A hybrid system is a dynamical with both discrete and continuous state changes. For analysis purposes, it often useful to abstract in way that preserves the properties being analysed while hiding details are of no interest. We show interesting classes systems can be abstracted purely preserving all definable temporal logic. The permit abstractions fall into two categories. Either dynamics must restricted, as case for timed rectangular systems, or o-minimal systems. In this paper, we survey...

A general strategy for solving the motion planning problem real analytic, controllable systems without drift is proposed. The procedure starts by computing a control that steers given initial point to desired target an extended system, in which number of Lie brackets system vector fields are added. Using formal calculations with product expansion relative P. Hall basis, another produced achieves result on level. This provides exact solution original if nilpotent. For iterative algorithm...

Large-scale control systems typically possess a hierarchical architecture in order to manage complexity. Higher levels of the hierarchy utilize coarser models system, resulting from aggregating detailed lower level models. In this layered paradigm, notion consistency is important, as it ensures implementation high-level objectives by system. paper, we define modeling for continuous and obtain characterizations hierarchically consistent linear with respect controllability objectives. As an...

The existence of two- and three-finger grasps in the presence arbitrarily small friction is shown for 2D 3D smooth objects using a simple technique. No convexity assumed. finger gaits rotating planar object three four fingers proved. Additional results convex which describe two different are presented. purpose to move one or more at any time same maintain grip with others, thereby further than other ways it could be moved fixed grip.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML"...

This paper investigates the stabilization of vehicle formations using techniques from algebraic graph theory. The vehicles exchange information according to a pre-specified (undirected) communication graph, G. feedback control is based only on relative about states shared via links. We prove that linear stabilizing always exists provided G connected. Moreover, we show how rate convergence formation governed by size smallest positive eigenvalue Laplacian Several numerical simulations are used...

We present a formula for stabilizing feedback law under the assumption that piecewise smooth control-Lyapunov function exists. The resulting is continuous at origin and everywhere except on hypersurface of codimension 1. provide an explicit 'universal' formula. Finally, we mention general result connecting asymptotic controllability existence functions in sense nonsmooth optimization.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The author discusses the applicability of a recently proposed strategy for effective calculation steering controls real analytic, controllable system without drift. approach uses an approximating nilpotent to compute controls. These provide exact solution original problem systems and which can be made by feedback transformation. For general drift, iterative algorithm is used. procedure also applied are obtained from drift dynamic extension.< <ETX...

We investigate stable maneuvers for a group of autonomous vehicles while moving in formation. The allowed decentralized feeback laws are factored through the Laplacian matrix communication graph. show that such allow circular or elliptical motions certain vehicle dynamics. find necessary and sufficient conditions on feedback gains dynamic parameters convergence to In particular, we prove undirected graphs there exist stabilize rotational (or elliptical) arbitrary radius eceentricity)....

Hierarchical decompositions of control systems are important for reducing the analysis and design large scale systems. Such depend on notion abstraction: given a system desired property, one tries to extract an abstracted model with equivalent properties, while ignoring details that irrelevant. Checking property abstraction should be checking original system. In this paper, we focus linear stabilizability. This results in hierarchy abstractions from stabilizability point view. is as high...

The authors address the problem of optimal force distribution among three point fingers holding a planar object. A scheme that reduces nonlinear optimization to an easily solved generalized eigenvalue is proposed. This generalizes and simplifies results Z. Ji B. Roth (1988). generalizations include all possible geometric arrangements extensions dimensions case variable coefficients friction. For two-dimensional with constant friction, it proved except for some special cases, grasping forces,...

An approach to manipulation tasks involving dextrous hands is presented. This treats the gripped object as a virtual finger and hence reduces description of task objectives target forces torques at reference points on object. Computations are carried out for case three fingers holding planar The authors implemented these ideas Four Finger Manipulator New York University. Experimental results presented door opening wall following with tool.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML"...

We generalize earlier results on the construction of discontinuous feedback laws from smooth but partially defined control Lyapunov functions. The resulting law is continuous at origin and except a hypersurface codimension 1. provide formula for which in sense "universal". new presented cover situations where trajectories closed loop system switch an infinite number times between regions functions exist. conditions vector fields can be verified without solving differential equations are...

In hierachical systems, higher levels of the hierarchy utilise coarser system models by aggregating detailed lower level models. this layered control paradigm, notion hierarchical consistency ensures implementation high objectives system. paper, we define a modeling for continuous systems and obtain characterizations hierarchically consistent linear with respect to controllability objectives. As an interesting by-product, criterion from which recover best known algorithm numerical algebra.

A unified approach to decidability questions for the verification of hybrid systems is obtained by construction a bisimulation. These are finite state quotients whose reachability properties equivalent those original infinite system. This has had some success in analysis timed automata and linear automata. We use results from stratification theory, subanalytic sets model theory fields order extend earlier on existence bisimulations certain classes analytic vector fields.