In this paper we propose a new approach to motion planning, based on the introduction of a lattice structure in the workspace of the robot, leading to efficient computations of plans for rather complex vehicles, and allowing for the implementation of optimization procedures in a rather straightforward way. The basic idea is the purposeful restriction of the set of possible inputfunctions to the vehicle to a finite set of symbols, or {\em control quanta},which, under suitable conditions, generate a regular lattice of reachable points. Once the lattice is generated and a convenient description computed, standard techniques in integer linear programming can be used to find a plan very efficiently. We also provide a correct and complete algorithm to the problem of finding an optimized plan (with respect e.g. to length minimization) consisting in a sequence of graph searches.

10aEmbedded Control10aRobotics1 aPancanti, S1 aPallottino, L.1 aSalvadorini, D1 aBicchi, A. uhttp://www.centropiaggio.unipi.it/publications/motion-planning-through-symbols-and-lattices.html01751nas a2200205 4500008004100000245006600041210006500107260001300172300001200185520111000197653002101307653001301328100001501341700001601356700001601372700001501388700002001403700001201423856011001435 2003 eng d00aReceding-Horizon Control of LTI Systems with Quantized Inputs0 aRecedingHorizon Control of LTI Systems with Quantized Inputs bElsevier a259-2643 aThis paper deals with the stabilization problem for a particular class of hybrid systems, namely discrete-time linear systems subject to a uniform (a priori fixed) quantization of the control set. Results of our previous work on the subject provided a description of minimal (in a specific sense) invariant sets that could be rendered maximally attractive under any quantized feedback strategy. In this paper, we consider the design of stabilizing laws that optimize a given cost index on the state and input evolution on a finite, receding horizon. Application of Model Predictive Control techniques for the solution of similar hybrid control problems through Mixed Logical Dynamical reformulations can provide a stabilizing control law, provided that the feasibility hypotheses are met. In this paper, we discuss precisely what are the shortest horizon length and the minimal invariant terminal set for which it can be guaranteed a stabilizing MPC scheme. The final paper will provide an example and simulations of the application of the control scheme to a practical quantized control problem.

10aEmbedded Control10aRobotics1 aPicasso, B1 aPancanti, S1 aBemporad, A1 aBicchi, A.1 aEngell, Gueguen1 aZaytoon uhttp://www.centropiaggio.unipi.it/publications/receding-horizon-control-lti-systems-quantized-inputs.html01569nas a2200217 4500008004100000245004700041210004700088260004100135300001200176490001400188520092000202653002101122653001301143100001601156700001601172700001901188700001501207700001401222700001901236856009601255 2002 eng d00aOptimal control of quantized input systems0 aOptimal control of quantized input systems aHeidelberg, GermanybSpringer-Verlag a351-3630 vLNCS 22893 aIn this paper we consider the problem of optimal control (specifically, minimum-time steering) for systems with quantized inputs. In particular, we propose a new approach to the solution of the optimal control problem for an important class of nonlinear systems, i.e. chained-form systems. By exploiting results on the structure of the reachability set of these systems under quantized control, the optimal solution is determined solving an integer linear programming problem. Our algorithm represents an improvement with respect to classical approaches in terms of exactness, as it does not resort to any a priori state-space discretization. Although the computational complexity of the problem in our formulation is still formally exponential, it lends itself to application of Branch and Bound techniques, which substantially cuts down computations in many cases, as it has been experimentally observed.

10aEmbedded Control10aRobotics1 aPancanti, S1 aLeonardi, L1 aPallottino, L.1 aBicchi, A.1 aTomlin, C1 aGreenstreet, M uhttp://www.centropiaggio.unipi.it/publications/optimal-control-quantized-input-systems.html01415nas a2200157 4500008004100000245005100041210004800092260001600140520092000156653002101076653001301097100001601110700001901126700001501145856009701160 2002 eng d00aOn Optimal Steering of Quantized Input Systems0 aOptimal Steering of Quantized Input Systems aUrbana, IL.3 aIn this paper we consider the problem of optimal control (specifically, minimum-time steering) for systems with quantized inputs. In particular, we propose a new approach to the solution of the optimal control problem for an important class of nonlinear systems, i.e. chained-form systems. By exploiting results on the structure of the reachability set of these systems under quantized control, the optimal solution is determined solving an integer linear programming problem. Our algorithm represents an improvement with respect to classical approaches in terms of exactness, as it does not resort to any a priori state-space discretization. Although the computational complexity of the problem in our formulation is still formally exponential, it lends itself to application of Branch and Bound techniques, which substantially cuts down computations in many cases, as it has been experimentally observed.

10aEmbedded Control10aRobotics1 aPancanti, S1 aPallottino, L.1 aBicchi, A. uhttp://www.centropiaggio.unipi.it/publications/optimal-steering-quantized-input-systems.html01471nas a2200169 4500008004100000245009700041210006900138260000800207300001200215520085500227653002101082653001301103100001901116700001501135700001601150856013501166 2002 eng d00aSafety of a decentralized scheme for Free-Flight ATMS using Mixed Integer Linear Programming0 aSafety of a decentralized scheme for FreeFlight ATMS using Mixed cMay a742-7473 aIn this paper we consider policies for free-flight management of air traffic. We consider instantaneous and bounded heading angle deviation as conflict avoidance maneuvers. The corresponding model, resulting in a Mixed Integer Linear Programming (MILP) problem allow to solve both conflict detection and conflict resolution problems. The developed algorithm proved successful in a centralized implementation with a large number of cooperating aircraft. However, the application of such algorithm to a Free Flight environment, where cooperation can only be expected from neighboring aircraft, poses many challenges. We consider a model of the decentralized conflict resolution strategy that is based on a hybrid system, and sufficient conditions under which a 3-aircraft Free Flight MILP-based scheme guarantees safety of flight are provided.

10aEmbedded Control10aRobotics1 aPallottino, L.1 aBicchi, A.1 aPancanti, S uhttp://www.centropiaggio.unipi.it/publications/safety-decentralized-scheme-free-flight-atms-using-mixed-integer-linear-programming