Methods for Coordination and Communication in Mixed Teams of Humans and Automata Kristi A. Morgansen Department of Aeronautics and Astronautics University of Washington

2 Modeling Estimation Control Heterogeneous coordinated control with limited communication Bioinspired system modeling for coordinated control Integrated communication and control Modeling and control of shape-actuated immersed mechanical systems Nonlinear Dynamics and Control Lab Cognitive dynamics models for human-in-the-loop systems Coordinated control with communication for UXVs

3 Outline Research overview Coordinated control Integrated communication and control Ongoing and future directions

4 Modeling and control of fin-actuated underwater vehicles Tail locomotion and pectoral fin maneuverability NSF CAREER UW RRF NSF BE (with Parrish and Grunbaum, UW) Goals Agile maneuverability Analytical control theoretic models of immersed shape-actuated devices Underwater localization Nonlinear control Coordinated control Challenges Small size Coriolis effects Unmodeled or approximated fluid dynamics elements Communication and sensing limitations

5 Coordinated Control with Limited Communication Goals Control in the presence of communication and sensing constraints Control over networks Deconfliction Schooling/swarming group behavior Challenges Managing time delays in local control Definition of attention Allocation of resources Construction of stabilizing controllers Modeling NSF CAREER AFOSR (with Javidi, UCSD) AFOSR (with The Insitu Group, Inc.) The Boeing Company NSF (with Javidi, UCSD and Scaglione, Cornell)

6 Hierarchical Integrated Communication and Control NSF CAREER AFOSR (with Javidi, UCSD) AFOSR (with The Insitu Group, Inc.) NSF (with Javidi, UCSD and Scaglione, Cornell) Goals Coordinated tracking of objects or boundaries Non-separated design of communication and control algorithms Data quantization Cooperative task management Control over networks Challenges Managing time delays in local control Allocation of resources Construction of stabilizing controllers Modeling for both communication and control

7 Bioinspired Coordinated Control Models of social aggregations Effects of heterogeneity (levels of hunger, familiarity) Relation to engineered systems Application to fishery management, population modeling NSF BE (with Parrish and Grunbaum, UW) Murdock Trust Goals Challenges Tracking of objects Data fusion Model representation

8 Cognitive Dynamics for Human-in-the-Loop Challenges Model representation Heterogeneity Information flow Levels of autonomy Goals Coordinated control for heterogeneous multivehicle system with human interaction Cognitive models and social psychology Dynamics and control AFOSR MURI (with J. Baillieul (BU), F. Bullo (UCSB), D. Castanon (BU), J. Cohen (Princeton), P. Holmes (Princeton), N. Leonard (Princeton), D. Prentice (Prentice), J. Vagners (UW))

9 Outline Research overview Coordinated control Integrated communication and control Ongoing and future directions

10 Planar Frenet-Serret Simplified Model Coordinated control Nonholonomic kinematics (UAV, UGV, USV, UUV) x y r

11 Coordinated control Goal: Maintain sensor coverage of a desired object or set of objects Given –Homogeneous group of constant speed vehicles –All-to-all communication –One target vehicle Extensions −Heterogeneous agents −Stochastic/hybrid dynamics −Dynamic communication

12 Coordinated control Goal: Match the velocity of the group centroid a given reference velocity. Group centroid: Centroid velocity: Extensions: −More generic tracking goals 50% 90% Matching a reference velocity

13 Coordinated control K = -0.1, N = 10, s ref = 0.5, t max = 100 Matching a reference velocity

14 Coordinated control Question What if the reference velocity is non-constant? In particular, such a result is relevant to biological aggregates for which data has not shown strong tendencies toward alignment or splay, but rather a moving group centroid. Dynamic reference velocity

15 Coordinated control Automatic transition in behavior

16 Coordinated control Want: Additive control term to keep individuals near the centroid. Analogous to the splay state. Have two constraints already. More than two vehicles are required. Matched set and tangent: Centroid spacing control

17 Coordinated control Spacing control (N=3)

18 Coordinated control Spacing control in 3D Desired acceleration Control Composed of four terms: Helix, Beacon, Speed, Plane Given: A group of N identical constant-speed non- holonomic vehicles and a single target vehicle Goals: The collective centroid should track the target; Individuals should “stay near” the collective centroid; Formal analysis Assumptions: SE(3); no collisions; all-to-all comm

19 Coordinated control Because communication events are discrete time, the controller will employ a zero order hold. The resulting system kinematics are governed by the discrete time Kuramoto model. Question: When is the model asymptotically stable to either the synchronized or balanced sets? Discrete-time Kuramoto model

20 Coordinated control Answer: –Convergence to synchronized set –Convergence to balanced set Asymptotic Stability

21 Coordinated control Define the order parameter When r=0, the vehicle headings are aligned and when r=1, the headings are in the balanced state. Motivating the Lyapunov function

22 Coordinated control Asymptotic synchronization:  T=1.0, K=-0.05 Given: A group of N identical constant-speed non-holonomic vehicles and either all-to-all communication or one-to-all random broadcast. Goals: Find a range of gains to guarantee stability to a common heading and evaluate performance based on settling time. Results: Stability in either case can be guaranteed for -2 ≤ KΔT ≤ 0. Settling time is minimal for K ΔT =-1. Settling time increases as K ΔT becomes near zero (loss of control authority). Settling time increases as K ΔT becomes near -2 (near stability limit, increasing oscillations). Challenges: Restriction of controllers to guarantee communication QoS; Task complexity

23 Outline Research overview Coordinated control Integrated communication and control Ongoing and future directions

24 Integrated communication and control Propose a (suboptimal) decomposition Coordinated control of nonlinear systems over a sequence of logical communication graphs G = {G 0,G 1,...}. –Focus on initial task of target tracking with centroid of group –Parameterized nonlinear control as sum of spacing and heading Energy optimal realization of logical communication graph G n with strict time bound of . Loss of optimality is in demanding a “perfect” behavior from network with over-design of a robust controller. Coordinated control over a wireless network

25 Integrated communication and control Main result: Logical communication graph G n with strict deadline  Given: Communicating the state variables every   seconds (one- all) guarantees control objectives Goal: What is the most energy efficient communication scheme achieve one-all communication? Simplest routing/relaying strategy is a single-hop wireless broadcast Other options include multi-hop gossiping (relaying) Results: For most practical applications, the simple single-hop broadcast is optimal Challenges: Inclusion of control performance in explicit optimization

26 Integrated communication and control Main result Integration of Communications and Control The normalized total communication energy consumption of vehicles to reach an aligned state is a non-monotonic function of discretization time step,  for various controllers (parameterized by K). Conclusion: A trade off exists between desired control performance and network realization energy: As  increases, the energy consumption of transmitting vehicles per  decreases but large  slows convergence Beyond some  slow convergence dominates per- slot efficiency

27 Conclusions and Ongoing Work Discrete Time Systems with Delay Time constants must be representative of physical scenarios Tracking Control Extend tracking to more generic scenarios than centroid tracking of single target Dynamic Communication Realistic models and effective designs Heterogeneous Systems Appropriate models for human interaction Biological Connections Cognition, interfacing, data representation This work was supported in part by the National Science Foundation, AFOSR and the University of Washington.