Rendezvous and Coordination in MultiVehicle Systems

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Rendezvous and Coordination in Multi-Vehicle
Systems

• Debasish Ghose
• Professor
• (with inputs from Vaibhav Ghadiok and K.
  Varunraj)
• Guidance, Control, and Decision Systems
  Laboratory
• Department of Aerospace Engineering
• Indian Institute of Science
• DRDO-IISc Programme on Mathematical Engineering
• Department of Electrical Communication
  Engineering Indian Institute of Science
• 15 March 2008

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Multi-Vehicle System

• Several autonomous vehicles that act as a group
  or a team with a common goal
• Each member has
• Limited capability
• Limited information
• Limited connectivity
• Problem How would they coordinate among
  themselves without the benefit of a central
  decision-maker?

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The Rendezvous Problem

• Converging to a common point at the same time
• Applications
• MAV swarms used for targeting geographical points
  of interest
• Robotic ground vehicle swarms for rescue,
  surveillance, fire fighting, disaster
  control, etc.
• Intense research interest in the decentralized
  control community
• Why is this problem difficult?

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The Coordination Problem

• If we have a centralized authority,
  with complete
  information about the environment,
  then the task is conceptually trivial.
• In the absence of complete information,
  each vehicle decides
  on its control action
  based upon limited knowledge of its
  environment.
• Absence of complete connectivity between vehicles
  prevents even an approximate implementation of
  centralized and complete information control
  schemes.
• How will the vehicles coordinate among themselves
  and achieve a common goal?

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Important Requirements

• The rendezvous point may not be explicitly
  identified and may also change midway
• Time staggered rendezvous
• Directionally constrained rendezvous with
  unspecified directions
• Need to camouflage information
• Need to make trajectories unpredictable
• Need to minimize information sent to vehicles

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An Example
Region of interest
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Cyclic Pursuit Strategies

• Vehicles are connected in a cyclic fashion
  through a communication network defining a
  pursuit sequence
• Pursuit may be defined as pursuit of another
  member or pursuit of a weighted mean of the
  positions of a subset of members.

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Cyclic Pursuit Model
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Basic Cyclic Pursuit Equations
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Basic Stability Result
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Rendezvous Points
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Available Theoretical Results

• Proof of rendezvous to unspecified location
  (Francis et al.)
• Controller gain selection and switching pursuit
  sequence can be effectively used to
• Change goal positions midway
• Change trajectories midway without changing goal
  positions
• Cover larger areas of interest
• Obtain directional movement by destabilizing the
  system of vehicles

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Objectives of this project

• When the vehicles have speed saturations (both
  lower and upper)
• Directional arrival Switching between unstable
  and stable behaviour
• Staggered arrival
• Controller gain selection for optimality

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Objectives of this project (Contd.)

• Implementation of trajectories (for various
  missions such as search and surveillance) using
  pursuit sequence paradigm
• Switching of trajectories to avoid tracking and
  easy detection.
• Constraints such as limited maneuverability,
  limited FOV, accuracy of sensors, limited
  information updates.
• Reconfiguration in case of failure of an agent.

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RendezvousInside and outside the convex hull of
initial positions
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Pursuit Sequence Invariance of Goal Point
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Switching Invariance of Goal Point
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Rendezvous with Speed Saturation
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Directional Movement
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Impact of Proposed Research

• Algorithms developed here will be useful to
  control swarms of autonomous vehicles (MAVs and
  ground vehicles)
• Theoretical developments will bring new insights
  into this extremely challenging class of problems
• Testing the application of recently developed
  theory for swarm control
• Multi-vehicle system is gradually becoming a
  reality
• Research in this area has picked up speed and
  fast progressing in the technologically advanced
  countries

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Implementation in a Simulated Environment

• A group of unmanned vehicles performing cyclic
  pursuit is simulated in the Player/Gazebo
  environment running on Linux.
• Player is a software package which provides an
  abstraction layer for robot control
• Gazebo is a 3-D simulator for the same and can be
  used for flying vehicles.

