Swarms of Small Flying Robots

Vijay KumarProfessor and Nemirovsky Family DeanUniversity of Pennsylvania

Department of Mechanical and Aerospace EngineeringNew York University

Dec 2, 2019

Acknowledgements

Spin off companies

Trefo.ai

applications to agriculture

aerial mapping mining, asset mapping

acquired by health, disaster response

Non profit

3

A Brief History of Aerial Robotics

• International Aerial Robotics Competition (1991)• Early work at GRASP (< 2000)

4

There are no new ideas, only good ideas!

George de Bothezat’s Quadrotor, 1922Breguet-Richet Gyroplane No.1, 1907

1907, Paul Cornu: First to Hover?

Wired Magazine, A hundred years of hovering, 2007

Flying windmill, 2007

5

A Brief History of Aerial Robotics

• International Aerial Robotics Competition (1991)• Early work at GRASP (< 2000)

6

Inertial Measurement Units

• Accelerometer, airbag sensors (Analog Devices), 1993

• MEMS gyros for electronic stability control (Bosch), 1997

• 3-axis accelerometers for Nintendo Wii, 2006• 3-axis accelerometer, iPhone (Apple), 2007• 3-axis accelerometer, 3-axis gyro, 3-axis

magnetometer, iPhone 4 (Apple), 2010inflexion point

7

A Brief History of Aerial Robotics

• International Aerial Robotics Competition (1991)• Early work at GRASP• 2008-9 – small multi rotor aircrafts become practical

Ascending Technologies KMel Robotics

Daniel Mellinger and Alex Kushleyev

N. Michael, D. Mellinger, Q. Lindsey, and V. Kumar. The GRASP multiple micro UAV testbed. IEEE Robotics and Automation Magazine, Vol. 17, No. 3. 2010.

Daniel Mellinger

Auton Robot

Lee, T. (2011). Geometric tracking control of the attitude dynamics ofa rigid body on SO(3). In Proc. of the Amer. control conf., SanFrancisco, CA.

Lee, T., Leok, M., & McClamroch, N. H. (2010). Geometric trackingcontrol of a quadrotor UAV on SE(3). In Proc. of the IEEE conf.on decision and control, Atlanta, GA.

Mellinger, D., & Kumar, V. (2011). Minimum snap trajectory genera-tion and control for quadrotors. In Proc. of the IEEE intl. conf. onrobot. and autom., Shanghai, China.

Mellinger, D., Michael, N., & Kumar, V. (2010). Trajectory generationand control for precise aggressive maneuvers with quadrotors. InProc. of the intl. sym. on exp. robot., Delhi, India.

Mesbahi, M. (2005). On state-dependent dynamic graphs and theircontrollability properties. IEEE Transactions on Automatic Con-trol, 50(3), 387–392.

Michael, N., Mellinger, D., Lindsey, Q., & Kumar, V. (2010). TheGRASP multiple micro UAV testbed. IEEE Robotics & Automa-tion Magazine, 17(3), 56–65.

Nieuwstadt, M. J. V., & Murray, R. M. (1998). Real-time trajectorygeneration for differentially flat systems. International Journal ofRobust and Nonlinear Control, 8 (11), 995–1020.

Ogren, P., Fiorelli, E., & Leonard, N. (2002). Formations with a mis-sion: stable coordination of vehicle group maneuvers. In Proc.of intl. sym. on mathematical theory networks and syst., NotreDame, IN.

Olfati-Saber, R., & Murray, R. M. (2002). Distributed cooperative con-trol of multiple vehicle formations using structural potential func-tions. In Proc. of the IFAC world congress, Barcelona, Spain.

Olfati-Saber, R., & Murray, R. M. (2004). Consensus problems in net-works of agents with switching topology and time-delays. IEEETransactions on Automatic Control, 49 (9), 1520–1533.

