The main ideas of path following by predictor-corrector and piecewise-linear methods, and their application in the direction of homotopy methods and non-linear eigenvalue problems are reviewed. Further new applications to areas such as polynomial systems of equations, linear eigenvalue problems, interior methods for linear programming, parametric programming and complex bifurcation are surveyed...

Second-order cone programming (SOCP) is the problem of minimizing linear objective function over cross-section of second-order cones and an a ne space. Recently this problem gets more attention because of its various important applications including quadratically constrained convex quadratic programming. In this paper we deal with a primal-dual path-following algorithm for SOCP to show many of ...

This paper addresses the path-following problem of steering an autonomous airplane along a predefined 3-D path, while performing a coordinated turn maneuver. The presented solution relies on the definition of a path-dependent error space to express the dynamic model of the vehicle, and of an output tracking error that guarantees both path-following and coordinated turn compliance. For controlle...

In this article a solution to the problem of following a curved path in the presence of a constant unknown ocean current disturbance is presented. The path is parametrised by a path variable that is used to propagate a path-tangential reference frame. The update law for the path variable is chosen such that the motion of the path-tangential frame ensures that the vessel remains on the normal of...

In this paper, we present a novel solution for a path following problem in partially-known static environments. Given linearized error dynamic equations, model predictive control (MPC) is employed to produce a sequence of angular velocities. Since the forward velocity of the robot has to be adapted to environmental constraints and robot dynamics while the robot is following a path, we propose a...

We present a new algorithm obtained by changing the search directions in the algorithm given in [8]. This algorithm is based on a new technique for finding the search direction and the strategy of the central path. At each iteration, we use only the full Nesterov-Todd (NT)step. Moreover, we obtain the currently best known iteration bound for the infeasible interior-point algorithms with full NT...

In this paper, we propose a path-following method for computing a curve of equilibria of a dynamical system, based upon the smooth Singular Value Decomposition (SVD) of the Jacobian matrix. Our method is capable of detecting fold points, and continuing past folds. It is also able to detect branch points and to switch branches at such points. Algorithmic details and examples are given.

Your position never gives you the right to command. It only imposes on you the duty of living your life so that others can receive your orders without being humiliated. grew up in Canberra in the 1920s and '30s, then, as now, a planned and favoured town awash with politics, politicians and public servants. Although interested in these dynamics, our caring, skilled family doctor was the person w...

We consider the problem of cooperative manipulation to improve positioning and path following abilities of humans. Using a specially designed actuated manipulator and “steady hand” manipulation we report on compliant path following strategies and their experimental evaluation. Detecting lines and simple curve by processing images from an endoscope mounted on the robot, we traverse these curves ...