基于庞特里亚金极小值原理的多运载体有限时间编队控制
|
摘要
研究基于庞特里亚金极小值原理的多运载体有限时间编队问题.运载体刻画为欧氏群切丛上演化的全驱动刚体动力学模型.编队机动时间以及队形的几何结构是由编队任务指定的.对于期望的队形,首先利用庞特里亚金最小值原理给出了开环最优控制.为了克服开环控制对扰动的敏感性并增加针对初始条件不确定性摄动的鲁棒性,在假定运载体间通讯为全联通的模式下,通过反馈将系统当前状态作为初始状态,当前时刻作为初始时刻,进一步将开环控制律转化为闭环形式.为了验证所得结果,给出了平面及空间运载体编队的仿真算例.
The paper studies the problem of finite time formation control for multiple vehicles based on Pontryagin s minimum principle. The vehicle is modeled as a fully actuated rigid body with the dynamics evolving on the tangent bundle of Euclidean group. Both the formation maneuver time and the geometric structure of the formation are specified by the formation task. For the required formation, an open loop optimal control law is derived by using Pontryagin s minimum principle. In order to overcome the sensitivity of the open-loop control to the disturbance and increase the robustness of the control law to the initial perturbation, the open loop control law is converted to the closed loop form.This is done by feeding the current state back and initializing the control law at the current time, under the assumption that the mode of communication between the vehicles is all-to-all. For demonstration of the result, some numerical examples of formations for both planar and spacial vehicles are included.
The paper studies the problem of finite time formation control for multiple vehicles based on Pontryagin s minimum principle. The vehicle is modeled as a fully actuated rigid body with the dynamics evolving on the tangent bundle of Euclidean group. Both the formation maneuver time and the geometric structure of the formation are specified by the formation task. For the required formation, an open loop optimal control law is derived by using Pontryagin s minimum principle. In order to overcome the sensitivity of the open-loop control to the disturbance and increase the robustness of the control law to the initial perturbation, the open loop control law is converted to the closed loop form.This is done by feeding the current state back and initializing the control law at the current time, under the assumption that the mode of communication between the vehicles is all-to-all. For demonstration of the result, some numerical examples of formations for both planar and spacial vehicles are included.
引文
1 Fiorelli E,Leonard N E,Bhatta P,Paley D A,Bachmayer RFrantonti D M.Multi-AUV control and adaptive sampling in Monterey Bay.IEEE Journal of Oceanic Engineering,200631(4):935-948
2 Alber M S,Kiskowski A.On aggregation in CA models in biology.Journal of Physics A:Mathematical and General2001,34(48):10707-10714
3 Leonard N E,Fiorelli E.Virtual leaders,artificial potential and coordinated control of groups.In:Proceedings of th40th IEEE Conference on Decision and Control.Orlando Florida USA:IEEE,2001.2968-2973
4 Jadbabaie A,Lin J,Morse A S.Coordination of group of mobile autonomous agents using nearest neighbor rules IEEE Transactions on Automatic Control,2003,48(6)988-1001
5 Saber R O,Dunbar W B,Murray R M.Cooperative contro of multi-vehicle systems using cost graphs and optimization In:Proceedings of the 2003 American Control Conference Denver,Colorado,USA:IEEE,2003.2217-2222
6 Fax J A,Murray R M.Information flow and cooperativ control of vehicle formations.IEEE Transactions on Auto matic Control,2004,49(9):1465-1476
7 Sepulchre R,Paley D A,Leonard N E.Stabilization o planar collective motion:all-to-all communication.IEEETransactions on Automatic Control,2007,52(5):811-824
8 Scardovi L,Leonard N E.Robustness of aggregation in net worked dynamical systems.In:Proceedings of the 2nd In ternational Conference on Robot Communication and Co ordination.Odense,Denmark:IEEE,2009.1-6
9 Chen Yang-Yang,Tian Yu-Ping.Directed coordinated con trol for multi-agent formation motion on a set of given curves.Acta Automatica Sinica,2009,35(12):1541-1549(陈杨杨,田玉平.多智能体沿多条给定路径编队运动的有向协同控制.自动化学报,2009,35(12):1541-1549)
