The problem of efficiently steering dynamical systems by generating finite input plans is considered. Finite plans are finite–length words constructed on a finite alphabet of input symbols, which could be e.g. transmitted through a limited capacity channel to a remote system, where they can be decoded in suitable control actions. Efficiency is considered in terms of the computational complexity of plans, and in terms of their description length (in number of bits). We show that, by suitable choice of the control encoding, finite plans can be efficiently built for a wide class of dynamical systems, computing arbitrarily close approximations of a desired equilibrium in polynomial time. The paper also investigates how the efficiency of planning is affected by the choice of inputs, and provides some results as to optimal performance in terms of accuracy and range.

%B IEEE Trans. on Automatic Control %V 51 %P 1-16 %G eng %0 Conference Paper %B Hybrid Systems: Computation and Control %D 2006 %T Improving efficiency of finite plans by optimal choice of input sets %A A. Bicchi %A A. Marigo %A B. Piccoli %E J. Hespanha %E A. Tiwari %K Embedded Control %K Robotics %XFinite plans proved to be an efficient method to steer complex control systems via feedback quantization. Such finite plans can be encoded by finite–length words constructed on suitable alphabets, thus permitting transmission on limited capacity channels. In particular flat systems can be steered computing arbitrarily close approximations of a desired equilibrium in polynomial time. The paper investigates how the efficiency of planning is affected by the choice of inputs, and provides some results as to optimal performance in terms of accuracy and range. Efficiency is here measured in terms of computational complexity and description length (in number of bits) of finite plans.

%B Hybrid Systems: Computation and Control %S Lecture Notes in Computer Science %I Springer-Verlag %V 3927 / 2006 %P 108-122 %G eng %0 Conference Paper %B Proc. IEEE Int. Conf. on Robotics and Automation %D 2006 %T Symbolic Control for Underactuated Differentially Flat Systems %A A. Fagiolini %A L. Greco %A A. Bicchi %A B. Piccoli %A A. Marigo %K Embedded Control %K Robotics %XIn this paper we address the problem of generating input plans to steer complex dynamical systems in an obstacle-free environment. Plans considered admit a finite description length and are constructed by words on an alphabet of input symbols, which could be e.g. transmitted through a limited capacity channel to a remote system, where they can be decoded in suitable control actions. We show that, by suitable choice of the control encoding, finite plans can be efficiently built for a wide class of dynamical systems, computing arbitrarily close approximations of a desired equilibrium in polynomial time. Moreover, we illustrate by simulations the power of the proposed method, solving the steering problem for two examples in the class of underactuated systems, which have attracted wide attention in the recent literature.

%B Proc. IEEE Int. Conf. on Robotics and Automation %P 1649-1654 %G eng %0 Conference Paper %B Hybrid Systems: Computation and Control %D 2004 %T Discrete and Hybrid Nonholonomy %A A. Bicchi %A A. Marigo %A B. Piccoli %E R. Alur %E G. Pappas %K Embedded Control %K Robotics %XIn this paper we consider the generalization of the classical notion of nonholonomy of smooth constraints in analytical mechanics, to a substantially wider set of systems, allowing for discrete and hybrid (mixed continuous and discrete) configurations and transitions. We show that the general notion of nonholonomy can be captured by the definition of two different types of nonholonomicbehaviours, which we call {\em internal}nd {\em external}, respectively. Examples are reported of systems exhibiting either the former only, or the latter only, or both. For some classes of systems, we provide equivalent or sufficient characterizations of such definitions, which allow for practical tests.

