From Low Thrust to Solar Sailing: A Homotopic Approach

This paper describes a novel method to solve solar-sail minimum-time-of-flight optimal control problems starting from a low-thrust solution. The method is based on a homotopic continuation. This technique allows to link the low-thrust with the solar-sail acceleration, so that the solar-sail solution can be computed starting from the usually easier low-thrust one by means of a numerical iterative approach. Earth-to-Mars transfers have been studied in order to validate the proposed method. A comparison is presented with a conventional solution approach, based on the use of a genetic algorithm. The results show that the novel technique has advantages, in terms of accuracy of the solution and computational time

A Parametric Non-Convex Decomposition Algorithm for Real-Time and Distributed NMPC

A novel decomposition scheme to solve parametric non-convex programs as they arise in Nonlinear Model Predictive Control (NMPC) is presented. It consists of a fixed number of alternating proximal gradient steps and a dual update per time step. Hence, the proposed approach is attractive in a real-time distributed context. Assuming that the Nonlinear Program (NLP) is semi-algebraic and that its critical points are strongly regular, contraction of the sequence of primal-dual iterates is proven, implying stability of the sub-optimality error, under some mild assumptions. Moreover, it is shown that the performance of the optimality-tracking scheme can be enhanced via a continuation technique. The efficacy of the proposed decomposition method is demonstrated by solving a centralised NMPC problem to control a DC motor and a distributed NMPC program for collaborative tracking of unicycles, both within a real-time framework. Furthermore, an analysis of the sub-optimality error as a function of the sampling period is proposed given a fixed computational power.Comment: 16 pages, 9 figure

Time-optimal Coordination of Mobile Robots along Specified Paths

In this paper, we address the problem of time-optimal coordination of mobile robots under kinodynamic constraints along specified paths. We propose a novel approach based on time discretization that leads to a mixed-integer linear programming (MILP) formulation. This problem can be solved using general-purpose MILP solvers in a reasonable time, resulting in a resolution-optimal solution. Moreover, unlike previous work found in the literature, our formulation allows an exact linear modeling (up to the discretization resolution) of second-order dynamic constraints. Extensive simulations are performed to demonstrate the effectiveness of our approach.Comment: Published in 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS

Recent Advances in Computational Methods for the Power Flow Equations

The power flow equations are at the core of most of the computations for designing and operating electric power systems. The power flow equations are a system of multivariate nonlinear equations which relate the power injections and voltages in a power system. A plethora of methods have been devised to solve these equations, starting from Newton-based methods to homotopy continuation and other optimization-based methods. While many of these methods often efficiently find a high-voltage, stable solution due to its large basin of attraction, most of the methods struggle to find low-voltage solutions which play significant role in certain stability-related computations. While we do not claim to have exhausted the existing literature on all related methods, this tutorial paper introduces some of the recent advances in methods for solving power flow equations to the wider power systems community as well as bringing attention from the computational mathematics and optimization communities to the power systems problems. After briefly reviewing some of the traditional computational methods used to solve the power flow equations, we focus on three emerging methods: the numerical polynomial homotopy continuation method, Groebner basis techniques, and moment/sum-of-squares relaxations using semidefinite programming. In passing, we also emphasize the importance of an upper bound on the number of solutions of the power flow equations and review the current status of research in this direction.Comment: 13 pages, 2 figures. Submitted to the Tutorial Session at IEEE 2016 American Control Conferenc