Randomized planning of dynamic motions avoiding forward singularities

The final publication is available at link.springer.comForward singularities, also known as direct, or actuator singularities, cause many problems to the planning and control of robot motions. They yield position errors and rigidity losses of the robot, and generate unbounded actions in typical control laws. To circumvent these issues, this paper proposes a randomized kinodynamic planner for computing trajectories avoiding such singularities. Given initial and final states for the robot, the planner attempts to connect them by means of a dynamically-feasible, singularity-free trajectory that also respects the force limits of the actuators. The performance of the strategy is illustrated in simulation by means of a parallel robot performing a highly- dynamic task.Peer ReviewedPostprint (author's final draft

A family of iterative methods that uses divided differences of first and second orders

The family of fourth-order Steffensen-type methods proposed by Zheng et al. (Appl. Math. Comput. 217, 9592-9597 (2011)) is extended to solve systems of nonlinear equations. This extension uses multidimensional divided differences of first and second orders. For a certain computational efficiency index, two optimal methods are identified in the family. Semilocal convergence is shown for one of these optimal methods under mild conditions. Moreover, a numerical example is given to illustrate the theoretical results.Peer ReviewedPostprint (author's final draft

An interior penalty method for a finite-dimensional linear complementarity problem in financial engineering

In this work we study an interior penalty method for a finite-dimensional large-scale linear complementarity problem (LCP) arising often from the discretization of stochastic optimal problems in financial engineering. In this approach, we approximate the LCP by a nonlinear algebraic equation containing a penalty term linked to the logarithmic barrier function for constrained optimization problems. We show that the penalty equation has a solution and establish a convergence theory for the approximate solutions. A smooth Newton method is proposed for solving the penalty equation and properties of the Jacobian matrix in the Newton method have been investigated. Numerical experimental results using three non-trivial test examples are presented to demonstrate the rates of convergence, efficiency and usefulness of the method for solving practical problems

PREDICTOR-CORRECTOR METHOD FOR LINEAR COMPLEMENTARITY-PROBLEMS WITH POLYNOMIAL COMPLEXITY AND SUPERLINEAR CONVERGENCE

We extend the Mizuno-Todd-Ye predictor-corrector algorithm for solving monotone linear complementary problems. We prove that the extended algorithm is globally Q-linearly convergent and solves problems with integer data of bitlength L in at most O(square-root nL) interations. We also prove that the duality gap converges to zero Q-superlinearly for problems having strictly complemetary solutions. Our results generalize the results obtained by Ye, Tapia, and Zhang for linear programming

A full-Newton step feasible interior-point algorithm for P*(k)-linear complementarity problems

In this paper, a full-Newton step feasible interior-point algorithm is proposed for solving P*(κ) -linear complementarity problems. We prove that the full-Newton step to the central path is local quadratically convergent and the proposed algorithm has polynomial iteration complexity, namely, O ((1+4κ) √nlogn/ε), which matches the currently best known iteration bound for P*(κ)-linear complementarity problems. Some preliminary numerical results are provided to demonstrate the computational performance of the proposed algorithm