A_Distributed_Model_Predictive_Control_Framework_f.pdf
这是一篇论文，关于mpc的编队控制to handle the challenges raised by the on-road driving settingWe adopt a fully distributed paradigm in which each vehicleis equipped with a MPC tracking controller. The modulecomputes a sequence of control inputs to track a referencetrajectory while satisfying various constraints(kinematics anddynamics, collision avoidance, etc. ) The reference trajectory(5037c)of a vehicle is computed froIn its leader,s trajectory basedon a pre-defined formation tree. The major contribution ofFig. 1: Approximation of an obstacle region by a parabolathis paper is the use of hybrid system techniques to organizethe collision avoidance behaviors of member vehicles. To theAs we consider on-road autonomous driving, we formulatebest of our knowledge, it is the first time that such design isthe kinematic bicycle model in the road-following coordinateproposed in this problem settingsystem as followsThe hybrid approach allows to combine the optimizationpart of the mpc technique with logic rules that relieve thes=Ucos 0optimization process from lengthy collision constraints com-rc(sputations. Moreover, logic rules can be made semanticallyr'=sin e(2bmeaningful. which could lead to easier interactions betweenautomated vehicles and people(be it other drivers or pedes0=uk- cos 0(2c)1-7c(s)trians,cyclists, etc. ) Finally, our framework allows to safelymodify the formation on-the-fly. In this article, we presentpreliminary results validated by simulation, demonstrating thish(2e)framework is suitable for actual implementationThe rest of the paper is organized as follows. In Section IL.c(s) is assumed to be known, for instance from maps. Otherstate variables r, v, 6 and k are respectively the lateral offset,we present the mpc-based trajectory generation for vehiclesthe vehicle speed, the heading alignment error of the vehicleSection Ill presents the modeling of the on-road formationwith regard to the centerline and the curvature of the vehiclescontrol problem. Section IV shows how this coordinationtrajectory. The chosen control inputs are the acceleration a andframework can be used for dynamic formation changes. Secthe firstprivative of curvature, hi. We note -[s, T, u, 0, k Etion v validates our approach through simulations, and Section X the state of the vehicle. and u=a. kl e U its control.XVI concludes the the paperand U are compactly written form of the state constraint andI. MPC-BASED TRAJECTORY GENERATION FORthe control constraint. We note i=f(a, u) the system(2a)INDIVIDUALⅤ EHICLES(2e). When there is a need to differentiate between differentvehicles, subscripts like 2. can be added to those variablesA. Road-following coordinate systemMore details on the transformation of the kinematic bicycleWe first define a road-following coordinate system We asmodel from a Cartesian frame to the frenet frame can be foundsume that the centerline of the road can be described as a curvein[16]TEri with C3 continuity, ensuring that the curvature c of theC. Obstacle Modelingcurve and its derivative k exist. We define a frenet coordinatesystem(s, r), where s is the curvilinear abscissa along I,andVehicle trajectories are generated using a receding horir the lateral deviation The left and right boundaries of the roadzon scheme based on optimization techniques. However, theare defined as continuous functions r(s) and r(s). To ensureconvergence to a global optimum cannot be guaranteed. Withthe bijection from the(s, r) frame to a Cartesian frame, we one obstacle in the middle of the road, there are two ho-require that for all (s, r) such that r(s) sd so that aerence trajectory. Therefore, we consider the following cost given vehicle needs only take information from the precedingfunction that penalizes the aggregated deviation from the refvehicles, al though it is not mandatory in our formulationerence trajectory over the planning horizon. More specifically, Example 1. Consider a triangular formation of three vehiclesthe cost function is given asas shown in Fig. 2 The shape S of the formation is defined(T)(3)asto+t(|()-mrer(t)|+|n(t))0/0003where to is the current time instant and T is the predictionhorizon. P, Q and R are positive diagonal weighting matricesof respective dimensions 5, 5 and 2. The running cost termThe formation tree g defined by the adjacency matrix g is(Il +I. R) penalizes the deviation from the desiredgiven astrajectory, as well as the control effort. The terminal cost term012p is set to 0 in this paper. We will further discuss the0/0001|100construction of the reference trajectory aref in the followingsection, as it is the major enabler of our formation control2(010frameworkAt each sampling time t= to, we solve the followingsuch that vehicle 1 computes its formation control trajectoryconstrained optimization problemrelative to vehicle 0, and vehicle 2 computes its trajectoryrelative to vehicle imin j(a, u(4)b, Formation control schemesubj.to∈[to,t+门],Vehicles in the formation are assumed to use the mpci(t)=∫((t),u(t)based trajectory generation scheme described in Section III(5a) We propose to adjust the reference trajectories of vehicles toc(t)∈ X and q(t)∈U,(5bdrive them into the desired formationCi,lat 0→9(3,)≤0,(9)deceleration behind vehicle 1. moving further to the rightC()
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