Shim, D., Kim, H., & Sastry, S. (2003). Decentralized nonlinear modelpredictive control of multiple flying robots. In Decision andcontrol, 2003. Proceedings. 42nd IEEE conference on (Vol. 4,pp. 3621–3626). New York: IEEE.

Tabuada, P., Pappas, G. J., & Lima, P. (2001). Feasible formations ofmulti-agent systems. In Proc. of the Amer. control conf., Arling-ton, VA (pp. 56–61).

Tanner, H., Pappas, G. J., & Kumar, V. (2002). Input-to-state stabilityon formation graphs. In Proc. of the IEEE intl. conf. on robot. andautom., Las Vegas, NV (pp. 2439–2444).

Turpin, M., Michael, N., & Kumar, V. (2011). Trajectory design andcontrol for aggressive formation flight with quadrotors. In Proc.of the intl. sym. of robotics research, Flagstaff, AZ.

Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I., & Shochet, O. (1995).Novel type of phase transition in a system of self-driven particles.Physical Review Letters, 75(6), 1226–1229.

Matthew Turpin is a Ph.D. candi-date in the Department of Mechan-ical Engineering and Applied Me-chanics at the University of Penn-sylvania. He works on formation de-sign and control of micro-aerial ve-hicles.

Nathan Michael is a Research As-sistant Professor in the Departmentof Mechanical Engineering and Ap-plied Mechanics at the University ofPennsylvania. He received his Ph.D.in Mechanical Engineering from theUniversity of Pennsylvania in 2008.He works in the areas of dynamics,estimation, and control for groundand aerial robot systems.

Vijay Kumar is the UPS Founda-tion Professor and the Deputy Deanfor Education in the School of En-gineering and Applied Science atthe University of Pennsylvania. Hereceived his Ph.D. in MechanicalEngineering from The Ohio StateUniversity in 1987. He has beenon the Faculty in the Departmentof Mechanical Engineering and Ap-plied Mechanics with a secondaryappointment in the Department ofComputer and Information Scienceat the University of Pennsylvaniasince 1987. He is a Fellow of the

American Society of Mechanical Engineers (ASME) and the Institu-tion of Electrical and Electronic Engineers (IEEE).

Author's personal copy

Alex Kushleyev

Jonathan Fink Nathan Michael

8

Aerial Robotics, 2009

Nathan Michael (CMU)

Jonathan Fink (ARL)

Daniel Mellinger, Nathan Michael, and Vijay Kumar. Trajectory Generation and Control for Precise Aggressive Maneuvers with Quadrotors.International Journal of Robotics Research, Apr. 2012.

9

9

Daniel Mellinger, and Vijay Kumar. “Minimum Snap Trajectory Generation and Control for Quadrotors,” Proc. IEEE International Conference onRobotics and Automation. Shanghai, China, May, 2011.

2012 – Swarm of 75 gm quadrotors

Daniel MellingerAlex Kushleyev

10

11

2015 – Drones everywhere!

12

Drone Racing

Drone Nationals, New York City, 2016

Yash Mulgaonkar

13

Beyond Quadrotors

S. Driessens and P. Pounds, “The triangular quadrotor: a more efficient quadrotor configuration,” 2015. Dario Brescianini and Raffaello

D’Andrea, “An omni-directional multirotor vehicle,” 2018.

Davide Falanga , Kevin Kleber, Stefano Mintchev , Dario Floreano , and Davide Scaramuzza, “The Foldable Drone: A Morphing Quadrotor That Can Squeeze and Fly,” 2019. David Saldana, Bruno Gabrich, Guanrui Li, Mark Yim, and

Vijay Kumar, “ModQuad: The Flying Modular Structure that Self-Assembles in Midair,” 2018.

David Saldana

14

Gartner Hype Cycle

20182017

2019 (10 years later)

Goldman Sachs Research

17%

70%

13%

military

b2b

consumer

Market Agriculture, Mining, Health

SmallSafe

SpeedSmartWe are here!

