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This paper presents an arbitrary high-order structure-preserving numerical method for the simulation and optimization of the articulated robot dynamics. The proposed numerical scheme is derived by using spectral variational integrators (SVI) to discretize the Lagrangian of multibody robot systems which are calculated by an efficient parallel Lie group formulation. The linear stability conditions of SVI for the simulation of the robot dynamics are given and proofed. The resulting algorithms are examined in a simplified industrial Selective Compliance Assembly Robot Arm (SCARA) and a wheel-leg hybrid mechanism. They exhibit salient advantages over conventional numerical methods. The algorithms converge exponentially, preserve the symplectic form and momentum automatically and exhibit excellent energy stability, which yield more qualitative simulation and optimization results for articulated multibody robot systems. • Efficient construction of structure-preserving numerical algorithm for robots. • Derivation of linear stability conditions of spectral variational integrators. • Dynamics simulation and trajectory optimization of articulated robots via SVI. [ABSTRACT FROM AUTHOR]

In this paper a two-step approach to approximate the invariant manifolds in the circular restricted three-body problem is presented. The method consists in a two-dimensional interpolation, followed by a nonlinear correction. A two-dimensional cubic convolution interpolation is implemented to reduce the computational effort. A nonlinear correction is applied to enforce the energy level of the approximated state. The manifolds are parameterized by using two scalars. Results show efficiency and moderate accuracy. The present method fits the needs of trajectory optimization algorithms, where a great number of manifold insertion points have to be evaluated online. [ABSTRACT FROM AUTHOR]

Abstract: This work deals with the design of transfers connecting LEOs with halo orbits around libration points of the Earth–Moon CRTBP using impulsive maneuvers. Exploiting the coupled circular restricted three-body problem approximation, suitable first guess trajectories are derived detecting intersections between stable manifolds related to halo orbits of EM spatial CRTBP and Earth-escaping trajectories integrated in planar Sun–Earth CRTBP. The accuracy of the intersections in configuration space and the discontinuities in terms of Δv are controlled through the box covering structure implemented in the software GAIO. Finally first guess solutions are optimized in the bicircular four-body problem and single-impulse and two-impulse transfers are presented. [Copyright &y& Elsevier]

Abstract: In this paper, we achieve the control and synchronization of Julia sets in coupled map lattice using gradient control and optimal control respectively. The control of the Julia sets is accomplished by controlling the stable space of the fixed plane. Moreover, the synchronization of two different Julia sets is also accomplished by their trajectories synchronization. To verify the feasibility of these control methods, we consider the Julia sets, whose lattice length is two, as examples to achieve their control and synchronization using different methods respectively. The numerical simulations are also shown to illustrate the effectiveness of these control methods. [Copyright &y& Elsevier]

Abstract: The trajectory planning of redundant robots is an important area of research and efficient optimization algorithms are needed. This paper presents a new technique that combines the closed-loop pseudoinverse method with genetic algorithms. The results are compared with a genetic algorithm that adopts the direct kinematics. In both cases the trajectory planning is formulated as an optimization problem with constraints. [Copyright &y& Elsevier]

Abstract: This paper considers the synchronization dynamics in a ring of four mutually coupled biological systems described by coupled Van der Pol oscillators. The coupling parameter are non-identical between oscillators. The stability boundaries of the process are first evaluated without the influence of the local injection using the eigenvalues properties and the fourth-order Runge–Kutta algorithm. The effects of a locally injected trajectory on the stability boundaries of the synchronized states are performed using numerical simulations. In both cases, the stability boundaries and the main dynamical states are reported on the stability maps in the (K 1, K 2) plane. [Copyright &y& Elsevier]