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.

10aEmbedded Control10aRobotics1 aBicchi, A.1 aMarigo, A1 aPiccoli, B uhttps://www.centropiaggio.unipi.it/publications/feedback-encoding-efficient-symbolic-control-dynamical-systems.html01363nas a2200205 4500008004100000245007300041210006900114260002000183300001200203490001600215520070100231653002100932653001300953100001500966700001400981700001500995700001601010700001401026856011701040 2006 eng d00aImproving efficiency of finite plans by optimal choice of input sets0 aImproving efficiency of finite plans by optimal choice of input bSpringer-Verlag a108-1220 v3927 / 20063 aFinite 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.

10aEmbedded Control10aRobotics1 aBicchi, A.1 aMarigo, A1 aPiccoli, B1 aHespanha, J1 aTiwari, A uhttps://www.centropiaggio.unipi.it/publications/improving-efficiency-finite-plans-optimal-choice-input-sets.html01437nas a2200181 4500008004100000245006700041210006700108300001400175520084200189653002101031653001301052100001701065700001301082700001501095700001501110700001401125856011601139 2006 eng d00aSymbolic Control for Underactuated Differentially Flat Systems0 aSymbolic Control for Underactuated Differentially Flat Systems a1649-16543 aIn 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.

10aEmbedded Control10aRobotics1 aFagiolini, A1 aGreco, L1 aBicchi, A.1 aPiccoli, B1 aMarigo, A uhttps://www.centropiaggio.unipi.it/publications/symbolic-control-underactuated-differentially-flat-systems.html01261nas a2200205 4500008004100000245003600041210003600077260002000113300001200133490000900145520070800154653002100862653001300883100001500896700001400911700001500925700001200940700001400952856008900966 2004 eng d00aDiscrete and Hybrid Nonholonomy0 aDiscrete and Hybrid Nonholonomy bSpringer-Verlag a157-1720 v29933 aIn 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.

10aEmbedded Control10aRobotics1 aBicchi, A.1 aMarigo, A1 aPiccoli, B1 aAlur, R1 aPappas, G uhttps://www.centropiaggio.unipi.it/publications/discrete-and-hybrid-nonholonomy.html02138nas a2200181 4500008004100000245008900041210006900130260000800199300001200207490000700219520151900226653002101745653001301766100001501779700001501794700001401809856013301823 2004 eng d00aReachability and Steering of Rolling Polyhedra: A Case Study in Discrete Nonholonomy0 aReachability and Steering of Rolling Polyhedra A Case Study in D cMay a710-7260 v493 aRolling 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.

10aEmbedded Control10aRobotics1 aBicchi, A.1 aChitour, Y1 aMarigo, A uhttps://www.centropiaggio.unipi.it/publications/reachability-and-steering-rolling-polyhedra-case-study-discrete-nonholonomy.html01246nas a2200157 4500008004100000245004300041210004300084300001400127520077800141653002100919653001300940100001500953700001400968700001500982856009100997 2003 eng d00aEncoding steering control with symbols0 aEncoding steering control with symbols a3343-33483 aIn 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.

10aEmbedded Control10aRobotics1 aBicchi, A.1 aMarigo, A1 aPiccoli, B uhttps://www.centropiaggio.unipi.it/publications/encoding-steering-control-symbols.html01454nas a2200181 4500008004100000245007200041210006900113260002400182300001400206520084400220653002101064653001301085100001401098700001901112700001401131700001501145856011201160 2003 eng d00aFrom nominal to robust planning: The plate-ball manipulation system0 aFrom nominal to robust planning The plateball manipulation syste aTaipei, TaiwancMay a3175-31803 aRobotic 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.