10 Wang Z X,Du D J,Fei M R.Average Consensus in Directed Networks of Multi-agents with Uncertain Time-varying De lays.Acta Automatica Sinica,2014,40(11):2602-2608
11 Min Hai-Bo,Liu Yuan,Wang Shi-Cheng,Sun Fu-Chun.An overview on coordination control problem of multi-agent sys tem.Acta Automatica Sinica,2012,38(10):1557-1570(闵海波,刘源,王仕成,孙富春.多个体协调控制问题综述.自动化学报,2012,38(10):1557-1570)
12 Oh K K,Park M C,Ahn H S.A survey of multi-agent for mation control.Automatica,2015,53:424-440
13 Tuna S E.Conditions for synchronizability in arrays of cou pled linear systems.IEEE Transactions on Automatic Con trol,2009,54(10):2416-2420
14 Qu Z,Wang J,Hull R A.Cooperative control of dynami cal systems with application to autonomous vehicles.IEEETransactions on Automatic Control,2008,53(4):894-911
15 Li Z,Duan Z,Chen G,Huang L.Consensus of multiagen systems and synchronization of complex networks:a unified viewpoint.IEEE Transactions on Circuits and Systems IRegular Papers,2010,57(1):213-224
16 CHEN Y Z,GE Y R,ZHANG Y X.Partial Stability Ap proach to Consensus Problem of Linear Multi-agent Sys tems.Acta Automatica Sinica,2014,40(11):2573-2584
17 Ren W.Distributed leaderless consensus algorithms for net worked Euler-Lagrange systems.International Journal o Control,2009,82(11):2137-2149
18 Chen G,Lewis F L.Distributed adaptive tracking control fo synchronization of unknown networked Lagrangian systems IEEE Transactions on Systems,Man,and Cybernetics,Par B:Cybernetics,2011,41(3):805-816
19 Mei J,Ren W,Ma G F.Distributed coordinated tracking with a dynamic leader for multiple Euler-Lagrange systems IEEE Transactions on Automatic Control,2011,56(6)1415-1421
20 Chen G,Yue Y L,Lin Q.Cooperative tracking control fo networked Lagrange systems:algorithms and experiments Acta Automatica Sinica,2014,40(11):2563-2572
21 Justh E W,Krishnaprasad P S.Equilibria and steering law for planar formations.Systems&Control Letters,200452(1):25-38
22 Justh E W,Krishnaprasad P S.Natural frames and interact ing particles in three dimensions.In:Proceedings of the 44th IEEE Conference on Decision and Control.Seville,Spain IEEE,2005.2841-2846
23 Sarlette A,Bonnabel S,Sepulchre R.Coordinated motion design on Lie groups.IEEE Transactions on Automatic Con trol,2010,55(5):1047-1058
24 Dong R S,Geng Z Y.Consensus based formation contro laws for systems on Lie groups.Systems&Control Letters2013,62(2):104-111
25 Dong R S,Geng Z Y.Consensus for formation control o multi-agent systems.International Journal of Robust and Nonlinear Control,2015,25(14):2481-2501
26 Dong R S,Geng Z Y.Formation tracking control of multi vehicle systems.Asian Journal of Control,2016,18(1)350-356
27 Liu Y F,Geng Z Y.Finite-time optimal formation control o multi-agent systems on the Lie group SE(3).Internationa Journal of Control,2013,86(10):1675-1686
28 Liu Y F,Geng Z Y.Finite-time optimal formation tracking control of vehicles in horizontal plane.Nonlinear Dynamics2014,76(1):481-495
29 Liu Y F,Geng Z Y.Finite-time optimal tracking control fo dynamic systems on Lie groups.Asian Journal of Control2015,17(3):994-1005
30 Liu Y F,Geng Z Y.Finite-time optimal formation contro for second-order multiagent systems.Asian Journal of Con trol,2014,16(1):138-148
31 Sun J,Geng Z,Liu Y.Distributed optimal tracking con trol for second-order multi-agent systems.In:Proceeding of the 33rd Chinese Control Conference.Nanjing,China IEEE,2014.1225-1230
32 Liu Y F,Geng Z Y.Finite-time formation control for linea multi-agent systems:a motion planning approach.System&Control Letters,2015,85:54-60
33 Justh E,Krishnaprasad P.A Simple Control Law for UAVFormation Flying,ISR,U.Maryland,Tech.Rep.2002-38USA,2002.
34 Lee J M.Riemannian Manifolds:An Introduction to Cur vature.New York:Springer-Verlag,1997.
35 Pontryagin L S,Boltyanskii V G,Gamkrelidze R VMishchenko E F.The Mathematical Theory of Optimal Pro cesses.New York:Gordon and Breach,1986.
