A numerical approach to trajectory planning for yoyo movement

Abstract

Based on nonlinear trajectory generation (NTG) software package, a general approach (i.e. numerical solution) to trajectory planning for yoyo motion is presented. For the real-time control of such periodical dynamic system, a critical problem is how to implement fast solving the optimal trajectory, so as to meet the real-time demand. However, traditional numerical solution methods are very time-consuming. In this paper, the optimization problem is solved by mapping the problem to a lower-dimension space. And combined with multithread programming technology, the computation time for solving the optimal trajectory is greatly reduced. Simulation results show that the numerical solution is identical to the analytic one, which demonstrates the correctness of the proposed method. The computation time of one cycle of yoyo simulation is about 10 ms, which shows that the proposed numerical method can be applied to the real-time control of yoyo playing.

Hybrid regularization methods for seismic reflectivity inversion

“…Therefore, many methods can be applied to solve the problem, e.g., primal-dual interior point methods, second-order cone program and Newton methods for logarithm barrier problem (Yuan 1993). An outline of solving the l 1 -norm minimization problem by linear programming is given in Appendix B.…”

“…, n and L i for all i form an n × (n + 1) matrix. For solving the above minimization problem, one may try Gauss-Newton method (Yuan 1993) since the gradient and Hessian can be easily computed. For simplicity of notation, we set ψ(r ) := 1 2 K r − d δ 2 l 2 .…”

Projected gradient methods for synchrotron radiation spectra distribution function reconstruction

“…For example, for the classical steepest descent (SD) method [21], the stepsize k is chosen such that J [x] is minimized along the line x k À k grad k [J ], that is,…”

Preconditioning non-monotone gradient methods for retrieval of seismic reflection signals

“…However, the steepest descent method is slow in convergence and zigzagging after several iterations [42]. The poor behavior is due to the optimal choice of the step size and not to the choice of the steepest descent direction g k .…”

“…This figure vividly shows Iterative steps Log scale of the objective function us the nonmonotonicity and speediness of the non-monotone gradient descent method. It is well known that the gradient descent method and the conjugate gradient method possess linear convergence rate [42]. And with proceeding of iterations, zigzagging phenomenon would occur for these two methods [33,34].…”