Multi-Robot Systems. Crop#Watering#Robots# (b) Crop irrigation. Mac Schwager Assistant Professor Aeronautics and Astronautics Stanford University

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1 Multi-Robot Systems Monitoring and Controlling Large-Scale Phenomena Crop#Watering#Robots# An&'fungus#Spraying#UAVs# Oil#Vacuuming#Autonomous#Boats# (a) Oil spill clean up (b) Crop irrigation Mac Schwager Assistant Professor Aeronautics and Astronautics Stanford University (c) Forest fungus control April 19, 2016 Platform Lab Seminar 1

2 Multi-Robot Systems Large scale environment Actuation Communication Sensing Distributed Computation April 19, 2016 Platform Lab Seminar 2

3 Nature is Distributed Morphogenesis Herding Flocking Swarming Human group dynamics Cities and human institutions April 19, 2016 Platform Lab Seminar 3

4 Prototypical Application Deployment and coverage Adaptive sampling Self maintenance Environmental estimation Model learning/ system ID Environmental control April 19, 2016 Platform Lab Seminar 4

5 Other Application Areas Crop#Watering#Robots# An&'fungus#Spraying#UAVs# Oil#Vacuuming#Autonomous#Boats# Chemical (a) Oil spill clean up up Agriculture (b) Crop irrigation Infestation (c) Forest funguscontrol control Disaster relief Urban surveillance Transportation systems April 19, 2016 Platform Lab Seminar 5

6 Multi-robot Systems Lab MSL$ April 19, 2016 Platform Lab Seminar 6

7 Multi-robot Systems Lab MSL$ Motion capture system Flying Arena, 10m x 5m x 3m Floor projection system Robot fleet April 19, 2016 Platform Lab Seminar 7

8 April 19, 2016 Platform Lab Seminar 8

9 Multi-robot Systems Research Deployment and coverage Coordinated agile maneuvers Model learning/ System ID Active estimation with guarantees Neighbor trust adversaries Multi- Robot Systems Active 3D vision and control Multi-robot manipulation Multi-robot herding Persistent monitoring April 19, 2016 Platform Lab Seminar 9

10 Multi-robot Systems Research Deployment and coverage Coordinated agile maneuvers Model learning/ System ID Active estimation with guarantees Neighbor trust adversaries Multi- Robot Systems Active 3D vision and control Multi-robot manipulation Multi-robot herding Persistent monitoring April 19, 2016 Platform Lab Seminar 10

11 Deployment and Coverage April 19, 2016 Platform Lab Seminar 11

12 Existing Methods Geometric: J. Cortes, S. Martinez, T. Karatas, F. Bullo. Coverage control for mobile sensing networks. IEEE TRA, 20(2): , A. Arsie, E. Frazzoli. Efficient routing of multiple vehicles with no explicit communications. IJRNC, 18(2): L. C. A. Pimenta, V. Kumar, R. C. Mesquita, G. A. S. Pereira. Sensing and coverage for a network of heterogeneous robots, CDC 08. M. Schwager, J.-J. Slotine, D. Rus. Decentralized, Adaptive Coverage Control for Networked ROBots. IJRR, 28(3): , Probabilistic: W. Li, C. G. Cassandras. Distributed cooperative coverage control of sensor networks, CDC 05. M. L. Hernandez, T. Kirubarajan y. Bar-Shalom. Multisensor resource deployment using posterior Cramer-Raobounds. IEEE TAES 40(2): , M. Pavone, S. L. Smith, F. Bullo, E. Frazzoli. Dynamics multi-vehicle routing with multiple classes of demands, ACC 09. Potential Fields: D. H. Kim, H. Wang, and S. Shin. Decentralized control of autonomous swarm systems using artificial potential functions: analytical design guidelines, JIRS, 45(4): , A. Howard, M. J. Mataric, G. S. Sukhatme. Mobile sensor network deployment using potential fields, DARS 02. V. Gazi, K. M. Passino. A class of repulsion/atteraction forces for stable swarm aggregations, IJC, 77(18): , April 19, 2016 Platform Lab Seminar 12

13 Deployment Optimization n robots in R 2 H(p 1,...,p n ) ṗ k H i = u i (t) ph i Gradient Theorem: Controller: Robots converge to a local minimum of the cost function. point in R 2n M. Schwager, D. Rus and J. J. Slotine, Unifying Geometric, Probabilistic, and Potential Field Approaches to Multi-Robot Deployment, International Journal of Robotics Research, March, 2011, vol. 30, no. 3. April 19, 2016 Platform Lab Seminar 13