%B Hybrid Systems: Computation and Control %S LNCS %I Springer-Verlag %V 2993 %P 157-172 %G eng %0 Journal Article %J IEEE Trans. on Automatic Control %D 2004 %T Reachability and Steering of Rolling Polyhedra: A Case Study in Discrete Nonholonomy %A A. Bicchi %A Y. Chitour %A A. Marigo %K Embedded Control %K Robotics %XRolling a ball on a plane is a standard example of nonholonomy reported in many textbooks, and the problem is also well understood for any smooth deformation of the surfaces. For non-smoothly deformed surfaces, however, much less is known. Although it may seem intuitive that nonholonomy is conserved (think e.g. to polyhedral approximations of smooth surfaces), current definitions of ``nonholonomy'' are inherently referred to systems described by ordinary differential equations, and are thus inapplicable to such systems. \İn this paper we study the set of positions and orientations that a polyhedral part can reach by rolling on a plane through sequences of adjacent faces. We provide a description of such reachable set, discuss conditions under which the set is dense, or discrete, or has a compound structure, and provide a method for steering the system to a desired reachable configuration, robustly with respect to model uncertainties. \\Based on ideas and concepts encountered in this case study, and in some other examples we provide, we turn back to the most general aspects of the problem and investigate the possible generalization of the notion of (kinematic) nonholonomy to non-smooth, discrete, and hybrid dynamical systems. To capture the essence of phenomena commonly regarded as ``nonholonomic'', at least two irreducible concepts are to be defined, of ``internal'' and ``external'' nonholonomy, which may coexist in the same system. These definitions are instantiated by examples.

%B IEEE Trans. on Automatic Control %V 49 %P 710-726 %8 May %G eng %0 Conference Paper %B Proc. IEEE Int. Conf. on Decision and Control %D 2003 %T Encoding steering control with symbols %A A. Bicchi %A A. Marigo %A B. Piccoli %K Embedded Control %K Robotics %XIn this paper, we consider the problem of steering complex dynamical systems among equilibria in their state space in efficient ways. Efficiency is considered as the possibility of compactly representing the (typically very large, or infinite) set of reachable equilibria and quickly computing plans to move among them. To this purpose, we consider the possibility of building lattice structures by purposefully introducing quantization of inputs. We consider different ways in which control actions can be encoded in a finite or numerable set of symbols, review different applications where symbolic encoding of control actions can be employed with success, and provide a unified framework in which to study the many different possible manifestations of the idea.

%B Proc. IEEE Int. Conf. on Decision and Control %P 3343-3348 %G eng %0 Conference Paper %B Proc. IEEE Int. Conf. on Robotics and Automation %D 2003 %T From nominal to robust planning: The plate-ball manipulation system %A G. Oriolo %A M. Vendittelli %A A. Marigo %A A. Bicchi %K Embedded Control %K Robotics %XRobotic manipulation by rolling contacts is an appealing method for achieving dexterity with relatively simple hardware. While there exist techniques for planning motions of rigid bodies in rolling contact under nominal conditions, an inescapable challenge is the design of robust controllers of provable performance in the presence of model perturbations. As a preliminary step in this direction, we present in this paper an iterative robust planner of arbitrary accuracy for the plate-ball manipulation system subject to perturbations on the sphere radius. The basic tool is an exact geometric planner for the nominal system, whose repeated application guarantees the desired robustness property on the basis of the Iterative Steering paradigm. Simulation results under perturbed conditions show the effectiveness of the method.

%B Proc. IEEE Int. Conf. on Robotics and Automation %C Taipei, Taiwan %P 3175-3180 %8 May %G eng %0 Journal Article %J Int. Jour. of Robotics Research %D 2002 %T Dexterous Grippers: Putting Nonholonomy to Work for Fine Manipulation %A A. Bicchi %A A. Marigo %K Robotics %B Int. Jour. of Robotics Research %V 21 %P 427-442 %8 May-June %G eng %0 Conference Paper %B Proc. IEEE Int. Conf. on Decision and Control %D 2002 %T A Group-Theoretic Characterization of Quantized Control Systems %A A. Marigo %A B. Piccoli %A A. Bicchi %K Embedded Control %K Robotics %XIn this paper we consider the reachability problem for quantized control systems, i.e. systems that take inputs from a finite set of symbols. Previous work addressed this problem for linear systems and for some specific classes of nonlinear driftless systems. In this paper we attack the study of more general nonlinear systems. To do so we find it useful to pose the problem in more abstract terms, and make use of the wealth of tools available in group theory, which enables us to proceed in our agenda of better understanding effects of quantization of inputs on dynamic systems.