10aEmbedded Control10aRobotics1 aOriolo, G1 aVendittelli, M1 aMarigo, A1 aBicchi, A. uhttps://www.centropiaggio.unipi.it/publications/nominal-robust-planning-plate-ball-manipulation-system.html00523nas a2200145 4500008004100000245007400041210006900115260001300184300001200197490000700209653001300216100001500229700001400244856011900258 2002 eng d00aDexterous Grippers: Putting Nonholonomy to Work for Fine Manipulation0 aDexterous Grippers Putting Nonholonomy to Work for Fine Manipula cMay-June a427-4420 v2110aRobotics1 aBicchi, A.1 aMarigo, A uhttps://www.centropiaggio.unipi.it/publications/dexterous-grippers-putting-nonholonomy-work-fine-manipulation.html01159nas a2200169 4500008004100000245006800041210006500109260001300174300001200187520059600199653002100795653001300816100001400829700001500843700001500858856011600873 2002 eng d00aA Group-Theoretic Characterization of Quantized Control Systems0 aGroupTheoretic Characterization of Quantized Control Systems cDecember a811-8163 aIn 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.

10aEmbedded Control10aRobotics1 aMarigo, A1 aPiccoli, B1 aBicchi, A. uhttps://www.centropiaggio.unipi.it/publications/group-theoretic-characterization-quantized-control-systems.html01143nas a2200157 4500008004100000245005700041210005400098260000800152300001400160520064400174653002100818653001300839100001400852700001500866856010400881 2002 eng d00aA local-local planning algorithm for rolling objects0 alocallocal planning algorithm for rolling objects cMay a1759-17643 aIn 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.

10aEmbedded Control10aRobotics1 aMarigo, A1 aBicchi, A. uhttps://www.centropiaggio.unipi.it/publications/local-local-planning-algorithm-rolling-objects.html01272nas a2200181 4500008004100000245005300041210004600094260001000140300001200150490000600162520074800168653002100916653001300937100001500950700001400965700001500979856009600994 2002 eng d00aOn the reachability of quantized control systems0 areachability of quantized control systems cApril a546-5630 v43 aIn 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.