Swarms

Aerial Robotics Research (and Commercialization)

Autonomy

Size

3000 g

3500 g

75 g

201120 g

2014650 g 2015

740 g

2012

1750 g

2013

1850 g

2011

2016

250 g

2016

rely on external infrastructure

vision + IMU

2-D laser scanner

3-D laser

The FalconFast Aggressive Lightweight flight in CONstrained Environments

Y. Mulgaonkar, A. Makineni, K. Mohta, C.J. Taylor, and V. Kumar, 2016 Hilton Head Workshop

. . . and at high speeds

Search and Rescue

Five Challenges

• Perception Action Loops for Autonomy

• State Estimation

• Navigation in Cluttered Environments

• Scaling Down in Size, Weight

• Perception Action Communication Loops for Swarms

1. Nested Perception/Action Loops

Continuous

DiscretePlan Control

Perception

Plan Control System

Perception

HybridPlan Control

Perception

System

System

JTY Wen and K Kreutz-Delgado, The attitude controlproblem, IEEE Transactions on Automatic control, 1991.D Mellinger and V Kumar, “Minimum Snap TrajectoryGeneration and Control for Quadrotors,” Proc. IEEEInternational Conference on Robotics and Automation.Shanghai, China, May, 2011.T Lee, M Leok, NH McClamroch, “Nonlinear RobustTracking Control of a Quadrotor UAV on SE(3),” AsianJournal of Control 2012.

Nonlinear controllers on SO(3)/SE(3)

2. State Estimation (Stereo + IMU)

K. Sun, K. Mohta, B. Pfrommer, M. Watterson, S. Liu, Y. Mulgaonkar, C. J. Taylor, and V. Kumar, “Robust Stereo Visual Inertial Odometry for Fast Autonomous Flight”, RAL 2018

Augmented State

Model

Stereo Camera Measurement

Orientation

Gyro bias Velocity PositionAcc bias

Cam-IMU extrinsics

Ke Sun

Kartik Mohta

Stereo Multistate Constraint Kalman Filter (S-MCKF)

Fast autonomous flight (Top speed at 18m/s)

Autonomous flight in unstructured environment● Includes various scenes (warehouse, woods,

open field, etc).● Round trip over 700m● Final drift under 0.5%

Multi-Sensor Unscented

KalmanFilter (200 Hz)

velocity

State Estimation

Visual odometry

Visual odometry

Laser odometry

Altitude estimator

DownwardCamera (40Hz)

StereoCamera (40 Hz)

Altimeter (20 Hz)

Laser Scanner(20 Hz)

GPS(10Hz)

Controller(200 Hz)

Shaojie Shen, Yash Mulgaonkar, Nathan Michael and Vijay Kumar, “Multi-Sensor Fusion for Robust Autonomous Flight in Indoor and Outdoor Environments with a Rotorcraft MAV,” Proceedings of IEEE International Conference on Robotics and Automation (ICRA), 2014.

IMU(1000 Hz)

Shaojie Shen (HKUST)

3. Autonomy: Perception and Action for Navigation

Trajectory Generator (20 Hz)

Planner(20 Hz)

GPS (10Hz)

Local Map(40 Hz)

position

Pose Graph SLAM

Multi-Sensor Unscented

KalmanFilter (200 Hz)

velocity

Visual odometry

Visual odometry

Laser odometry

Altitude estimator

DownwardCamera (40Hz)

StereoCamera (40 Hz)

Altimeter (20 Hz)

Laser Scanner(20 Hz)

GPS(10Hz)

Controller(200 Hz)IMU

(1000 Hz)

DARPA Fast Lightweight Autonomy (FLA)

Cameras + IMU

Lidar

Yash Mulgaonkar

3 Planning in Cluttered Environments

– Relative degree 4 (input and state constraints)

– Non convex

– Safe corridors in different homology classes

– Partially known environment (limited field of view sensors)

