A Guide to M.D.I. Statistics for Planning and Management Model Building

This monograph is intended as a practical guide to business applications of the theory of discrimination information statistics as developed by Kullback (1959) and Charnes and Cooper (1975 et seq.). A guide to modeling and computation methods is presented, with references to published applications and a discussion of their implications for business and planning. These implications are developed by means of detailed examples showing MDI to be a practically workable unifying principle for the analysis of demand and market structure. Some applications in other management areas are also noted.IC2 Institut

Bang-Bang Boosting of RRTs

This paper explores the use of time-optimal controls to improve the performance of sampling-based kinodynamic planners. A computationally efficient steering method is introduced that produces time-optimal trajectories between any states for a vector of double integrators. This method is applied in three ways: 1) to generate RRT edges that quickly solve the two-point boundary-value problems, 2) to produce an RRT (quasi)metric for more accurate Voronoi bias, and 3) to time-optimize a given collision-free trajectory. Experiments are performed for state spaces with up to 2000 dimensions, resulting in improved computed trajectories and orders of magnitude computation time improvements over using ordinary metrics and constant controls

Optimal Sampling-Based Motion Planning under Differential Constraints: the Driftless Case

Motion planning under differential constraints is a classic problem in robotics. To date, the state of the art is represented by sampling-based techniques, with the Rapidly-exploring Random Tree algorithm as a leading example. Yet, the problem is still open in many aspects, including guarantees on the quality of the obtained solution. In this paper we provide a thorough theoretical framework to assess optimality guarantees of sampling-based algorithms for planning under differential constraints. We exploit this framework to design and analyze two novel sampling-based algorithms that are guaranteed to converge, as the number of samples increases, to an optimal solution (namely, the Differential Probabilistic RoadMap algorithm and the Differential Fast Marching Tree algorithm). Our focus is on driftless control-affine dynamical models, which accurately model a large class of robotic systems. In this paper we use the notion of convergence in probability (as opposed to convergence almost surely): the extra mathematical flexibility of this approach yields convergence rate bounds - a first in the field of optimal sampling-based motion planning under differential constraints. Numerical experiments corroborating our theoretical results are presented and discussed