%B Proc. IEEE Int. Conf. on Decision and Control %P 811-816 %8 December %G eng %0 Conference Paper %B Proc. IEEE Int. Conf. on Robotics and Automation %D 2002 %T A local-local planning algorithm for rolling objects %A A. Marigo %A A. Bicchi %K Embedded Control %K Robotics %XIn this paper, we consider planning motions of objects of regular shape rolling on a plane among obstacles. Theoretical foundations and applications of this type of operations in robotic manipulation and locomotion have been discussed elsewhere. In this paper, we propose a novel algorithm that improves upon existing techniques in that: i) it is finitely computable and predictable (an upper bound on the computations necessary to reach a given goal within a tolerance can be given), and ii) it possesses a topological (local-local) property which enables obstacles and workspace limitations to be dealt with in an effective way.

%B Proc. IEEE Int. Conf. on Robotics and Automation %P 1759-1764 %8 May %G eng %0 Journal Article %J IEEE Trans. on Automatic Control %D 2002 %T On the reachability of quantized control systems %A A. Bicchi %A A. Marigo %A B. Piccoli %K Embedded Control %K Robotics %XIn this paper we study control systems whose input sets are quantized, i.e. finite or regularly distributed on a mesh. We specifically focus on problems relating to the structure of the reachable set of such systems, which may turn out to be either dense or discrete. We report results on the reachable set of linear quantized systems, and on a particular but interesting class of nonlinear systems, i.e. nonholonomic chained-form systems. For such systems, we provide a complete characterization of the reachable set, and, in the case the set is discrete, a computable method to completely and succinctly describe its structure. Implications and open problems in the analysis and synthesis of quantized control systems are addressed.

%B IEEE Trans. on Automatic Control %V 4 %P 546-563 %8 April %G eng %0 Conference Paper %B Proc. IEEE Int. Conf. on Robotics and Automation %D 2001 %T Optimal exploratory paths for a mobile rover %A F. Lorussi %A A. Marigo %A A. Bicchi %K Autonomous Vehicles %K Localization and Mapping %K Sensors and Observers %B Proc. IEEE Int. Conf. on Robotics and Automation %P 2078-2083 %G eng %0 Journal Article %J Algorithmica %D 2000 %T Planning Motions of Polyhedral Parts by Rolling %A A. Marigo %A M. Ceccarelli %A S. Piccinocchi %A A. Bicchi %K Hybrid and Embedded Control Systems %K Nonlinear Control Systems %K Quantized Control Systems %K Robot Hands %B Algorithmica %V 26 %P 560-576 %G eng %0 Conference Paper %B Proc. IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control %D 2000 %T Quantized Control Systems and Discrete Nonholonomy %A A. Bicchi %A A. Marigo %A B. Piccoli %K Hybrid and Embedded Control Systems %K Nonlinear Control Systems %K Quantized Control Systems %B Proc. IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control %I Elsevier %C Princeton, NJ, USA %G eng %0 Conference Paper %B Proc. IEEE Int. Conf. on Decision and Control %D 2000 %T Reachability Analysis for a Class of Quantized Control Systems %A A. Marigo %A B. Piccoli %A A. Bicchi %K Hybrid and Embedded Control Systems %K Nonlinear Control Systems %K Quantized Control Systems %B Proc. IEEE Int. Conf. on Decision and Control %C Sydney, AU %P 3963-3968 %8 December %G eng %0 Journal Article %J IEEE Trans. on Automatic Control %D 2000 %T Rolling Bodies with Regular Surface: Controllability Theory and Applications %A A. Marigo %A A. Bicchi %K Nonlinear Control Systems %K Robot Hands %B IEEE Trans. on Automatic Control %V 45 %P 1586-1599 %8 September %G eng %0 Conference Paper %B Proc. IEEE Int. Conf. on Robotics and Automation %D 2000 %T Rolling Contacts and Dextrous Manipulation %A A. Bicchi %A A. Marigo %K Nonholonomic Systems %K Nonlinear Control Systems %K Robot Hands %B Proc. IEEE Int. Conf. on Robotics and Automation %C San Francisco, CA %P 282-287 %8 May %G eng %0 Conference Paper %B Proc. IEEE Int. Conf. on Robotics and Automation %D 1999 %T Dexterity through rolling: Manipulation of unknown objects %A A. Bicchi %A A. Marigo %A D Prattichizzo %K Nonlinear Control Systems %K Robot Hands %B Proc. IEEE Int. Conf. on Robotics and Automation %P 1583-1568 %G eng %0 Book Section %B Differential geometry and control %D 1999 %T Rolling bodies with regular surfaces: the holonomic case %A A. Marigo %A A. Bicchi %E G. Ferreyra %E R. Gardner %E H. Hermes %E H. Sussmann %B Differential geometry and control %S Proceedings of Symposia in Pure Mathematics %I American Mathematical Society %V 64 %P 241-256 %G eng %0 Conference Paper %B Proc. IFAC Workshop on Motion Control %D 1998 %T Decentralized Air Traffic Management Systems: Performance and Fault Tolerance %A A. Bicchi %A A. Marigo %A G. Pappas %A M. Pardini %A G. Parlangeli %A C. Tomlin %A S. Sastry %K Air Traffic Management Systems %K Autonomous Vehicles %K Hybrid and Embedded Control Systems %K Nonlinear Control Systems %B Proc. IFAC Workshop on Motion Control %G eng %0 Conference Paper %B Proc. IEEE Mediterranean Conf. On Control And Systems %D 1998 %T On the observability of mobile vehicles localization %A A. Bicchi %A D Prattichizzo %A A. Marigo %A A. Balestrino %K Autonomous Vehicles %K Localization and Mapping %K Sensors and Observers %XIn this paper, we consider the problem of localizing a mobile vehicle moving in an unstructured environment, based on triangulation measurements derived from processed optical information. The problem is shown to be intrinsically nonlinear, in the sense that the linear approximation of the system has different structural properties than the original model. In particular, linearized approximations are non–observable, while results obtained from differential–geometric nonlinear system theory prove the possibility of reconstructing the position and orientation of the vehicle and the position of the obstacles in the environment from optical information.