X goal ⇢ X free

x = Ax(t) +Bu(t), u(t) 2 U , 8t 2 [0, T ]

x(0) = x0, x(T ) 2 X goal, x(t) 2 X free

minu(t), T

J(x(t), u(t)) + ⇢T

1. Optimal Control

Sarah Tang

Sikang Liu

SubhrajitBhattacharya

Mike Watterson

FLA (5-20 m/s)

S. Bhattacharya, M. Likhachev and V. Kumar, “Topological Constraints in Search-based Robot Path Planning.” Autonomous Robots, 33(3):273-290, 2012.S. Liu, M. Watterson, S. Tang, and V. Kumar, “High speed navigation for quadrotors with limited onboard sensing,” Robotics and Automation Letters, 2016.S. Liu, N. Atanasov, K. Mohta, and V. Kumar, “Search-based Motion Planning for Quadrotors using Linear Quadratic Minimum Time Control,” IROS 2017.

Sarah Tang

Sikang Liu

SubhrajitBhattacharya

Mike Watterson

Planning in Cluttered Environments

Minimum snap primitives

Search over induced discretization on state space

Results for different functionals

2. Search-Based Planning with Motion Primitives

S. Liu, N. Atanasov, K. Mohta, V. Kumar, Search-based motion planning for quadrotors using linear quadratic minimum time control, IROS 2017

Sikang Liu

Nikolay Atanasov(UCSD)

Resolution complete but …

p1

M

gpk(tk)

v = 20 m/s, max acceleration 1 g Stopping time ~ 2 sStopping distance ~ 20 m

limited field of view creates challenges

Safety Certificate

p1

M

gpk(tk)

pk+1(tk+1)

g0 k

�k

xk(tk) =

2

664

pkpkpk...p k

3

775 xk+1(tk+1) =

2

664

pk+1

pk+1

pk+1...p k+1

3

775xk+1(tk+1) =

2

664

pk+1

pk+1

pk+1...p k+1

3

775

k

xg0 =

2

664

g0

000

3

775

● Safety● Completeness● Suboptimality

Autonomous Flight in Unknown GPS-Denied Environment (5 m/s)

CJ Taylor

Yash Mulgaonkar

Sikang Liu

Mike Watterson

Ke Sun

Kartik Mohta

Search of Collapsed Buildings

S. S. Shivakumar, K. Mohta, B. Pfrommer, V. Kumar and C. J. Taylor, Guided Semi Global Optimization for Real Time Dense Depth Estimation, ICRA 2019.

Shreyas Shivakumar

CJ Taylor

Sikang Liu

Mike Watterson

Ke Sun

Kartik Mohta

Brandon Duick

Amilcar Cipriano Monica DeGuzman

Jason Derenick

Raghu Balasa Alex Burka

www.exyn.ai

Nader Elm

Pete Furlong Gray Greene Vinutha Kallem Nick Lynch

Billy Sisson James Sui Justin Thomas

Xuchu (Dennis) Ding

Denise Wong

38

A. Weinstein, A. Cho, and G. Loianno, and V. Kumar, “VIO-Swarm: A Swarm of 250 gram autonomous quadrotors ” ICRA 2018.

4. Light Weight Autonomy

250 gram quadrotor (2018)Qualcomm® Snapdragon Flight™ development board running Snapdragon Navigator™ flight controller and Machine Vision (MV) SDK

GiuseppeLoianno

Shreyas Shivakumar

Ke Sun

Kartik Mohta

CJ Taylor

S. S. Shivakumar, K. Mohta, B. Pfrommer, V. Kumar and C. J. Taylor, Guided Semi Global Optimization for Real Time Dense Depth Estimation, ICRA 2019.