10aEmbedded Control10aRobotics1 aBicchi, A.1 aMarigo, A1 aPiccoli, B uhttps://www.centropiaggio.unipi.it/publications/reachability-quantized-control-systems.html00531nas a2200157 4500008004100000245004900041210004900090300001400139653002400153653002900177653002600206100001600232700001400248700001500262856009600277 2001 eng d00aOptimal exploratory paths for a mobile rover0 aOptimal exploratory paths for a mobile rover a2078-208310aAutonomous Vehicles10aLocalization and Mapping10aSensors and Observers1 aLorussi, F.1 aMarigo, A1 aBicchi, A. uhttps://www.centropiaggio.unipi.it/publications/optimal-exploratory-paths-mobile-rover.html00639nas a2200193 4500008004100000245005200041210005200093300001200145490000700157653004000164653003000204653003000234653001600264100001400280700001800294700001900312700001500331856009900346 2000 eng d00aPlanning Motions of Polyhedral Parts by Rolling0 aPlanning Motions of Polyhedral Parts by Rolling a560-5760 v2610aHybrid and Embedded Control Systems10aNonlinear Control Systems10aQuantized Control Systems10aRobot Hands1 aMarigo, A1 aCeccarelli, M1 aPiccinocchi, S1 aBicchi, A. uhttps://www.centropiaggio.unipi.it/publications/planning-motions-polyhedral-parts-rolling.html00594nas a2200157 4500008004100000245005500041210005500096260003300151653004000184653003000224653003000254100001500284700001400299700001500313856010800328 2000 eng d00aQuantized Control Systems and Discrete Nonholonomy0 aQuantized Control Systems and Discrete Nonholonomy aPrinceton, NJ, USAbElsevier10aHybrid and Embedded Control Systems10aNonlinear Control Systems10aQuantized Control Systems1 aBicchi, A.1 aMarigo, A1 aPiccoli, B uhttps://www.centropiaggio.unipi.it/publications/quantized-control-systems-and-discrete-nonholonomy.html00639nas a2200169 4500008004100000245006700041210006700108260002500175300001400200653004000214653003000254653003000284100001400314700001500328700001500343856011100358 2000 eng d00aReachability Analysis for a Class of Quantized Control Systems0 aReachability Analysis for a Class of Quantized Control Systems aSydney, AUcDecember a3963-396810aHybrid and Embedded Control Systems10aNonlinear Control Systems10aQuantized Control Systems1 aMarigo, A1 aPiccoli, B1 aBicchi, A. uhttps://www.centropiaggio.unipi.it/publications/reachability-analysis-class-quantized-control-systems.html00587nas a2200157 4500008004100000245008100041210006900122260001400191300001400205490000700219653003000226653001600256100001400272700001500286856012800301 2000 eng d00aRolling Bodies with Regular Surface: Controllability Theory and Applications0 aRolling Bodies with Regular Surface Controllability Theory and A cSeptember a1586-15990 v4510aNonlinear Control Systems10aRobot Hands1 aMarigo, A1 aBicchi, A. uhttps://www.centropiaggio.unipi.it/publications/rolling-bodies-regular-surface-controllability-theory-and-applications.html00532nas a2200157 4500008004100000245004700041210004700088260002700135300001200162653002500174653003000199653001600229100001500245700001400260856010000274 2000 eng d00aRolling Contacts and Dextrous Manipulation0 aRolling Contacts and Dextrous Manipulation aSan Francisco, CAcMay a282-28710aNonholonomic Systems10aNonlinear Control Systems10aRobot Hands1 aBicchi, A.1 aMarigo, A uhttps://www.centropiaggio.unipi.it/publications/rolling-contacts-and-dextrous-manipulation.html00533nas a2200145 4500008004100000245006300041210006200104300001400166653003000180653001600210100001500226700001400241700002000255856011200275 1999 eng d00aDexterity through rolling: Manipulation of unknown objects0 aDexterity through rolling Manipulation of unknown objects a1583-156810aNonlinear Control Systems10aRobot Hands1 aBicchi, A.1 aMarigo, A1 aPrattichizzo, D uhttps://www.centropiaggio.unipi.it/publications/dexterity-through-rolling-manipulation-unknown-objects.html00591nas a2200181 4500008004100000245006100041210006000102260003400162300001200196490000700208100001400215700001500229700001600244700001500260700001400275700001600289856010400305 1999 eng d00aRolling bodies with regular surfaces: the holonomic case0 aRolling bodies with regular surfaces the holonomic case bAmerican Mathematical Society a241-2560 v641 aMarigo, A1 aBicchi, A.1 aFerreyra, G1 aGardner, R1 aHermes, H1 aSussmann, H uhttps://www.centropiaggio.unipi.it/publications/rolling-bodies-regular-surfaces-holonomic-case.html00765nas a2200205 4500008004100000245008200041210006900123653003500192653002400227653004000251653003000291100001500321700001400336700001400350700001500364700001800379700001400397700001400411856013400425 1998 eng d00aDecentralized Air Traffic Management Systems: Performance and Fault Tolerance0 aDecentralized Air Traffic Management Systems Performance and Fau10aAir Traffic Management Systems10aAutonomous Vehicles10aHybrid and Embedded Control Systems10aNonlinear Control Systems1 aBicchi, A.1 aMarigo, A1 aPappas, G1 aPardini, M1 aParlangeli, G1 aTomlin, C1 aSastry, S uhttps://www.centropiaggio.unipi.it/publications/decentralized-air-traffic-management-systems-performance-and-fault-tolerance.html01237nas a2200169 4500008004100000245005700041210005000098520067300148653002400821653002900845653002600874100001500900700002000915700001400935700001800949856010000967 1998 eng d00aOn the observability of mobile vehicles localization0 aobservability of mobile vehicles localization3 aIn 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.