%B Proc. IEEE Mediterranean Conf. On Control And Systems %G eng %0 Conference Paper %B Proc. IEEE Int. Conf. on Decision and Control %D 1998 %T Steering Driftless Nonholonomic Systems by Control Quanta %A A. Marigo %A A. Bicchi %K Hybrid and Embedded Control Systems %K Nonlinear Control Systems %K Quantized Control Systems %B Proc. IEEE Int. Conf. on Decision and Control %P 4164-4169 %G eng %0 Conference Paper %B Proc. IEEE Int. Conf. on Robotics and Automation %D 1997 %T Manipulation of polyhedral parts by rolling %A A. Marigo %A Y. Chitour %A A. Bicchi %K Hybrid and Embedded Control Systems %K Nonlinear Control Systems %K Quantized Control Systems %B Proc. IEEE Int. Conf. on Robotics and Automation %G eng %0 Book Section %B Control Problems in Robotics and Automation %D 1997 %T Robotic Dexterity via Nonholonomy %A A. Bicchi %A A. Marigo %A D Prattichizzo %E B. Siciliano %E K. Valavanis %K Haptics %K Robotics %B Control Problems in Robotics and Automation %S LNCIS 230 %I Springer Verlag %C Berlin Heidelberg, Germany %P 35-49 %G eng %0 Book Section %B Algorithms for Robotic Motion and Manipulation %D 1997 %T Rolling Polyhedra on a Plane: Analysis of the Reachable Set %A Y. Chitour %A A. Marigo %A D Prattichizzo %A A. Bicchi %E J.P. Laumond %E M. Overmars %K Embedded Control %K Robotics %B Algorithms for Robotic Motion and Manipulation %I A. K. Peters %C Wellesley, MA, U.S.A. %P 277-286 %G eng %0 Conference Paper %B Proc. Third Int. Symp. on Methods and Models for Automation and Robotics %D 1996 %T Dexterity through Rolling: Towards Manipulation of Unknown Objects %A A. Bicchi %A Y. Chitour %A A. Marigo %A D Prattichizzo %K Nonlinear Control Systems %K Robot Hands %B Proc. Third Int. Symp. on Methods and Models for Automation and Robotics %C Miedzyzdroje, Poland %G eng %0 Book Section %B Advances in Robotics: The ERNET Perspective %D 1996 %T Reachability of Rolling Parts %A Y. Chitour %A A. Marigo %A D Prattichizzo %A A. Bicchi %E C. Bonivento %E C. Melchiorri %E H. Tolle %K Haptics %K Robotics %B Advances in Robotics: The ERNET Perspective %I World Scientific Publisher Corp. %C Singapore %P 51-60 %G eng