1 kg quadrotor (2018)

Stereo camera synced with Vector NAV IMU, NVDIA Jetson TX2 + FPGA (low-level pixel-wise operations) – OSRF

TOF 3-D camera, 6m range, 100x65 deg, 60 Hz – PMD technologies

2.5 kg quadrotor (2017)Stereo camera synced with Vector NAV IMU, LiDar, Intel i7

42

Robustness to Collisions

250 gram quadrotorQualcomm® Snapdragon Flight™ board with Snapdragon Navigator™ flight controller

133 gram quadrotor capable of sustaining collisionsQualcomm® Snapdragon Flight™ board with forward-facing stereo cameras, a downward facing camera for VIO, onboard WiFi and GPS

TiercelWenxin Liu

Yash Mulgaonkar, Wenxin Liu, Dinesh Thakur, Kostas Daniilidis, Vijay Kumar, The Tiercel: A novel autonomous micro aerial vehicle that can map the environment by flying into obstacles, IEEE Robotics and Automation Letters, submitted (2020)

Yash Mulgaonkar

Fig. 4: Onboad LEDs and drive board mounted on the MAV (left). The lighting payload is equipped with A) LEDiL C16029STRADA-SQ-C lens and B) LEDiL C12727 STRADA-SQ-VSM lens. Cree XP-G3 illumination distribution is used for thelenses. The concentric rings on the test target indicate fields of view of 100� and 120� captured with bottom camera.

Fig. 5: Picture of mock-up PCV viewed from a camera located at X100B (left), Point cloud of test fixture captured viaKAARATA Stencil (center), OctoMap and automatically generated JPS 3D navigation path (right)

widest and most uniform central illumination spot while(LEDiL C12727 STRADA-SQ-VSM [15]) generated themost uniform illumination spot over the entire FOV of thecamera. The Cree LEDs have 125� directional viewing angle.The forward cameras have much narrower FOV of 90�, henceno lens were added.

We have designed and fabricated a custom LED drivecontroller board for use with the MAV. Constant current LEDdrivers are used in the lighting payload. A constant currentdriver generates consistent illumination throughout the flightand protects the LED from thermal runaway if the ambienttemperature or the temperature of the LED increases duringthe flight. The board is equipped with trim pot resistors tocontrol the Lux output of the LEDs. Fig. 4 shows the LEDdrive board with two different lenses and the correspondingillumination distribution and also a picture of the lightingpayload installed on the MAV platform. The lighting payloadadds only 8g to the MAV weight and draws a maximumcurrent of 1.5A at maximum light output of all three LEDs.

B. Waterproof System

Waterproofing the vehicle requires careful considerationof each component. A multi-step conformal coating processis performed on the Snapdragon Flight board, ElectronicSpeed Control (ESC) and the LED driver board. Specifically,

the pins, connectors, and cameras are removed and a firstconformal coating is applied with Arathane 5750-A/B (LV),which is a soft translucent urethane composite designed forinsulating printed circuit boards and electronic components.Once the initial coating process is completed, the connectorsare reattached, and the second coating process is performedusing RTV silicone. To protect the LEDs from the adverseeffects of dripping water, the front PCB surface of the LEDswas coated with RTV silicone. The downward-facing camerais also coated with a hydrophobic coating. Glass coverslipswith a hydrophobic coating were installed on the forward-facing stereo cameras. A waterproof coating is added to thebattery cell, balancing cable, and circuit.

III. AUTONOMOUS NAVIGATION

In this section, we describe the main algorithms enablingthe autonomous capabilities of the aerial vehicle in unknownand unstructured environments.

