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.

VL - 51 ER - TY - CONF T1 - Improving efficiency of finite plans by optimal choice of input sets T2 - Hybrid Systems: Computation and Control Y1 - 2006 A1 - A. Bicchi A1 - A. Marigo A1 - B. Piccoli ED - J. Hespanha ED - A. Tiwari KW - Embedded Control KW - Robotics AB -Finite 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.

JF - Hybrid Systems: Computation and Control T3 - Lecture Notes in Computer Science PB - Springer-Verlag VL - 3927 / 2006 ER - TY - CONF T1 - Symbolic Control for Underactuated Differentially Flat Systems T2 - Proc. IEEE Int. Conf. on Robotics and Automation Y1 - 2006 A1 - A. Fagiolini A1 - L. Greco A1 - A. Bicchi A1 - B. Piccoli A1 - A. Marigo KW - Embedded Control KW - Robotics AB -In 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.

JF - Proc. IEEE Int. Conf. on Robotics and Automation ER - TY - CONF T1 - Discrete and Hybrid Nonholonomy T2 - Hybrid Systems: Computation and Control Y1 - 2004 A1 - A. Bicchi A1 - A. Marigo A1 - B. Piccoli ED - R. Alur ED - G. Pappas KW - Embedded Control KW - Robotics AB -In 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.

JF - Hybrid Systems: Computation and Control T3 - LNCS PB - Springer-Verlag VL - 2993 ER - TY - JOUR T1 - Reachability and Steering of Rolling Polyhedra: A Case Study in Discrete Nonholonomy JF - IEEE Trans. on Automatic Control Y1 - 2004 A1 - A. Bicchi A1 - Y. Chitour A1 - A. Marigo KW - Embedded Control KW - Robotics AB -Rolling 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.

VL - 49 ER - TY - CONF T1 - Encoding steering control with symbols T2 - Proc. IEEE Int. Conf. on Decision and Control Y1 - 2003 A1 - A. Bicchi A1 - A. Marigo A1 - B. Piccoli KW - Embedded Control KW - Robotics AB -In 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.

JF - Proc. IEEE Int. Conf. on Decision and Control ER - TY - CONF T1 - From nominal to robust planning: The plate-ball manipulation system T2 - Proc. IEEE Int. Conf. on Robotics and Automation Y1 - 2003 A1 - G. Oriolo A1 - M. Vendittelli A1 - A. Marigo A1 - A. Bicchi KW - Embedded Control KW - Robotics AB -Robotic 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.

JF - Proc. IEEE Int. Conf. on Robotics and Automation CY - Taipei, Taiwan ER - TY - JOUR T1 - Dexterous Grippers: Putting Nonholonomy to Work for Fine Manipulation JF - Int. Jour. of Robotics Research Y1 - 2002 A1 - A. Bicchi A1 - A. Marigo KW - Robotics VL - 21 N1 -Special Issue on Nonholonomy on Purpose, H. Arai, A. Bicchi, eds.

ER - TY - CONF T1 - A Group-Theoretic Characterization of Quantized Control Systems T2 - Proc. IEEE Int. Conf. on Decision and Control Y1 - 2002 A1 - A. Marigo A1 - B. Piccoli A1 - A. Bicchi KW - Embedded Control KW - Robotics AB -In 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.

JF - Proc. IEEE Int. Conf. on Decision and Control ER - TY - CONF T1 - A local-local planning algorithm for rolling objects T2 - Proc. IEEE Int. Conf. on Robotics and Automation Y1 - 2002 A1 - A. Marigo A1 - A. Bicchi KW - Embedded Control KW - Robotics AB -In 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.

JF - Proc. IEEE Int. Conf. on Robotics and Automation ER - TY - JOUR T1 - On the reachability of quantized control systems JF - IEEE Trans. on Automatic Control Y1 - 2002 A1 - A. Bicchi A1 - A. Marigo A1 - B. Piccoli KW - Embedded Control KW - Robotics AB -In 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.

