How to Do Things With Words

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

By a switched system, we mean a hybrid dynamical system consisting of a family of continuous-time subsystems and a rule that orchestrates the switching between them. The article surveys developments in three basic problems regarding stability and design of switched systems. These problems are: stability for arbitrary switching sequences, stability for certain useful classes of switching sequences, and construction of stabilizing switching sequences. We also provide motivation for studying these problems by discussing how they arise in connection with various questions of interest in control theory and applications.

Basic problems in stability and design of switched systems

This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct.

Coverage control for mobile sensing networks

Recently introduced cost-effective depth sensors coupled with the real-time skeleton estimation algorithm of Shotton et al. [16] have generated a renewed interest in skeleton-based human action recognition. Most of the existing skeleton-based approaches use either the joint locations or the joint angles to represent a human skeleton. In this paper, we propose a new skeletal representation that explicitly models the 3D geometric relationships between various body parts using rotations and translations in 3D space. Since 3D rigid body motions are members of the special Euclidean group SE(3), the proposed skeletal representation lies in the Lie group SE(3)×…×SE(3), which is a curved manifold. Using the proposed representation, human actions can be modeled as curves in this Lie group. Since classification of curves in this Lie group is not an easy task, we map the action curves from the Lie group to its Lie algebra, which is a vector space. We then perform classification using a combination of dynamic time warping, Fourier temporal pyramid representation and linear SVM. Experimental results on three action datasets show that the proposed representation performs better than many existing skeletal representations. The proposed approach also outperforms various state-of-the-art skeleton-based human action recognition approaches.

http://ravitejav.weebly.com/uploads/2/4/7/2/24725306/action_recognition_presentation.pdf

Human Action Recognition by Representing 3D Skeletons as Points in a Lie Group

This paper addresses the problem of generating smooth trajectories between an initial and a final position and orientation in space. The main idea is to define a functional depending on velocity or its derivatives that measures smoothness of trajectories and find a trajectory that minimizes this functional. In order to ensure that the computed trajectories are independent of the parametrization of positions and orientations, we use the notions of Riemannian metric and covariant derivative from differential geometry and formulate the problem as a variational problem on the Lie group of spatial rigid body displacements. We show that by choosing an appropriate measure of smoothness, the trajectories can be made to satisfy boundary conditions on the velocities or higher order derivatives. Dynamically smooth trajectories can be obtained by incorporating the inertia of the system into the definition of the Riemannian metric. We state the necessary conditions for the shortest distance, minimum acceleration and minimum jerk trajectories.

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On the generation of smooth three-dimensional rigid body motions

We propose a notion of passivity for hybrid systems. Our work is motivated by problems in haptics and teleoperation where several computer controlled mechanical systems are connected through a communication channel. To account for time delays and to better react to user actions it is desirable to design controllers that can switch between different operating modes. Each of the interacting systems can be therefore naturally modeled as a hybrid system. A traditional passivity definition requires that a storage function exists that is common to all operating modes. We show that stability of the system can be guaranteed even if different storage function is found for each of the modes, provided appropriate conditions are satisfied when the system switches.

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A notion of passivity for hybrid systems

Haptic technology (sense of touch) along with 3D-virtual reality (VR) graphics, creating lifelike training simulations, was used to develop a dental training simulator system (PerioSim). This preliminary study was designed to evaluate whether faculty considered PerioSim realistic and useful for training and evaluating basic procedural skills of students. The haptic device employed was a PHANToM and the simulator a Dell Xeon 530 workstation with 3D, VR oral models and instruments viewed on a stereoscopic monitor. An onscreen VR periodontal probe or explorer was manipulated by operating the PHANToM for sensing lifelike contact and interactions with the teeth and gingiva. Thirty experienced clinical dental and dental hygiene faculty judged the realism of the system. A PowerPoint presentation on one screen provided instructions for the simulator use with the 3D, VR simulator on a second stereoscopic monitor viewed with 3D goggles. Faculty/practitioners found the images very realistic for teeth and instruments, but less so for gingiva. Tactile sensation was realistic for teeth but not so for gingiva. The onscreen instructions were very useful with high potential for teaching. Faculty members anticipated incorporating this device into teaching and were enthusiastic about its potential for evaluating students' basic procedural skills. This study suggests that the preliminary "evidence-of-concept" was successful and PerioSim may aid students in developing necessary dental tactile skills.

Assessment of faculty perception of content validity of PerioSim, a haptic-3D virtual reality dental training simulator.

The paper describes a framework for solving the coverage problem for a class of non-convex domains. In we have shown how a diffeomorphism can be used to transform a non-convex coverage problem to a convex one to which the Lloyd?s algorithm can be applied. In this paper we show how a diffeomorphism can be constructed for convex regions with obstacles in its interior, so that the solution of the transformed problem yields the solution of the original non-convex problem. As part of this investigation we also identify stationary points of the Lloyd?s algorithm in non-convex domains. We provide the formal analysis of the approach and demonstrate its effectiveness through simulations.

/pdf/a-coverage-algorithm-for-a-class-of-non-convex-regions-9ub85tk9ax.pdf

A coverage algorithm for a class of non-convex regions

Motion planning for a mechanical system addresses the problem of finding a trajectory and actuator forces that are consistent with a given set of constraints and perform a desired task. In general, the problem is under-determined and admits a large number of solutions. The main claim of this dissertation is that a natural way to resolve the indeterminacy is to define performance of a motion and find a solution with the best performance. The motion planning problem is thus formulated as a variational problem. The proposed approach is continuous in the sense that the motion planning problem is not discretized.
A distinction is made between dynamic and kinematic motion planning. Dynamic motion planning provides the actuator forces as part of the motion plan and requires finding a motion that is consistent with the dynamic equations of the system, satisfies a given set of equality and inequality constraints, and minimizes a chosen cost functional. In kinematic motion planning, dynamic equations of the system are not taken into account and it is therefore simpler.
For dynamic motion planning, a novel numerical method for solving a variational problem is developed. The method combines discretization of the continuous problem motivated by the finite-element analysis with techniques from nonlinear programming. It is used to find smooth trajectories and actuator forces for two planar cooperating manipulators holding an object. The method is then extended for systems that change the dynamic equations as they move. An example of a simple grasping task illustrates that for such systems variational approach unifies motion planning and task planning.
Kinematic motion planning is formulated as a variational problem on a Riemannian manifold. A Riemannian metric and an affine connection are introduced to define cost functionals that measure smoothness of trajectories. Kinematic motion planning is normally used in the task space, which can be represented by the group of spatial rigid body displacements, SE(3). It is shown how the group structure of SE(3) can be used to find smooth trajectories that have certain invariance properties with respect to the choice of the inertial and body fixed frames.

/pdf/continuous-methods-for-motion-planning-2ueeijoxuo.pdf

Milos Zefran

Papers

On the generation of smooth three-dimensional rigid body motions

A notion of passivity for hybrid systems

Assessment of faculty perception of content validity of PerioSim, a haptic-3D virtual reality dental training simulator.

A coverage algorithm for a class of non-convex regions

Continuous methods for motion planning