A. Control and EstimationThe system combines the Inertial Measurement Unit

(IMU) data and the VGA downward camera image data in anExtended Kalman Filter (EKF) framework in order to local-ize the vehicle in the environment [12]. The prediction stepis based on integration of the IMU data. The measurementupdate step is given by the standard 3D landmark perspective

Giuseppe Loianno

Dinesh Thakur

Autonomous Flight in Fukushima Daiichi Reactor Unit 1

Monica Garcia (SWRI), Richard Garcia (SWRI), Wataru Sato (TEPCO)

Giuseppe Loianno

Dinesh Thakur

Laura Jarin-Lipschitz

Wenxin Liu

Elijah Lee

5. Aerial Robot Swarms

Perception Action

• observations inform actions• move for better observations

Perception—Action Loops

5. Aerial Robot Swarms

Perception Action

Communication

• share private perceptions

• observations inform actions• move for better observations

• messages inform actions• move to communicate better

Task

Perception—Action—Communication Loops

• communicate to make better observations

Decentralized Multi-Robot Teams

• Decentralized, correct-by-construction policies available only for very simple cases

– simple communication and sensing models

– edge or cloud computation – point robots

A. Weinstein, A. Cho, and G. Loianno, and V. Kumar, “VIO-Swarm: A Swarm of 250 gram autonomous quadrotors ” ICRA 2018.

Tanner, Pappas and Jadbabaie, 2004Sensor CoverageCortes, 2004

Belta and Kumar, 2005

Aaron Weinstein

Giuseppe Loianno

• Centralized methods are not practical for real-world robot deployments (Turpin, ‘14)

– Partial observability by individual agents

– Limited communication

Distributed Learning: PAC Loops

Perception Action

Communication

Task

Ø Key Ideas:o Learn communication policieso Learn action policieso Learn planning policies

Jimmy Paulos

Ekaterina Tolstaya

Arbaaz Khan

Steven Chen

(with Professor Alejandro Ribeiro)

Dinesh Thakur

Laura Jarin-Lipschitz

Graph Neural Networks

• Robots act on relative position and velocity information– Must stay close to each other– Must avoid collisions

– Must “align” themselves

ChoiceofParametrization

IThereisoverwhelmingempiricalandtheoreticaljustificationtochooseaneuralnetwork

IChallengeiswewanttolearnoverthisIAndwearegoodatlearningoverthis

ITheNeuralNetworksthatweknowgeneralizewellareConvolutionalNeuralNetworks

IWeknowhowtolearnovertimeandimages.Wedon’tknowhowtolearnoveragraph.

A.RibeiroLearningDecentralizedControllersforRobotSwarmswithGraphNeuralNetworks6/28

CNNs GNNs

Aggregate information at each node from neighboring node using graph adjacency properties

49

Aggregate over belief states of neighbors

z =KX

k=0

hkSkx(k) = H(S)x

<latexit sha1_base64="SY4t/wzZstDd8eWBFh8xN2m9gdM=">AAACOnicbVDLSsNAFJ34rPVVdelmsAjtpiQq6KZQdFNw06J9QNOGyXTSDpk8mJmINeS73PgV7ly4caGIWz/ASZuFth4YOJxzL3fOsUNGhdT1F21peWV1bT23kd/c2t7ZLeztt0UQcUxaOGAB79pIEEZ90pJUMtINOUGezUjHdq9Sv3NHuKCBfysnIel7aORTh2IklWQVmqaH5Nh24ocEVqEpIs+K3aqeDOLrBI4tF8am7cCbZOBOyb0ySm45qc70elLK/HJmw7xVKOoVfQq4SIyMFEGGhlV4NocBjjziS8yQED1DD2U/RlxSzEiSNyNBQoRdNCI9RX3kEdGPp9ETeKyUIXQCrp4v4VT9vREjT4iJZ6vJNKiY91LxP68XSeeiH1M/jCTx8eyQEzEoA5j2CIeUEyzZRBGEOVV/hXiMOMJStZ2WYMxHXiTtk4pxWtGbZ8XaZVZHDhyCI1ACBjgHNVAHDdACGDyCV/AOPrQn7U371L5mo0tatnMA/kD7/gEFlaxE</latexit>

50

FlockingGNN-learned control

policy (K=3)

(a) Average difference in velocities (b) Average minimum distance to a neighbor

(c) Flock positions using the GNN (d) Flock positions using the local controller

Figure 1. The GNN (K = 3) maintains a cohesive flock, while the local controller allows the flock to scatter.

using 400 trajectories, each of length 200 steps total. For testing, 20 trajectories of length 200 wereobserved by using the learned controller only.

