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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
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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
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?
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?
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?
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
An Example Region of interest
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.
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
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”
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.
RendezvousInside and outside the convex hull of initial positions
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
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.
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.
Experiments Conducted • Leader-follower: where the initial orientations of robots are such that the i-th robot’s initial angular orientation is towards (i+1 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.
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.
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.
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 MAV’s start on the same plane as well as when they start at different planes while varying the pitch and yaw rates.
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.
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.
Relevant Publications • A. Sinha and D. Ghose: Some generalizations of linear cyclic pursuit Proc. IEEE INDICON’04,Dec 2004, pp. 210-213. • A. Sinha and D. Ghose: Generalization of the cyclic pursuit problem Proc. American Control Conference (ACC’05),June 2005, pp. 2995-3000. • A. Sinha and D. Ghose: Behaviour of autonomous mobile agents using linear cyclic pursuit laws, Proc. American Control Conference (ACC’06), 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 (IJCAI’07), 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 (ACODS’2007), Feb 2007.