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Rendezvous of Wheeled Robots

• Model of a car-like robot in Player/Stage.
• Incorporates kinematic constraints of a wheeled
  vehicle moving normal to its main axis.
• A real robot would take a non-zero finite time to
  realize a velocity command issued to it from the
  control program. This is implemented by using a
  trapezoidal velocity profile.
• Obstacle avoidance model has not been used in
  these simulations yet.

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Experiments Conducted

• Leader-follower where the initial orientations
  of robots are such that the i-th robots initial
  angular orientation is towards (i1 mod n)-th
  robot.
• Randomly oriented robots where the initial
  orientations of the robots are selected randomly.
• Swapped robot position Where the robots
  positions are swapped but follow cyclic
  leader-follower orientations.
• Maximum speed limit
• Variation in number of robots Experiments with 5
  and 10 robots.

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Realistic Constraints and Control

• A vehicle cannot change its heading direction
  instantaneously.
• The vehicle has finite pitch and yaw rate limits.
• The angle between the vehicles is calculated in
  the x-y as well x-z planes and these are used to
  decide the target heading for the pursuing
  vehicle.
• The pursuing vehicle is given a constant pitch or
  yaw rate in the appropriate direction until
  desired heading is achieved.

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Convergence to a Point

• Simulations carried out successfully for
• A wide range of yaw and pitch rates.
• Cases where the vehicles are separated in all 3
  axes.
• Cases where the vehciles have a maximum
  achievable speed.
• A case where the vehicle can fly vertically.

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Convergence to a Vertical Stack Formation

• Each vehicle pursues a point that is directly
  above or below the position of the vehicle being
  pursued so as to a form an ordered stack at the
  point of convergence and to prevent collision.
• Simulations are carried out for cases where the
  MAVs start on the same plane as well as when
  they start at different planes while varying the
  pitch and yaw rates.

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Convergence to a Polygonal Formation

• Each vehicle is made to pursue a point that is
  offset from the position of the vehicle being
  pursued such that the final configuration
  achieved is a square or a pentagonal formation.
• It may be extended to circular or other regular
  polygonal configurations.

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UAV Specification
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Realistic Dynamics
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Forces and Torques
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Coefficients
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Preliminary Simulations
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Relevant Publications

• P.B. Sujit, A. Sinha, and D. Ghose, Team, game,
  and negotiation based intelligent autonomous UAV
  task allocation for wide area applications
  Studies in
  Computational Intelligence, Vol. 70,
  Springer-Verlag, Berlin, 2007, pp. 39-75.
• A. Sinha and D. Ghose Generalization of
  nonlinear cyclic pursuit
  Automatica (Accepted for publication)
• A. Sinha and D. Ghose Control of multi-agent
  systems using linear cyclic pursuit with
  heterogenous controller gains
  
  ASME Journal of Dynamic Systems,
  Measurement, and Control (Accepted for
  publication)
• A. Sinha and D. Ghose Generalization of linear
  cyclic pursuit with application to rendezvous of
  multiple autonomous agents
  IEEE
  Transactions on Automatic Control, Vol. 51, No.
  11, pp. 1819-1824, Nov 2006.

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Relevant Publications

• A. Sinha and D. Ghose Some generalizations of
  linear cyclic pursuit Proc.
  IEEE INDICON04, Dec 2004, pp. 210-213.
• A. Sinha and D. Ghose Generalization of the
  cyclic pursuit problem Proc.
  American Control Conference (ACC05), June 2005,
  pp. 2995-3000.
• A. Sinha and D. Ghose Behaviour of autonomous
  mobile agents using linear cyclic pursuit laws,
  Proc. American Control Conference (ACC06), June
  2006, pp. 4963-4968.
• A. Sinha and D. Ghose Control of agent swarms
  using generalized centroidal cyclic pursuit laws
  
  
  Proc. International Joint Conference on
  Artificial Intelligence (IJCAI07), Jan 2007.
• A. Sinha and D. Ghose Line formation of a swarm
  of autonomous agents with centroidal cyclic
  pursuit, Proc. Advances in Control and
  Optimization of Dynamical Systems (ACODS2007),
  Feb 2007.

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Thank You