Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.

Planning Algorithms: Introductory Material

This article provides a tutorial introduction to visual servo control of robotic manipulators. Since the topic spans many disciplines our goal is limited to providing a basic conceptual framework. We begin by reviewing the prerequisite topics from robotics and computer vision, including a brief review of coordinate transformations, velocity representation, and a description of the geometric aspects of the image formation process. We then present a taxonomy of visual servo control systems. The two major classes of systems, position-based and image-based systems, are then discussed in detail. Since any visual servo system must be capable of tracking image features in a sequence of images, we also include an overview of feature-based and correlation-based methods for tracking. We conclude the tutorial with a number of observations on the current directions of the research field of visual servo control.

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A tutorial on visual servo control

Level set methods have been widely used in image processing and computer vision. In conventional level set formulations, the level set function typically develops irregularities during its evolution, which may cause numerical errors and eventually destroy the stability of the evolution. Therefore, a numerical remedy, called reinitialization, is typically applied to periodically replace the degraded level set function with a signed distance function. However, the practice of reinitialization not only raises serious problems as when and how it should be performed, but also affects numerical accuracy in an undesirable way. This paper proposes a new variational level set formulation in which the regularity of the level set function is intrinsically maintained during the level set evolution. The level set evolution is derived as the gradient flow that minimizes an energy functional with a distance regularization term and an external energy that drives the motion of the zero level set toward desired locations. The distance regularization term is defined with a potential function such that the derived level set evolution has a unique forward-and-backward (FAB) diffusion effect, which is able to maintain a desired shape of the level set function, particularly a signed distance profile near the zero level set. This yields a new type of level set evolution called distance regularized level set evolution (DRLSE). The distance regularization effect eliminates the need for reinitialization and thereby avoids its induced numerical errors. In contrast to complicated implementations of conventional level set formulations, a simpler and more efficient finite difference scheme can be used to implement the DRLSE formulation. DRLSE also allows the use of more general and efficient initialization of the level set function. In its numerical implementation, relatively large time steps can be used in the finite difference scheme to reduce the number of iterations, while ensuring sufficient numerical accuracy. To demonstrate the effectiveness of the DRLSE formulation, we apply it to an edge-based active contour model for image segmentation, and provide a simple narrowband implementation to greatly reduce computational cost.

Distance Regularized Level Set Evolution and Its Application to Image Segmentation

This tutorial/survey paper: (1) provides a concise point of departure for researchers and practitioners alike wishing to assess the current state of the art in the control and monitoring of civil engineering structures; and (2) provides a link between structural control and other fields of control theory, pointing out both differences and similarities, and points out where future research and application efforts are likely to prove fruitful. The paper consists of the following sections: section 1 is an introduction; section 2 deals with passive energy dissipation; section 3 deals with active control; section 4 deals with hybrid and semiactive control systems; section 5 discusses sensors for structural control; section 6 deals with smart material systems; section 7 deals with health monitoring and damage detection; and section 8 deals with research needs. An extensive list of references is provided in the references section.

Structural control: past, present, and future

Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:

http://ieeexplore.ieee.org/iel5/5/31307/01456462.pdf

Linear systems

By using the structural parenthood of induction motors equations and the generalized nonholonomic integrator, the present note shows how singularity-free versions of the field-oriented control method are derived by direct application of the transverse function (t.f.) control approach developed by the authors for the stabilization of general controllable driftless systems [P. Morin and C. Samson, 2003].

http://ieeexplore.ieee.org/iel5/8969/28476/01271952.pdf

Field-oriented control of induction motors by application of the transverse function control approach

Advanced Robotics and Autonomous Systems

The control of a wheeled vehicle with front and rear steering wheels is addressed. With respect to more classical car-like vehicles, an advantage of this type of mechanism is its enhanced maneuverability. The Transverse Function approach is used to derive feedback laws which ensure practical stabilization of arbitrary reference trajectories in the cartesian space, and asymptotic stabilization when the trajectory is feasible by the nonholonomic vehicle. Concerning this latter issue, previous results are extended to the case of transverse functions defined on the Special Orthogonal Group SO(3).

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Control of two-steering-wheels vehicles with the Transverse Function approach

The stabilization to a desired pose of a nonholonomic mobile robot carrying a manipulator arm, based on sensory data provided by a camera mounted on the end-effector of the arm, is considered. Instances of this problem occur in practice during docking or parallel parking maneuvers of such vehicles. The visual data obtained as the camera tracks a target of known geometry are used to implement a continuous time-varying state feedback for the stabilization of the mobile robot. We focus on the case where the camera moves parallel to the plane supporting the mobile robot. The experimental evaluation of the proposed techniques uses a mobile manipulator prototype developed in our laboratory and dedicated multiprocessor real-time image processing and control systems. The real-time programming aspects of the experiments are handled in the context of the ORCCAD control architecture development environment.

Experiments in real-time vision-based point stabilization of a nonholonomic mobile manipulator

The Transverse Function (TF) approach is applied to the tracking control problem for a nonholonomic three-segments/snake-like wheeled mechanism similar to a planar low-dimensional version of Hirose's Active Cord Mechanism (ACM). Unlike earlier studies devoted to this type of serpentine mechanism and based on the computation and sequential application of a discrete number of open-loop control primitives, the proposed control design yields smooth (nonlinear) feedbacks in the spirit, and prolongation, of Linear Control Theory. It is also supported by a rigorous stability analysis, and it further includes a solution to the delicate -often overlooked-problem of mechanical singularities avoidance. Another asset of the approach is that the ultimate boundedness of the tracking errors, with arbitrary tracking precision obtained via the tuning of the considered transverse function parameters, is achieved for any motion of the reference frame used to specify the desired gross motion of the mechanism. These properties are illustrated by simulation results. The fact that the TF approach involves periodic functions with time-derivatives depending on frequencies used as extra control variables points out connections between this approach and biologically inspired Central Pattern Generators (CPG) often evoked in the literature on systems exhibiting internal oscillatory behavior.

Claude Samson

Papers

Field-oriented control of induction motors by application of the transverse function control approach

Advanced Robotics and Autonomous Systems

Control of two-steering-wheels vehicles with the Transverse Function approach

Experiments in real-time vision-based point stabilization of a nonholonomic mobile manipulator

Feedback control of a wheeled snake mechanism with the Transverse Function approach