14 Deployment of a Flying Camera Network M. Schwager, B. Julian, M. Angermann and D. Rus, Proceedings of the IEEE, M. Schwager, B. Julian and D. Rus, In Proceedings of the International Conference on Robotics and Automation (ICRA), April 19, 2016 Platform Lab Seminar 14

15 Sensor Cost from Optics camera one pixel height area/pixel From optics and geometry: field of view April 19, 2016 Platform Lab Seminar 15

16 Coverage Cost Function Combined cost for multiple cameras prior area/pixel Cost function: April 19, 2016 Platform Lab Seminar 16

17 Gradient Based Controller Controller: Components: Lateral Component: Move inside Q Move away from neighbors April 19, 2016 Platform Lab Seminar 17

18 Gradient Based Controller Vertical Component: Move up to see more of Q Move down away from neighbors Move down to see Q better April 19, 2016 Platform Lab Seminar 18

19 Convergence LaSalle s invariance principle Trajectories are bounded autonomous and locally Lipschitz Time derivative of non-increasing Therefore converges to largest invariant set where which implies April 19, 2016 Platform Lab Seminar 19

20 April 19, 2016 Platform Lab Seminar 20

21 April 19, 2016 Platform Lab Seminar 21

22 Harvard Forest April 19, 2016 Platform Lab Seminar 22

23 April 19, 2016 Platform Lab Seminar 23

24 Simulation Results x April 19, 2016 Platform Lab Seminar 24

25 April 19, 2016 Platform Lab Seminar 25

26 Five Quadrotors Landing Autonomously April 19, 2016 Platform Lab Seminar 26

27 Forest Reconstruction April 19, 2016 Platform Lab Seminar 27

28 Multi-robot Systems Research Deployment and coverage Coordinated agile maneuvers Model learning/ System ID Active estimation with guarantees Neighbor trust adversaries Multi- Robot Systems Active 3D vision and control Multi-robot manipulation Multi-robot herding Persistent monitoring April 19, 2016 Platform Lab Seminar 28

29 Multi-robot Systems Research Deployment and coverage Coordinated agile maneuvers Model learning/ System ID Active estimation with guarantees Neighbor trust adversaries Multi- Robot Systems Active 3D vision and control Multi-robot manipulation Multi-robot herding Persistent monitoring April 19, 2016 Platform Lab Seminar 29

30 Coordinated Agile Maneuvers Dingjiang Zhou April 19, 2016 Platform Lab Seminar 30

31 Dealing with Dynamics ẋ = f(x, u(t)) ṗ = u(t) April 19, 2016 Platform Lab Seminar 31

32 Quadrotor Dynamics Velocity Angular Velocity Position Orientation v = qe m Rf ze 3 = J 1 J 1 J ṗ = v Ṙ = R x =(v,, p, R) 12 dimensional state space, 4 dimensional input space Nonlinear dynamics Non-Euclidean, evolve on SE(3) se(3) Potentially difficult control and planning problem April 19, 2016 Platform Lab Seminar 32

33 Trajectory Planning Desired trajectory x(t) How can we ensure that ẋ = f(x, u(t))? For what control input trajectory u(t) will this be true? April 19, 2016 Platform Lab Seminar 33

34 Differential Flatness A small miracle: quadrotor dynamics are differentially flat x = (,,..., (q) ) State trajectory x(t) planned flat output trajectory (t) (t) =(p(t), (t)) u = (,,..., (q) ) Input trajectory u(t) April 19, 2016 Platform Lab Seminar 34

35 Related Work Differential Flatness Theory Fliess, Levine, Martin, Rouchon, IJC Fliess, Levine, Martin, Rouchon, TCA Martin, Murray, Rouchon, CDC Martin, Murray, and Rouchon, Technical report, Caltech, CDS Richard M Murray. Optimization-based control. Caltech, Differential Flatness for Quadrotors Mellinger, Kumar, ICRA 2011 Mellinger, Michael, Kumar, IJRR 2012 Zhou, Schwager, ICRA Zhou, Schwager, ICRA Control Assuming Single Integrator Agents Olfati-Saber and Murray, TAC Jadbabaie, Lin, and Morse, TAC Cortes, Martinez, Karatas, and Bullo, TRO Zavlanos and Pappas, TRO Van den Berg, Lin, and Manocha, ICRA Schwager, Julian, Angermann, and Rus, Proc. IEEE Reynolds, Computer Graphics, Dimarogonas and Johansson, ICRA Ayanian and Kumar, TRO Habets and van Schuppen, Automatica April 19, 2016 Platform Lab Seminar 35

