proved. Moreover, numerical experiments are given in the last section to illustrate our results.