36 Chernous ko F L,Ananievski I M,Reshmin S A.Control o Nonlinear Dynamical Systems:Methods and Applications Berlin Heidelberg:Springer-Verlag,2008.
37 Oteo J A.The Baker-Campbell-Hausdorff formula and nested commutator identities.Journal of Mathematica Physics,1991,32(2):419-424
38 Higham N J.Functions of Matrices:Theory and Compu tation.Philadelphia,PA,USA:Society for Industrial and Applied Mathematics,2008.
39 Bullo F,Murray R M.Proportional derivative(PD)con trol on the Euclidean group.In:Proceedings of the 1995European Control Conference,volume 2.Rome,Italy,19951091-1097
2 Alber M S,Kiskowski A.On aggregation in CA models in biology.Journal of Physics A:Mathematical and General2001,34(48):10707-10714
3 Leonard N E,Fiorelli E.Virtual leaders,artificial potential and coordinated control of groups.In:Proceedings of th40th IEEE Conference on Decision and Control.Orlando Florida USA:IEEE,2001.2968-2973
4 Jadbabaie A,Lin J,Morse A S.Coordination of group of mobile autonomous agents using nearest neighbor rules IEEE Transactions on Automatic Control,2003,48(6)988-1001
5 Saber R O,Dunbar W B,Murray R M.Cooperative contro of multi-vehicle systems using cost graphs and optimization In:Proceedings of the 2003 American Control Conference Denver,Colorado,USA:IEEE,2003.2217-2222
6 Fax J A,Murray R M.Information flow and cooperativ control of vehicle formations.IEEE Transactions on Auto matic Control,2004,49(9):1465-1476
7 Sepulchre R,Paley D A,Leonard N E.Stabilization o planar collective motion:all-to-all communication.IEEETransactions on Automatic Control,2007,52(5):811-824
8 Scardovi L,Leonard N E.Robustness of aggregation in net worked dynamical systems.In:Proceedings of the 2nd In ternational Conference on Robot Communication and Co ordination.Odense,Denmark:IEEE,2009.1-6
9 Chen Yang-Yang,Tian Yu-Ping.Directed coordinated con trol for multi-agent formation motion on a set of given curves.Acta Automatica Sinica,2009,35(12):1541-1549(陈杨杨,田玉平.多智能体沿多条给定路径编队运动的有向协同控制.自动化学报,2009,35(12):1541-1549)
10 Wang Z X,Du D J,Fei M R.Average Consensus in Directed Networks of Multi-agents with Uncertain Time-varying De lays.Acta Automatica Sinica,2014,40(11):2602-2608
11 Min Hai-Bo,Liu Yuan,Wang Shi-Cheng,Sun Fu-Chun.An overview on coordination control problem of multi-agent sys tem.Acta Automatica Sinica,2012,38(10):1557-1570(闵海波,刘源,王仕成,孙富春.多个体协调控制问题综述.自动化学报,2012,38(10):1557-1570)
12 Oh K K,Park M C,Ahn H S.A survey of multi-agent for mation control.Automatica,2015,53:424-440
13 Tuna S E.Conditions for synchronizability in arrays of cou pled linear systems.IEEE Transactions on Automatic Con trol,2009,54(10):2416-2420
14 Qu Z,Wang J,Hull R A.Cooperative control of dynami cal systems with application to autonomous vehicles.IEEETransactions on Automatic Control,2008,53(4):894-911
15 Li Z,Duan Z,Chen G,Huang L.Consensus of multiagen systems and synchronization of complex networks:a unified viewpoint.IEEE Transactions on Circuits and Systems IRegular Papers,2010,57(1):213-224
16 CHEN Y Z,GE Y R,ZHANG Y X.Partial Stability Ap proach to Consensus Problem of Linear Multi-agent Sys tems.Acta Automatica Sinica,2014,40(11):2573-2584
17 Ren W.Distributed leaderless consensus algorithms for net worked Euler-Lagrange systems.International Journal o Control,2009,82(11):2137-2149