In practice, following the optimal policy to collect training data results in a distribution of statesthat is not representative of those seen at test time. To resolve this we use the Dataset Aggregation(DAgger) algorithm and follow the learner’s policy instead of the expert’s with probability 1�bwhen collecting training trajectories [33]. The probability b of choosing the expert action whiletraining is decayed by a factor of 0.993 after each trajectory to a minimum of 0.5.

5 Results

We report results comparing (11) and (10) for point masses with fully controllable accelerations inSection 5.1. This simple setting allows for an exploration of the effect of different system parameterssuch as initial velocity or communication radius, to determine experimentally the scenarios on whichthe aggregation GNN offers good performance. In Section 5.2 we study the case of transfer learning,where we train the model in one network but test it in another (for example, with different numberof agents), and also by exporting the trained architecture to other physical models beyond the point-mass model, as shown in the AirSim simulator (Sec. 7.2).

5.1 Learning to flock with point masses

First, we compare the performance of the GNN controller with K = 3 to the local controller u†i

(11). Figure 1a depicts the magnitude of velocity differences between agents over the course of atrajectory in terms of the population mean and standard devision. The GNN converges much morerapidly and, unlike the local controller, approaches a perfect velocity consensus. Part of the reasonfor this is explained in Figure 1b, which plots agents’ minimum distance to any neighbor overtime. The GNN control approaches a uniform flock spacing, but the local controller fails to stopagents from dispersing quickly enough. Soon the local controller’s network has become completelydisconnected as agent distances exceed their communication range of R = 1. One flock trajectory isdepicted for the GNN controller in Fig. 1c and the local controller in Fig. 1d. Each diagram showsthe initial agent positions and velocities at time n = 0 and then at n = 300, qualitatively illustratingthe stable flocking of the GNN and failure of the local controller.

6

Tanner, Pappas and Jadbabaie, 2004

Graph Policy Gradients

• Train GNNs on a small number of robots– Information from k-hop neighbors is aggregated by each robot

– Local controllers are learned by each robot– Centralized reward used to train the robots

• Extend to swarms with larger numbers– Transfer of policies to larger groups with similar “local” graph properties

Arbaaz Khan

Arbaaz Khan, Vijay Kumar, and Alejandro Ribeiro, Graph Policy Gradients for Large Scale Unlabeled Motion Planning with Constraints , IEEE International Conference on Robotics and Automation, submitted (2020)

Graph Policy Gradients for Large Scale Formation Control

53

Conclusion

• Autonomy using smartphone grade processors/sensors

• 10x improvement in performance/price • Applications to search and rescue and precision

agriculture• Integration of model-based and data-driven methods

AI 1.0 AI 2.0 AI 3.0

Ed Steager Dinesh Thakur

Laura Jarin-Lipschitz

Ty NguyenYash Mulgaonkar

Avi Cohen

Ekaterina Tolstaya

Monroe Kennedy

Ke Sun

Jim Keller

Mickey Whitzer

Sambeeta Das

Chao Qu

Jnaneshwar DasElizabeth Beattie

Sarah Tang

Kelsey SaulnierTolga Özaslan

Kartik MohtaRebecca Li

James SvachaRattanachai Ramaithitima

Steven Chen

Giuseppe Loianno

http://kumar.grasp.upenn.edu/

Mike Watterson

Luis Guerrero

Arbaaz Khan Elijah Lee Sikang Liu Wenxin Liu

Ian Miller

Dan Mox

Daigo ShishikaDavid Saldana Aaron Weinstein

Jimmy Paulos