10aAutonomous Vehicles10aLocalization and Mapping10aSensors and Observers1 aBicchi, A.1 aPrattichizzo, D1 aMarigo, A1 aBalestrino, A uhttps://www.centropiaggio.unipi.it/publications/observability-mobile-vehicles-localization.html00566nas a2200145 4500008004100000245006200041210006200103300001400165653004000179653003000219653003000249100001400279700001500293856011200308 1998 eng d00aSteering Driftless Nonholonomic Systems by Control Quanta0 aSteering Driftless Nonholonomic Systems by Control Quanta a4164-416910aHybrid and Embedded Control Systems10aNonlinear Control Systems10aQuantized Control Systems1 aMarigo, A1 aBicchi, A. uhttps://www.centropiaggio.unipi.it/publications/steering-driftless-nonholonomic-systems-control-quanta.html00522nas a2200145 4500008004100000245004800041210004800089653004000137653003000177653003000207100001400237700001500251700001500266856009500281 1997 eng d00aManipulation of polyhedral parts by rolling0 aManipulation of polyhedral parts by rolling10aHybrid and Embedded Control Systems10aNonlinear Control Systems10aQuantized Control Systems1 aMarigo, A1 aChitour, Y1 aBicchi, A. uhttps://www.centropiaggio.unipi.it/publications/manipulation-polyhedral-parts-rolling.html00552nas a2200181 4500008004100000245003800041210003800079260004800117300001000165653001200175653001300187100001500200700001400215700002000229700001700249700001700266856008700283 1997 eng d00aRobotic Dexterity via Nonholonomy0 aRobotic Dexterity via Nonholonomy aBerlin Heidelberg, GermanybSpringer Verlag a35-4910aHaptics10aRobotics1 aBicchi, A.1 aMarigo, A1 aPrattichizzo, D1 aSiciliano, B1 aValavanis, K uhttps://www.centropiaggio.unipi.it/publications/robotic-dexterity-nonholonomy.html00649nas a2200193 4500008004100000245006400041210006300105260004000168300001200208653002100220653001300241100001500254700001400269700002000283700001500303700001700318700001600335856010400351 1997 eng d00aRolling Polyhedra on a Plane: Analysis of the Reachable Set0 aRolling Polyhedra on a Plane Analysis of the Reachable Set aWellesley, MA, U.S.A.bA. K. Peters a277-28610aEmbedded Control10aRobotics1 aChitour, Y1 aMarigo, A1 aPrattichizzo, D1 aBicchi, A.1 aLaumond, J P1 aOvermars, M uhttps://www.centropiaggio.unipi.it/publications/rolling-polyhedra-plane-analysis-reachable-set.html00594nas a2200157 4500008004100000245007100041210006900112260002500181653003000206653001600236100001500252700001500267700001400282700002000296856012000316 1996 eng d00aDexterity through Rolling: Towards Manipulation of Unknown Objects0 aDexterity through Rolling Towards Manipulation of Unknown Object aMiedzyzdroje, Poland10aNonlinear Control Systems10aRobot Hands1 aBicchi, A.1 aChitour, Y1 aMarigo, A1 aPrattichizzo, D uhttps://www.centropiaggio.unipi.it/publications/dexterity-through-rolling-towards-manipulation-unknown-objects.html00594nas a2200205 4500008004100000245003400041210003400075260004800109300001000157653001200167653001300179100001500192700001400207700002000221700001500241700001700256700001800273700001300291856008400304 1996 eng d00aReachability of Rolling Parts0 aReachability of Rolling Parts aSingaporebWorld Scientific Publisher Corp. a51-6010aHaptics10aRobotics1 aChitour, Y1 aMarigo, A1 aPrattichizzo, D1 aBicchi, A.1 aBonivento, C1 aMelchiorri, C1 aTolle, H uhttps://www.centropiaggio.unipi.it/publications/reachability-rolling-parts.html