VL - 4 ER - TY - CONF T1 - Optimal exploratory paths for a mobile rover T2 - Proc. IEEE Int. Conf. on Robotics and Automation Y1 - 2001 A1 - F. Lorussi A1 - A. Marigo A1 - A. Bicchi KW - Autonomous Vehicles KW - Localization and Mapping KW - Sensors and Observers JF - Proc. IEEE Int. Conf. on Robotics and Automation ER - TY - JOUR T1 - Planning Motions of Polyhedral Parts by Rolling JF - Algorithmica Y1 - 2000 A1 - A. Marigo A1 - M. Ceccarelli A1 - S. Piccinocchi A1 - A. Bicchi KW - Hybrid and Embedded Control Systems KW - Nonlinear Control Systems KW - Quantized Control Systems KW - Robot Hands VL - 26 ER - TY - CONF T1 - Quantized Control Systems and Discrete Nonholonomy T2 - Proc. IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control Y1 - 2000 A1 - A. Bicchi A1 - A. Marigo A1 - B. Piccoli KW - Hybrid and Embedded Control Systems KW - Nonlinear Control Systems KW - Quantized Control Systems JF - Proc. IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control PB - Elsevier CY - Princeton, NJ, USA ER - TY - CONF T1 - Reachability Analysis for a Class of Quantized Control Systems T2 - Proc. IEEE Int. Conf. on Decision and Control Y1 - 2000 A1 - A. Marigo A1 - B. Piccoli A1 - A. Bicchi KW - Hybrid and Embedded Control Systems KW - Nonlinear Control Systems KW - Quantized Control Systems JF - Proc. IEEE Int. Conf. on Decision and Control CY - Sydney, AU ER - TY - JOUR T1 - Rolling Bodies with Regular Surface: Controllability Theory and Applications JF - IEEE Trans. on Automatic Control Y1 - 2000 A1 - A. Marigo A1 - A. Bicchi KW - Nonlinear Control Systems KW - Robot Hands VL - 45 ER - TY - CONF T1 - Rolling Contacts and Dextrous Manipulation T2 - Proc. IEEE Int. Conf. on Robotics and Automation Y1 - 2000 A1 - A. Bicchi A1 - A. Marigo KW - Nonholonomic Systems KW - Nonlinear Control Systems KW - Robot Hands JF - Proc. IEEE Int. Conf. on Robotics and Automation CY - San Francisco, CA ER - TY - CONF T1 - Dexterity through rolling: Manipulation of unknown objects T2 - Proc. IEEE Int. Conf. on Robotics and Automation Y1 - 1999 A1 - A. Bicchi A1 - A. Marigo A1 - D Prattichizzo KW - Nonlinear Control Systems KW - Robot Hands JF - Proc. IEEE Int. Conf. on Robotics and Automation ER - TY - CHAP T1 - Rolling bodies with regular surfaces: the holonomic case T2 - Differential geometry and control Y1 - 1999 A1 - A. Marigo A1 - A. Bicchi ED - G. Ferreyra ED - R. Gardner ED - H. Hermes ED - H. Sussmann JF - Differential geometry and control T3 - Proceedings of Symposia in Pure Mathematics PB - American Mathematical Society VL - 64 ER - TY - CONF T1 - Decentralized Air Traffic Management Systems: Performance and Fault Tolerance T2 - Proc. IFAC Workshop on Motion Control Y1 - 1998 A1 - A. Bicchi A1 - A. Marigo A1 - G. Pappas A1 - M. Pardini A1 - G. Parlangeli A1 - C. Tomlin A1 - S. Sastry KW - Air Traffic Management Systems KW - Autonomous Vehicles KW - Hybrid and Embedded Control Systems KW - Nonlinear Control Systems JF - Proc. IFAC Workshop on Motion Control ER - TY - CONF T1 - On the observability of mobile vehicles localization T2 - Proc. IEEE Mediterranean Conf. On Control And Systems Y1 - 1998 A1 - A. Bicchi A1 - D Prattichizzo A1 - A. Marigo A1 - A. Balestrino KW - Autonomous Vehicles KW - Localization and Mapping KW - Sensors and Observers AB -In 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.

JF - Proc. IEEE Mediterranean Conf. On Control And Systems ER - TY - CONF T1 - Steering Driftless Nonholonomic Systems by Control Quanta T2 - Proc. IEEE Int. Conf. on Decision and Control Y1 - 1998 A1 - A. Marigo A1 - A. Bicchi KW - Hybrid and Embedded Control Systems KW - Nonlinear Control Systems KW - Quantized Control Systems JF - Proc. IEEE Int. Conf. on Decision and Control ER - TY - CONF T1 - Manipulation of polyhedral parts by rolling T2 - Proc. IEEE Int. Conf. on Robotics and Automation Y1 - 1997 A1 - A. Marigo A1 - Y. Chitour A1 - A. Bicchi KW - Hybrid and Embedded Control Systems KW - Nonlinear Control Systems KW - Quantized Control Systems JF - Proc. IEEE Int. Conf. on Robotics and Automation ER - TY - CHAP T1 - Robotic Dexterity via Nonholonomy T2 - Control Problems in Robotics and Automation Y1 - 1997 A1 - A. Bicchi A1 - A. Marigo A1 - D Prattichizzo ED - B. Siciliano ED - K. Valavanis KW - Haptics KW - Robotics JF - Control Problems in Robotics and Automation T3 - LNCIS 230 PB - Springer Verlag CY - Berlin Heidelberg, Germany ER - TY - CHAP T1 - Rolling Polyhedra on a Plane: Analysis of the Reachable Set T2 - Algorithms for Robotic Motion and Manipulation Y1 - 1997 A1 - Y. Chitour A1 - A. Marigo A1 - D Prattichizzo A1 - A. Bicchi ED - J.P. Laumond ED - M. Overmars KW - Embedded Control KW - Robotics JF - Algorithms for Robotic Motion and Manipulation PB - A. K. Peters CY - Wellesley, MA, U.S.A. ER - TY - CONF T1 - Dexterity through Rolling: Towards Manipulation of Unknown Objects T2 - Proc. Third Int. Symp. on Methods and Models for Automation and Robotics Y1 - 1996 A1 - A. Bicchi A1 - Y. Chitour A1 - A. Marigo A1 - D Prattichizzo KW - Nonlinear Control Systems KW - Robot Hands JF - Proc. Third Int. Symp. on Methods and Models for Automation and Robotics CY - Miedzyzdroje, Poland ER - TY - CHAP T1 - Reachability of Rolling Parts T2 - Advances in Robotics: The ERNET Perspective Y1 - 1996 A1 - Y. Chitour A1 - A. Marigo A1 - D Prattichizzo A1 - A. Bicchi ED - C. Bonivento ED - C. Melchiorri ED - H. Tolle KW - Haptics KW - Robotics JF - Advances in Robotics: The ERNET Perspective PB - World Scientific Publisher Corp. CY - Singapore ER -