36 Differential Flatness A small miracle: quadrotor dynamics are differentially flat x = (,,..., (q) ) State trajectory x(t) planned flat output trajectory (t) (t) =(p(t), (t)) u = (,,..., (q) ) Input trajectory u(t) April 19, 2016 Platform Lab Seminar 36

37 Trajectory Following Control Flat output trajectory u ff (t) p(t), (t) u fb (t) ẋ = f(x, u) Differential Flatness Pipeline SE(3) controller x d (t) x(t) April 19, 2016 Platform Lab Seminar 37

38 April 19, 2016 Platform Lab Seminar 38

39 Vector Field Following We would like to deal with kinematic points in a vector field. We have: We want: ẋ = f(x, u) u = (p,...,... x d = (p,...,... p ) p ) u(p) = (p,...,... p (p)) x d (p) = (p,...,... p (p)) ṗ = v(p) p = v(p) T ṗ = v(p) T v(p). p (k) (k 1) = v(p)p Zhou, Schwager, ICRA April 19, 2016 Platform Lab Seminar 39

40 Multi-Robot Control n copies Vector Field Differential Derivatives Flatness u(p) = (p,...,... p (p)) u ff (t) Differential Flatness Pipeline x d (t) Vector Field SE(3) ṗ controller = v(p). u fb (t) p (k) = v(p)p (k 1) x(t) ẋ = f(x, u) ẋ = f(x, u) ṗ i = v(p) 1,...,p n ) Back to our kinematic multi-robot system. Zhou, Schwager, ICRA April 19, 2016 Platform Lab Seminar 40

41 April 19, 2016 Platform Lab Seminar 41

42 Virtual Rigid Body (VRB) r 1 Plan 6DoF trajectory for VRB p vrb (t),r vrb (t) r 3 VRB r 2 Multi-robot Formation = {r 1,...,r n } Flat output trajectories World p vrb (t),r vrb (t) p(t) i = p vrb (t)+r vrb (t)r i i(t) arbitrary Zhou, Schwager, ICRA April 19, 2016 Platform Lab Seminar 42

43 Formations and Transformations Formation A A Transformation B A VRB trajectory Formation B B April 19, 2016 Platform Lab Seminar 43

44 April 19, 2016 Platform Lab Seminar 44

45 VRB for Human Swarm Interface user input ẋ = f(x, u) chosen dynamics VRB user driven trajectory ABC scalable swarm trajectory April 19, 2016 Platform Lab Seminar 45

46 Nov 6, 2015 Grad Happy Hour 46

47 Multi-robot Systems Research Deployment and coverage Coordinated agile maneuvers Model learning/ System ID Active estimation with guarantees Neighbor trust adversaries Multi- Robot Systems Active 3D vision and control Multi-robot manipulation Multi-robot herding Persistent monitoring April 19, 2016 Platform Lab Seminar 47

48 My Approach Provable distributed control algorithms Multi-robot experiments Theoretical tools Control theory Estimation, filtering, machine learning Optimization April 19, 2016 Platform Lab Seminar 48

49 Current Work Cloud Robotics Local low level control Centralized computation in the cloud Using cell phone and WiFi networks April 19, 2016 Platform Lab Seminar 49

50 Current Work Active 3D Forest Modeling UAV$Surveillance$Mission$ Nov 6, 2015 Grad Happy Hour 50

51 Current Work Intelligent Controlled Vision Eric Cristofalo 3D Printed Forest Model Structure from Motion Reconstruction Nov 6, 2015 Grad Happy Hour 51

52 Summary Multi-robot Systems Coverage with cameras Virtual Rigid Bodies for agile coordination Multi-robot systems will fundamentally change the way we interact with the world at large scales April 19, 2016 Platform Lab Seminar 52

53 Thanks! My Collaborators: Prof. Daniela Rus, MIT Prof. Vijay Kumar, UPenn Prof. Mark Friedl, BU Dr. Josh Gray, BU Dr. Brian Julian, Google My Funding Sources: April 19, 2016 Platform Lab Seminar 53

54 Summary Multi-robot Systems Coverage with cameras Virtual Rigid Bodies for agile coordination Multi-robot systems will fundamentally change the way we interact with the world at large scales April 19, 2016 Platform Lab Seminar 54