18 Chen G,Lewis F L.Distributed adaptive tracking control fo synchronization of unknown networked Lagrangian systems IEEE Transactions on Systems,Man,and Cybernetics,Par B:Cybernetics,2011,41(3):805-816
19 Mei J,Ren W,Ma G F.Distributed coordinated tracking with a dynamic leader for multiple Euler-Lagrange systems IEEE Transactions on Automatic Control,2011,56(6)1415-1421
20 Chen G,Yue Y L,Lin Q.Cooperative tracking control fo networked Lagrange systems:algorithms and experiments Acta Automatica Sinica,2014,40(11):2563-2572
21 Justh E W,Krishnaprasad P S.Equilibria and steering law for planar formations.Systems&Control Letters,200452(1):25-38
22 Justh E W,Krishnaprasad P S.Natural frames and interact ing particles in three dimensions.In:Proceedings of the 44th IEEE Conference on Decision and Control.Seville,Spain IEEE,2005.2841-2846
23 Sarlette A,Bonnabel S,Sepulchre R.Coordinated motion design on Lie groups.IEEE Transactions on Automatic Con trol,2010,55(5):1047-1058
24 Dong R S,Geng Z Y.Consensus based formation contro laws for systems on Lie groups.Systems&Control Letters2013,62(2):104-111
25 Dong R S,Geng Z Y.Consensus for formation control o multi-agent systems.International Journal of Robust and Nonlinear Control,2015,25(14):2481-2501
26 Dong R S,Geng Z Y.Formation tracking control of multi vehicle systems.Asian Journal of Control,2016,18(1)350-356
27 Liu Y F,Geng Z Y.Finite-time optimal formation control o multi-agent systems on the Lie group SE(3).Internationa Journal of Control,2013,86(10):1675-1686
28 Liu Y F,Geng Z Y.Finite-time optimal formation tracking control of vehicles in horizontal plane.Nonlinear Dynamics2014,76(1):481-495
29 Liu Y F,Geng Z Y.Finite-time optimal tracking control fo dynamic systems on Lie groups.Asian Journal of Control2015,17(3):994-1005
30 Liu Y F,Geng Z Y.Finite-time optimal formation contro for second-order multiagent systems.Asian Journal of Con trol,2014,16(1):138-148
31 Sun J,Geng Z,Liu Y.Distributed optimal tracking con trol for second-order multi-agent systems.In:Proceeding of the 33rd Chinese Control Conference.Nanjing,China IEEE,2014.1225-1230
32 Liu Y F,Geng Z Y.Finite-time formation control for linea multi-agent systems:a motion planning approach.System&Control Letters,2015,85:54-60
33 Justh E,Krishnaprasad P.A Simple Control Law for UAVFormation Flying,ISR,U.Maryland,Tech.Rep.2002-38USA,2002.
34 Lee J M.Riemannian Manifolds:An Introduction to Cur vature.New York:Springer-Verlag,1997.
35 Pontryagin L S,Boltyanskii V G,Gamkrelidze R VMishchenko E F.The Mathematical Theory of Optimal Pro cesses.New York:Gordon and Breach,1986.
36 Chernous ko F L,Ananievski I M,Reshmin S A.Control o Nonlinear Dynamical Systems:Methods and Applications Berlin Heidelberg:Springer-Verlag,2008.
37 Oteo J A.The Baker-Campbell-Hausdorff formula and nested commutator identities.Journal of Mathematica Physics,1991,32(2):419-424
38 Higham N J.Functions of Matrices:Theory and Compu tation.Philadelphia,PA,USA:Society for Industrial and Applied Mathematics,2008.
39 Bullo F,Murray R M.Proportional derivative(PD)con trol on the Euclidean group.In:Proceedings of the 1995European Control Conference,volume 2.Rome,Italy,19951091-1097
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |